Defining parameters
| Level: | \( N \) | = | \( 2075 = 5^{2} \cdot 83 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 12 \) | ||
| Sturm bound: | \(344400\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2075))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2326 | 1680 | 646 |
| Cusp forms | 30 | 19 | 11 |
| Eisenstein series | 2296 | 1661 | 635 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 19 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2075))\)
We only show spaces with odd 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 |
|---|---|---|---|---|
| 2075.1.c | \(\chi_{2075}(1576, \cdot)\) | 2075.1.c.a | 1 | 1 |
| 2075.1.c.b | 1 | |||
| 2075.1.c.c | 1 | |||
| 2075.1.c.d | 1 | |||
| 2075.1.c.e | 1 | |||
| 2075.1.c.f | 1 | |||
| 2075.1.c.g | 1 | |||
| 2075.1.c.h | 4 | |||
| 2075.1.d | \(\chi_{2075}(2074, \cdot)\) | 2075.1.d.a | 2 | 1 |
| 2075.1.d.b | 2 | |||
| 2075.1.d.c | 2 | |||
| 2075.1.d.d | 2 | |||
| 2075.1.f | \(\chi_{2075}(582, \cdot)\) | None | 0 | 2 |
| 2075.1.h | \(\chi_{2075}(414, \cdot)\) | None | 0 | 4 |
| 2075.1.i | \(\chi_{2075}(331, \cdot)\) | None | 0 | 4 |
| 2075.1.k | \(\chi_{2075}(167, \cdot)\) | None | 0 | 8 |
| 2075.1.n | \(\chi_{2075}(24, \cdot)\) | None | 0 | 40 |
| 2075.1.o | \(\chi_{2075}(76, \cdot)\) | None | 0 | 40 |
| 2075.1.q | \(\chi_{2075}(7, \cdot)\) | None | 0 | 80 |
| 2075.1.u | \(\chi_{2075}(6, \cdot)\) | None | 0 | 160 |
| 2075.1.v | \(\chi_{2075}(14, \cdot)\) | None | 0 | 160 |
| 2075.1.x | \(\chi_{2075}(3, \cdot)\) | None | 0 | 320 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2075))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2075)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(415))\)\(^{\oplus 2}\)