Defining parameters
Level: | \( N \) | = | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(10329792\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8035))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2588872 | 2372057 | 216815 |
Cusp forms | 2576025 | 2362425 | 213600 |
Eisenstein series | 12847 | 9632 | 3215 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8035))\)
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 |
---|---|---|---|---|
8035.2.a | \(\chi_{8035}(1, \cdot)\) | 8035.2.a.a | 1 | 1 |
8035.2.a.b | 114 | |||
8035.2.a.c | 127 | |||
8035.2.a.d | 140 | |||
8035.2.a.e | 153 | |||
8035.2.b | \(\chi_{8035}(6429, \cdot)\) | n/a | 802 | 1 |
8035.2.e | \(\chi_{8035}(3213, \cdot)\) | n/a | 1604 | 2 |
8035.2.g | \(\chi_{8035}(1046, \cdot)\) | n/a | 5360 | 10 |
8035.2.j | \(\chi_{8035}(444, \cdot)\) | n/a | 8020 | 10 |
8035.2.l | \(\chi_{8035}(1163, \cdot)\) | n/a | 16040 | 20 |
8035.2.m | \(\chi_{8035}(96, \cdot)\) | n/a | 38592 | 72 |
8035.2.p | \(\chi_{8035}(34, \cdot)\) | n/a | 57744 | 72 |
8035.2.r | \(\chi_{8035}(38, \cdot)\) | n/a | 115488 | 144 |
8035.2.s | \(\chi_{8035}(6, \cdot)\) | n/a | 385920 | 720 |
8035.2.t | \(\chi_{8035}(4, \cdot)\) | n/a | 577440 | 720 |
8035.2.w | \(\chi_{8035}(7, \cdot)\) | n/a | 1154880 | 1440 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8035))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1607))\)\(^{\oplus 2}\)