Defining parameters
Level: | \( N \) | = | \( 264 = 2^{3} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(3840\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(264))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 270 | 54 | 216 |
Cusp forms | 30 | 18 | 12 |
Eisenstein series | 240 | 36 | 204 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 18 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(264))\)
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 |
---|---|---|---|---|
264.1.c | \(\chi_{264}(67, \cdot)\) | None | 0 | 1 |
264.1.e | \(\chi_{264}(109, \cdot)\) | None | 0 | 1 |
264.1.g | \(\chi_{264}(263, \cdot)\) | None | 0 | 1 |
264.1.i | \(\chi_{264}(89, \cdot)\) | None | 0 | 1 |
264.1.j | \(\chi_{264}(241, \cdot)\) | None | 0 | 1 |
264.1.l | \(\chi_{264}(199, \cdot)\) | None | 0 | 1 |
264.1.n | \(\chi_{264}(221, \cdot)\) | None | 0 | 1 |
264.1.p | \(\chi_{264}(131, \cdot)\) | 264.1.p.a | 1 | 1 |
264.1.p.b | 1 | |||
264.1.r | \(\chi_{264}(35, \cdot)\) | 264.1.r.a | 4 | 4 |
264.1.r.b | 4 | |||
264.1.t | \(\chi_{264}(5, \cdot)\) | 264.1.t.a | 4 | 4 |
264.1.t.b | 4 | |||
264.1.v | \(\chi_{264}(31, \cdot)\) | None | 0 | 4 |
264.1.x | \(\chi_{264}(73, \cdot)\) | None | 0 | 4 |
264.1.y | \(\chi_{264}(113, \cdot)\) | None | 0 | 4 |
264.1.ba | \(\chi_{264}(95, \cdot)\) | None | 0 | 4 |
264.1.bc | \(\chi_{264}(13, \cdot)\) | None | 0 | 4 |
264.1.be | \(\chi_{264}(91, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(264))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(264)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)