Defining parameters
| Level: | \( N \) | = | \( 476 = 2^{2} \cdot 7 \cdot 17 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(13824\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(476))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 506 | 160 | 346 |
| Cusp forms | 26 | 8 | 18 |
| Eisenstein series | 480 | 152 | 328 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(476))\)
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 |
|---|---|---|---|---|
| 476.1.c | \(\chi_{476}(69, \cdot)\) | None | 0 | 1 |
| 476.1.d | \(\chi_{476}(239, \cdot)\) | None | 0 | 1 |
| 476.1.g | \(\chi_{476}(407, \cdot)\) | None | 0 | 1 |
| 476.1.h | \(\chi_{476}(237, \cdot)\) | None | 0 | 1 |
| 476.1.j | \(\chi_{476}(13, \cdot)\) | None | 0 | 2 |
| 476.1.m | \(\chi_{476}(183, \cdot)\) | None | 0 | 2 |
| 476.1.n | \(\chi_{476}(33, \cdot)\) | None | 0 | 2 |
| 476.1.o | \(\chi_{476}(67, \cdot)\) | 476.1.o.a | 2 | 2 |
| 476.1.o.b | 2 | |||
| 476.1.o.c | 4 | |||
| 476.1.r | \(\chi_{476}(375, \cdot)\) | None | 0 | 2 |
| 476.1.s | \(\chi_{476}(341, \cdot)\) | None | 0 | 2 |
| 476.1.v | \(\chi_{476}(15, \cdot)\) | None | 0 | 4 |
| 476.1.x | \(\chi_{476}(321, \cdot)\) | None | 0 | 4 |
| 476.1.y | \(\chi_{476}(89, \cdot)\) | None | 0 | 4 |
| 476.1.bb | \(\chi_{476}(123, \cdot)\) | None | 0 | 4 |
| 476.1.bc | \(\chi_{476}(29, \cdot)\) | None | 0 | 8 |
| 476.1.bf | \(\chi_{476}(27, \cdot)\) | None | 0 | 8 |
| 476.1.bg | \(\chi_{476}(151, \cdot)\) | None | 0 | 8 |
| 476.1.bi | \(\chi_{476}(117, \cdot)\) | None | 0 | 8 |
| 476.1.bk | \(\chi_{476}(3, \cdot)\) | None | 0 | 16 |
| 476.1.bn | \(\chi_{476}(37, \cdot)\) | None | 0 | 16 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(476))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(476)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 2}\)