Defining parameters
Level: | \( N \) | = | \( 625 = 5^{4} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 45 \) | ||
Sturm bound: | \(62500\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(625))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16175 | 14784 | 1391 |
Cusp forms | 15076 | 14016 | 1060 |
Eisenstein series | 1099 | 768 | 331 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)
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 |
---|---|---|---|---|
625.2.a | \(\chi_{625}(1, \cdot)\) | 625.2.a.a | 2 | 1 |
625.2.a.b | 2 | |||
625.2.a.c | 2 | |||
625.2.a.d | 2 | |||
625.2.a.e | 8 | |||
625.2.a.f | 8 | |||
625.2.a.g | 8 | |||
625.2.b | \(\chi_{625}(624, \cdot)\) | 625.2.b.a | 4 | 1 |
625.2.b.b | 4 | |||
625.2.b.c | 8 | |||
625.2.b.d | 16 | |||
625.2.d | \(\chi_{625}(126, \cdot)\) | 625.2.d.a | 4 | 4 |
625.2.d.b | 4 | |||
625.2.d.c | 4 | |||
625.2.d.d | 4 | |||
625.2.d.e | 4 | |||
625.2.d.f | 4 | |||
625.2.d.g | 4 | |||
625.2.d.h | 4 | |||
625.2.d.i | 4 | |||
625.2.d.j | 4 | |||
625.2.d.k | 8 | |||
625.2.d.l | 8 | |||
625.2.d.m | 16 | |||
625.2.d.n | 16 | |||
625.2.d.o | 16 | |||
625.2.d.p | 16 | |||
625.2.d.q | 16 | |||
625.2.e | \(\chi_{625}(124, \cdot)\) | 625.2.e.a | 8 | 4 |
625.2.e.b | 8 | |||
625.2.e.c | 8 | |||
625.2.e.d | 8 | |||
625.2.e.e | 8 | |||
625.2.e.f | 8 | |||
625.2.e.g | 8 | |||
625.2.e.h | 8 | |||
625.2.e.i | 8 | |||
625.2.e.j | 32 | |||
625.2.e.k | 32 | |||
625.2.g | \(\chi_{625}(26, \cdot)\) | 625.2.g.a | 220 | 20 |
625.2.g.b | 480 | |||
625.2.h | \(\chi_{625}(24, \cdot)\) | 625.2.h.a | 240 | 20 |
625.2.h.b | 440 | |||
625.2.j | \(\chi_{625}(6, \cdot)\) | 625.2.j.a | 6100 | 100 |
625.2.k | \(\chi_{625}(4, \cdot)\) | 625.2.k.a | 6200 | 100 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(625))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(625)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 2}\)