First, take a look at gertvdijk's comment. I'm an unaware of Dynamic Disks. As evident from his links, it seems that Ubuntu cannot be dual-booted with Windows on dynamic disks. So, if you managed to convert the disk to basic and everything is intact, you can follow my answer.
"Free space" or "unallocated space" means a space that is unpartitioned. In your case, you shrunk the D: drive by 45 GB and then you created an NTFS partition from that space (partition J).
At this point, you have two options to install Ubuntu: either manually install Ubuntu on that partition, or delete the partition to make an "unallocated space". Here are their explanations:
Delete the partition to leave an unallocated space
Go to the Windows Disk Management, right click on the New Volume (J:) partition and choose to delete it. That way, you deleted the partition, but the space is still there as "unallocated". Now, when you start the Ubuntu installation, you'll get an Install Ubuntu alongside Windows 7 option. This option will tell Ubuntu to use up all that unallocated space we created. So choose that option. I think this option was the one you were going for, but you made the mistake of created a partition from that free space, therefore that option was not available to you.
Install Ubuntu on that partition:
I advice against using this method. I'll mention why in the end. Now, since you've already created a partition from that space you shrunk, you can manually instruct Ubuntu to install itself there. To do this: choose the Something Else option while installing. You say you didn't see the partition, but you probably missed it because it should be there. It will probably be marked as
/dev/sda5, logical partition, with an ntfs type. Once you identify that 45 GB partition, double click it, choose the file system to be
ext, choose the mount point as
/, choose to "format it" if you get the option, hit OK, and then click Next (or Install) to begin installation. Make sure you chose the correct partition! Now, when you begin the installation, Ubuntu will install on that partition. The reason why I advice against this method is that there's actually an extra step that should be taken. You'll have to shrink that 45 GB space a bit (let's say to 40 GB) and use that remaining 5 GB space for a
swap partition. This is an extra partition that is optional, but is essential for Ubuntu to work fast, and is almost always created. This step will be already taken care of if you go with the first method I explained and chose "Install Ubuntu alongside Windows 7". Ubuntu, on it's own, will create one partition for itself and another partition for swap. That's why, if you with that "alongside" option, you'll actually find that the Ubuntu partition is not all of that 45 GB, but will be about 41 GB.