Defining parameters
| Level: | \( N \) | = | \( 2303 = 7^{2} \cdot 47 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 13 \) | ||
| Sturm bound: | \(432768\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2303))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2906 | 2303 | 603 |
| Cusp forms | 146 | 120 | 26 |
| Eisenstein series | 2760 | 2183 | 577 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 120 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2303))\)
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 |
|---|---|---|---|---|
| 2303.1.b | \(\chi_{2303}(48, \cdot)\) | None | 0 | 1 |
| 2303.1.d | \(\chi_{2303}(2255, \cdot)\) | 2303.1.d.a | 1 | 1 |
| 2303.1.d.b | 1 | |||
| 2303.1.d.c | 2 | |||
| 2303.1.d.d | 4 | |||
| 2303.1.d.e | 4 | |||
| 2303.1.f | \(\chi_{2303}(422, \cdot)\) | 2303.1.f.a | 2 | 2 |
| 2303.1.f.b | 4 | |||
| 2303.1.f.c | 4 | |||
| 2303.1.f.d | 8 | |||
| 2303.1.h | \(\chi_{2303}(1599, \cdot)\) | None | 0 | 2 |
| 2303.1.j | \(\chi_{2303}(281, \cdot)\) | 2303.1.j.a | 6 | 6 |
| 2303.1.j.b | 24 | |||
| 2303.1.l | \(\chi_{2303}(377, \cdot)\) | None | 0 | 6 |
| 2303.1.o | \(\chi_{2303}(236, \cdot)\) | None | 0 | 12 |
| 2303.1.q | \(\chi_{2303}(46, \cdot)\) | 2303.1.q.a | 12 | 12 |
| 2303.1.q.b | 48 | |||
| 2303.1.r | \(\chi_{2303}(99, \cdot)\) | None | 0 | 22 |
| 2303.1.t | \(\chi_{2303}(97, \cdot)\) | None | 0 | 22 |
| 2303.1.v | \(\chi_{2303}(68, \cdot)\) | None | 0 | 44 |
| 2303.1.x | \(\chi_{2303}(30, \cdot)\) | None | 0 | 44 |
| 2303.1.z | \(\chi_{2303}(6, \cdot)\) | None | 0 | 132 |
| 2303.1.bb | \(\chi_{2303}(15, \cdot)\) | None | 0 | 132 |
| 2303.1.bd | \(\chi_{2303}(11, \cdot)\) | None | 0 | 264 |
| 2303.1.bf | \(\chi_{2303}(3, \cdot)\) | None | 0 | 264 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2303))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2303)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(329))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2303))\)\(^{\oplus 1}\)