Defining parameters
Level: | \( N \) | = | \( 8012 = 2^{2} \cdot 2003 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(8024016\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8012))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2011009 | 1172171 | 838838 |
Cusp forms | 2001000 | 1168167 | 832833 |
Eisenstein series | 10009 | 4004 | 6005 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8012))\)
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 |
---|---|---|---|---|
8012.2.a | \(\chi_{8012}(1, \cdot)\) | 8012.2.a.a | 79 | 1 |
8012.2.a.b | 88 | |||
8012.2.b | \(\chi_{8012}(8011, \cdot)\) | n/a | 1000 | 1 |
8012.2.e | \(\chi_{8012}(485, \cdot)\) | n/a | 1002 | 6 |
8012.2.f | \(\chi_{8012}(685, \cdot)\) | n/a | 1670 | 10 |
8012.2.g | \(\chi_{8012}(89, \cdot)\) | n/a | 2004 | 12 |
8012.2.j | \(\chi_{8012}(5035, \cdot)\) | n/a | 6000 | 6 |
8012.2.m | \(\chi_{8012}(1243, \cdot)\) | n/a | 10000 | 10 |
8012.2.p | \(\chi_{8012}(87, \cdot)\) | n/a | 12000 | 12 |
8012.2.q | \(\chi_{8012}(57, \cdot)\) | n/a | 10020 | 60 |
8012.2.r | \(\chi_{8012}(53, \cdot)\) | n/a | 12024 | 72 |
8012.2.s | \(\chi_{8012}(113, \cdot)\) | n/a | 20040 | 120 |
8012.2.t | \(\chi_{8012}(99, \cdot)\) | n/a | 60000 | 60 |
8012.2.w | \(\chi_{8012}(295, \cdot)\) | n/a | 72000 | 72 |
8012.2.z | \(\chi_{8012}(11, \cdot)\) | n/a | 120000 | 120 |
8012.2.bc | \(\chi_{8012}(9, \cdot)\) | n/a | 120240 | 720 |
8012.2.bf | \(\chi_{8012}(7, \cdot)\) | n/a | 720000 | 720 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8012))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2003))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4006))\)\(^{\oplus 2}\)