Defining parameters
| Level: | \( N \) | = | \( 453 = 3 \cdot 151 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(15200\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(453))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 334 | 176 | 158 |
| Cusp forms | 34 | 28 | 6 |
| Eisenstein series | 300 | 148 | 152 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 24 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(453))\)
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 |
|---|---|---|---|---|
| 453.1.c | \(\chi_{453}(152, \cdot)\) | None | 0 | 1 |
| 453.1.d | \(\chi_{453}(301, \cdot)\) | None | 0 | 1 |
| 453.1.g | \(\chi_{453}(184, \cdot)\) | None | 0 | 2 |
| 453.1.h | \(\chi_{453}(32, \cdot)\) | 453.1.h.a | 4 | 2 |
| 453.1.j | \(\chi_{453}(8, \cdot)\) | 453.1.j.a | 4 | 4 |
| 453.1.l | \(\chi_{453}(238, \cdot)\) | None | 0 | 4 |
| 453.1.o | \(\chi_{453}(46, \cdot)\) | None | 0 | 8 |
| 453.1.q | \(\chi_{453}(2, \cdot)\) | None | 0 | 8 |
| 453.1.r | \(\chi_{453}(28, \cdot)\) | None | 0 | 20 |
| 453.1.t | \(\chi_{453}(20, \cdot)\) | 453.1.t.a | 20 | 20 |
| 453.1.v | \(\chi_{453}(5, \cdot)\) | None | 0 | 40 |
| 453.1.x | \(\chi_{453}(7, \cdot)\) | None | 0 | 40 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(453))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(453)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 2}\)