Defining parameters
| Level: | \( N \) | = | \( 603 = 3^{2} \cdot 67 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(26928\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(603))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 567 | 304 | 263 |
| Cusp forms | 39 | 11 | 28 |
| Eisenstein series | 528 | 293 | 235 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 11 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(603))\)
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 |
|---|---|---|---|---|
| 603.1.b | \(\chi_{603}(334, \cdot)\) | 603.1.b.a | 1 | 1 |
| 603.1.c | \(\chi_{603}(269, \cdot)\) | None | 0 | 1 |
| 603.1.i | \(\chi_{603}(230, \cdot)\) | None | 0 | 2 |
| 603.1.j | \(\chi_{603}(97, \cdot)\) | None | 0 | 2 |
| 603.1.n | \(\chi_{603}(305, \cdot)\) | None | 0 | 2 |
| 603.1.o | \(\chi_{603}(172, \cdot)\) | None | 0 | 2 |
| 603.1.p | \(\chi_{603}(499, \cdot)\) | None | 0 | 2 |
| 603.1.q | \(\chi_{603}(68, \cdot)\) | None | 0 | 2 |
| 603.1.r | \(\chi_{603}(133, \cdot)\) | None | 0 | 2 |
| 603.1.s | \(\chi_{603}(29, \cdot)\) | None | 0 | 2 |
| 603.1.w | \(\chi_{603}(62, \cdot)\) | None | 0 | 10 |
| 603.1.x | \(\chi_{603}(109, \cdot)\) | 603.1.x.a | 10 | 10 |
| 603.1.bd | \(\chi_{603}(23, \cdot)\) | None | 0 | 20 |
| 603.1.be | \(\chi_{603}(43, \cdot)\) | None | 0 | 20 |
| 603.1.bf | \(\chi_{603}(14, \cdot)\) | None | 0 | 20 |
| 603.1.bg | \(\chi_{603}(7, \cdot)\) | None | 0 | 20 |
| 603.1.bh | \(\chi_{603}(28, \cdot)\) | None | 0 | 20 |
| 603.1.bi | \(\chi_{603}(17, \cdot)\) | None | 0 | 20 |
| 603.1.bm | \(\chi_{603}(31, \cdot)\) | None | 0 | 20 |
| 603.1.bn | \(\chi_{603}(65, \cdot)\) | None | 0 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(603))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(603)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(603))\)\(^{\oplus 1}\)