Defining parameters
Level: | \( N \) | = | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(1000000\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1875))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 377200 | 259968 | 117232 |
Cusp forms | 372800 | 258432 | 114368 |
Eisenstein series | 4400 | 1536 | 2864 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1875))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
1875.4.a | \(\chi_{1875}(1, \cdot)\) | 1875.4.a.a | 10 | 1 |
1875.4.a.b | 10 | |||
1875.4.a.c | 10 | |||
1875.4.a.d | 10 | |||
1875.4.a.e | 14 | |||
1875.4.a.f | 14 | |||
1875.4.a.g | 14 | |||
1875.4.a.h | 14 | |||
1875.4.a.i | 16 | |||
1875.4.a.j | 16 | |||
1875.4.a.k | 24 | |||
1875.4.a.l | 24 | |||
1875.4.a.m | 32 | |||
1875.4.a.n | 32 | |||
1875.4.b | \(\chi_{1875}(1249, \cdot)\) | n/a | 240 | 1 |
1875.4.e | \(\chi_{1875}(182, \cdot)\) | n/a | 928 | 2 |
1875.4.g | \(\chi_{1875}(376, \cdot)\) | n/a | 960 | 4 |
1875.4.i | \(\chi_{1875}(124, \cdot)\) | n/a | 960 | 4 |
1875.4.l | \(\chi_{1875}(68, \cdot)\) | n/a | 3744 | 8 |
1875.4.m | \(\chi_{1875}(76, \cdot)\) | n/a | 4520 | 20 |
1875.4.o | \(\chi_{1875}(49, \cdot)\) | n/a | 4480 | 20 |
1875.4.r | \(\chi_{1875}(32, \cdot)\) | n/a | 17760 | 40 |
1875.4.s | \(\chi_{1875}(16, \cdot)\) | n/a | 37400 | 100 |
1875.4.v | \(\chi_{1875}(4, \cdot)\) | n/a | 37600 | 100 |
1875.4.x | \(\chi_{1875}(2, \cdot)\) | n/a | 149600 | 200 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1875))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1875)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 2}\)