Defining parameters
Level: | \( N \) | = | \( 502 = 2 \cdot 251 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(31500\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(502))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8125 | 2624 | 5501 |
Cusp forms | 7626 | 2624 | 5002 |
Eisenstein series | 499 | 0 | 499 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)
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 |
---|---|---|---|---|
502.2.a | \(\chi_{502}(1, \cdot)\) | 502.2.a.a | 2 | 1 |
502.2.a.b | 2 | |||
502.2.a.c | 5 | |||
502.2.a.d | 5 | |||
502.2.a.e | 6 | |||
502.2.c | \(\chi_{502}(113, \cdot)\) | 502.2.c.a | 40 | 4 |
502.2.c.b | 44 | |||
502.2.e | \(\chi_{502}(5, \cdot)\) | 502.2.e.a | 200 | 20 |
502.2.e.b | 220 | |||
502.2.g | \(\chi_{502}(3, \cdot)\) | 502.2.g.a | 1000 | 100 |
502.2.g.b | 1100 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(502))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(502)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 2}\)