Defining parameters
Level: | \( N \) | = | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(41760\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(531))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10904 | 8516 | 2388 |
Cusp forms | 9977 | 8004 | 1973 |
Eisenstein series | 927 | 512 | 415 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(531))\)
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 |
---|---|---|---|---|
531.2.a | \(\chi_{531}(1, \cdot)\) | 531.2.a.a | 2 | 1 |
531.2.a.b | 2 | |||
531.2.a.c | 2 | |||
531.2.a.d | 3 | |||
531.2.a.e | 5 | |||
531.2.a.f | 5 | |||
531.2.a.g | 5 | |||
531.2.d | \(\chi_{531}(530, \cdot)\) | 531.2.d.a | 20 | 1 |
531.2.e | \(\chi_{531}(178, \cdot)\) | 531.2.e.a | 4 | 2 |
531.2.e.b | 42 | |||
531.2.e.c | 70 | |||
531.2.f | \(\chi_{531}(176, \cdot)\) | 531.2.f.a | 12 | 2 |
531.2.f.b | 104 | |||
531.2.i | \(\chi_{531}(19, \cdot)\) | 531.2.i.a | 112 | 28 |
531.2.i.b | 140 | |||
531.2.i.c | 140 | |||
531.2.i.d | 280 | |||
531.2.j | \(\chi_{531}(8, \cdot)\) | 531.2.j.a | 560 | 28 |
531.2.m | \(\chi_{531}(4, \cdot)\) | 531.2.m.a | 3248 | 56 |
531.2.p | \(\chi_{531}(2, \cdot)\) | 531.2.p.a | 3248 | 56 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(531))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(531)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)