Defining parameters
Level: | \( N \) | = | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(6144\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(320))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 298 | 69 | 229 |
Cusp forms | 10 | 3 | 7 |
Eisenstein series | 288 | 66 | 222 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(320))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
320.1.b | \(\chi_{320}(191, \cdot)\) | None | 0 | 1 |
320.1.e | \(\chi_{320}(159, \cdot)\) | None | 0 | 1 |
320.1.g | \(\chi_{320}(31, \cdot)\) | None | 0 | 1 |
320.1.h | \(\chi_{320}(319, \cdot)\) | 320.1.h.a | 1 | 1 |
320.1.i | \(\chi_{320}(177, \cdot)\) | None | 0 | 2 |
320.1.k | \(\chi_{320}(79, \cdot)\) | None | 0 | 2 |
320.1.m | \(\chi_{320}(33, \cdot)\) | None | 0 | 2 |
320.1.p | \(\chi_{320}(193, \cdot)\) | 320.1.p.a | 2 | 2 |
320.1.r | \(\chi_{320}(111, \cdot)\) | None | 0 | 2 |
320.1.t | \(\chi_{320}(17, \cdot)\) | None | 0 | 2 |
320.1.v | \(\chi_{320}(57, \cdot)\) | None | 0 | 4 |
320.1.w | \(\chi_{320}(71, \cdot)\) | None | 0 | 4 |
320.1.y | \(\chi_{320}(39, \cdot)\) | None | 0 | 4 |
320.1.bb | \(\chi_{320}(137, \cdot)\) | None | 0 | 4 |
320.1.bc | \(\chi_{320}(53, \cdot)\) | None | 0 | 8 |
320.1.bg | \(\chi_{320}(11, \cdot)\) | None | 0 | 8 |
320.1.bh | \(\chi_{320}(19, \cdot)\) | None | 0 | 8 |
320.1.bi | \(\chi_{320}(13, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(320)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)