Defining parameters
Level: | \( N \) | = | \( 296 = 2^{3} \cdot 37 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(5472\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(296))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 242 | 76 | 166 |
Cusp forms | 26 | 6 | 20 |
Eisenstein series | 216 | 70 | 146 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 2 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)
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 |
---|---|---|---|---|
296.1.b | \(\chi_{296}(295, \cdot)\) | None | 0 | 1 |
296.1.d | \(\chi_{296}(223, \cdot)\) | None | 0 | 1 |
296.1.f | \(\chi_{296}(75, \cdot)\) | None | 0 | 1 |
296.1.h | \(\chi_{296}(147, \cdot)\) | 296.1.h.a | 2 | 1 |
296.1.h.b | 2 | |||
296.1.k | \(\chi_{296}(105, \cdot)\) | 296.1.k.a | 2 | 2 |
296.1.m | \(\chi_{296}(117, \cdot)\) | None | 0 | 2 |
296.1.n | \(\chi_{296}(11, \cdot)\) | None | 0 | 2 |
296.1.p | \(\chi_{296}(195, \cdot)\) | None | 0 | 2 |
296.1.r | \(\chi_{296}(47, \cdot)\) | None | 0 | 2 |
296.1.t | \(\chi_{296}(159, \cdot)\) | None | 0 | 2 |
296.1.v | \(\chi_{296}(29, \cdot)\) | None | 0 | 4 |
296.1.x | \(\chi_{296}(97, \cdot)\) | None | 0 | 4 |
296.1.z | \(\chi_{296}(3, \cdot)\) | None | 0 | 6 |
296.1.bb | \(\chi_{296}(83, \cdot)\) | None | 0 | 6 |
296.1.bd | \(\chi_{296}(95, \cdot)\) | None | 0 | 6 |
296.1.be | \(\chi_{296}(7, \cdot)\) | None | 0 | 6 |
296.1.bg | \(\chi_{296}(5, \cdot)\) | None | 0 | 12 |
296.1.bi | \(\chi_{296}(17, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(296))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(296)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)