Defining parameters
Level: | \( N \) | = | \( 3004 = 2^{2} \cdot 751 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(1128000\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3004))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 283875 | 165250 | 118625 |
Cusp forms | 280126 | 163750 | 116376 |
Eisenstein series | 3749 | 1500 | 2249 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3004))\)
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 |
---|---|---|---|---|
3004.2.a | \(\chi_{3004}(1, \cdot)\) | 3004.2.a.a | 1 | 1 |
3004.2.a.b | 2 | |||
3004.2.a.c | 28 | |||
3004.2.a.d | 31 | |||
3004.2.d | \(\chi_{3004}(3003, \cdot)\) | n/a | 374 | 1 |
3004.2.e | \(\chi_{3004}(1429, \cdot)\) | n/a | 126 | 2 |
3004.2.f | \(\chi_{3004}(569, \cdot)\) | n/a | 248 | 4 |
3004.2.g | \(\chi_{3004}(679, \cdot)\) | n/a | 748 | 2 |
3004.2.j | \(\chi_{3004}(291, \cdot)\) | n/a | 1496 | 4 |
3004.2.m | \(\chi_{3004}(437, \cdot)\) | n/a | 504 | 8 |
3004.2.n | \(\chi_{3004}(53, \cdot)\) | n/a | 1240 | 20 |
3004.2.q | \(\chi_{3004}(583, \cdot)\) | n/a | 2992 | 8 |
3004.2.r | \(\chi_{3004}(195, \cdot)\) | n/a | 7480 | 20 |
3004.2.u | \(\chi_{3004}(61, \cdot)\) | n/a | 2520 | 40 |
3004.2.v | \(\chi_{3004}(45, \cdot)\) | n/a | 6200 | 100 |
3004.2.y | \(\chi_{3004}(11, \cdot)\) | n/a | 14960 | 40 |
3004.2.ba | \(\chi_{3004}(7, \cdot)\) | n/a | 37400 | 100 |
3004.2.bc | \(\chi_{3004}(5, \cdot)\) | n/a | 12600 | 200 |
3004.2.be | \(\chi_{3004}(3, \cdot)\) | n/a | 74800 | 200 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3004))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(3004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(751))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1502))\)\(^{\oplus 2}\)