Defining parameters
Level: | \( N \) | = | \( 8044 = 2^{2} \cdot 2011 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(8088240\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8044))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2027085 | 1181545 | 845540 |
Cusp forms | 2017036 | 1177525 | 839511 |
Eisenstein series | 10049 | 4020 | 6029 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8044))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
8044.2.a | \(\chi_{8044}(1, \cdot)\) | 8044.2.a.a | 80 | 1 |
8044.2.a.b | 87 | |||
8044.2.d | \(\chi_{8044}(8043, \cdot)\) | n/a | 1004 | 1 |
8044.2.e | \(\chi_{8044}(205, \cdot)\) | n/a | 336 | 2 |
8044.2.f | \(\chi_{8044}(2809, \cdot)\) | n/a | 668 | 4 |
8044.2.g | \(\chi_{8044}(6239, \cdot)\) | n/a | 2008 | 2 |
8044.2.j | \(\chi_{8044}(63, \cdot)\) | n/a | 4016 | 4 |
8044.2.m | \(\chi_{8044}(1201, \cdot)\) | n/a | 1344 | 8 |
8044.2.p | \(\chi_{8044}(1099, \cdot)\) | n/a | 8032 | 8 |
8044.2.q | \(\chi_{8044}(133, \cdot)\) | n/a | 11022 | 66 |
8044.2.r | \(\chi_{8044}(147, \cdot)\) | n/a | 66264 | 66 |
8044.2.u | \(\chi_{8044}(117, \cdot)\) | n/a | 22176 | 132 |
8044.2.v | \(\chi_{8044}(13, \cdot)\) | n/a | 44088 | 264 |
8044.2.y | \(\chi_{8044}(15, \cdot)\) | n/a | 132528 | 132 |
8044.2.bb | \(\chi_{8044}(27, \cdot)\) | n/a | 265056 | 264 |
8044.2.bc | \(\chi_{8044}(5, \cdot)\) | n/a | 88704 | 528 |
8044.2.bd | \(\chi_{8044}(3, \cdot)\) | n/a | 530112 | 528 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8044))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2011))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4022))\)\(^{\oplus 2}\)