Defining parameters
Level: | \( N \) | = | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(1370880\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2151))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 515984 | 408031 | 107953 |
Cusp forms | 512176 | 405899 | 106277 |
Eisenstein series | 3808 | 2132 | 1676 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2151))\)
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 |
---|---|---|---|---|
2151.4.a | \(\chi_{2151}(1, \cdot)\) | 2151.4.a.a | 22 | 1 |
2151.4.a.b | 28 | |||
2151.4.a.c | 28 | |||
2151.4.a.d | 32 | |||
2151.4.a.e | 32 | |||
2151.4.a.f | 37 | |||
2151.4.a.g | 59 | |||
2151.4.a.h | 59 | |||
2151.4.b | \(\chi_{2151}(2150, \cdot)\) | n/a | 240 | 1 |
2151.4.e | \(\chi_{2151}(718, \cdot)\) | n/a | 1428 | 2 |
2151.4.h | \(\chi_{2151}(716, \cdot)\) | n/a | 1436 | 2 |
2151.4.i | \(\chi_{2151}(10, \cdot)\) | n/a | 1794 | 6 |
2151.4.l | \(\chi_{2151}(215, \cdot)\) | n/a | 1440 | 6 |
2151.4.m | \(\chi_{2151}(163, \cdot)\) | n/a | 4784 | 16 |
2151.4.n | \(\chi_{2151}(283, \cdot)\) | n/a | 8616 | 12 |
2151.4.q | \(\chi_{2151}(107, \cdot)\) | n/a | 3840 | 16 |
2151.4.r | \(\chi_{2151}(38, \cdot)\) | n/a | 8616 | 12 |
2151.4.u | \(\chi_{2151}(22, \cdot)\) | n/a | 22976 | 32 |
2151.4.v | \(\chi_{2151}(23, \cdot)\) | n/a | 22976 | 32 |
2151.4.y | \(\chi_{2151}(55, \cdot)\) | n/a | 28704 | 96 |
2151.4.z | \(\chi_{2151}(26, \cdot)\) | n/a | 23040 | 96 |
2151.4.bc | \(\chi_{2151}(4, \cdot)\) | n/a | 137856 | 192 |
2151.4.bf | \(\chi_{2151}(14, \cdot)\) | n/a | 137856 | 192 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2151))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(2151)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(239))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(717))\)\(^{\oplus 2}\)