Defining parameters
Level: | \( N \) | = | \( 258 = 2 \cdot 3 \cdot 43 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 38 \) | ||
Sturm bound: | \(7392\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(258))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2016 | 463 | 1553 |
Cusp forms | 1681 | 463 | 1218 |
Eisenstein series | 335 | 0 | 335 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(258))\)
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 |
---|---|---|---|---|
258.2.a | \(\chi_{258}(1, \cdot)\) | 258.2.a.a | 1 | 1 |
258.2.a.b | 1 | |||
258.2.a.c | 1 | |||
258.2.a.d | 1 | |||
258.2.a.e | 1 | |||
258.2.a.f | 1 | |||
258.2.a.g | 1 | |||
258.2.d | \(\chi_{258}(257, \cdot)\) | 258.2.d.a | 2 | 1 |
258.2.d.b | 2 | |||
258.2.d.c | 6 | |||
258.2.d.d | 6 | |||
258.2.e | \(\chi_{258}(49, \cdot)\) | 258.2.e.a | 2 | 2 |
258.2.e.b | 2 | |||
258.2.e.c | 2 | |||
258.2.e.d | 2 | |||
258.2.e.e | 2 | |||
258.2.e.f | 2 | |||
258.2.e.g | 4 | |||
258.2.f | \(\chi_{258}(179, \cdot)\) | 258.2.f.a | 2 | 2 |
258.2.f.b | 2 | |||
258.2.f.c | 4 | |||
258.2.f.d | 4 | |||
258.2.f.e | 8 | |||
258.2.f.f | 8 | |||
258.2.i | \(\chi_{258}(97, \cdot)\) | 258.2.i.a | 6 | 6 |
258.2.i.b | 6 | |||
258.2.i.c | 6 | |||
258.2.i.d | 6 | |||
258.2.i.e | 12 | |||
258.2.j | \(\chi_{258}(65, \cdot)\) | 258.2.j.a | 48 | 6 |
258.2.j.b | 48 | |||
258.2.m | \(\chi_{258}(13, \cdot)\) | 258.2.m.a | 12 | 12 |
258.2.m.b | 12 | |||
258.2.m.c | 24 | |||
258.2.m.d | 24 | |||
258.2.m.e | 24 | |||
258.2.p | \(\chi_{258}(5, \cdot)\) | 258.2.p.a | 84 | 12 |
258.2.p.b | 84 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(258))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(258)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)