Defining parameters
Level: | \( N \) | = | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(6000\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(275))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 291 | 194 | 97 |
Cusp forms | 11 | 9 | 2 |
Eisenstein series | 280 | 185 | 95 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 9 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(275))\)
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 |
---|---|---|---|---|
275.1.c | \(\chi_{275}(76, \cdot)\) | 275.1.c.a | 1 | 1 |
275.1.d | \(\chi_{275}(274, \cdot)\) | None | 0 | 1 |
275.1.f | \(\chi_{275}(232, \cdot)\) | None | 0 | 2 |
275.1.m | \(\chi_{275}(41, \cdot)\) | None | 0 | 4 |
275.1.o | \(\chi_{275}(79, \cdot)\) | None | 0 | 4 |
275.1.p | \(\chi_{275}(39, \cdot)\) | None | 0 | 4 |
275.1.q | \(\chi_{275}(24, \cdot)\) | None | 0 | 4 |
275.1.r | \(\chi_{275}(19, \cdot)\) | None | 0 | 4 |
275.1.s | \(\chi_{275}(54, \cdot)\) | 275.1.s.a | 4 | 4 |
275.1.u | \(\chi_{275}(61, \cdot)\) | None | 0 | 4 |
275.1.v | \(\chi_{275}(21, \cdot)\) | 275.1.v.a | 4 | 4 |
275.1.w | \(\chi_{275}(116, \cdot)\) | None | 0 | 4 |
275.1.x | \(\chi_{275}(51, \cdot)\) | None | 0 | 4 |
275.1.bc | \(\chi_{275}(6, \cdot)\) | None | 0 | 4 |
275.1.bd | \(\chi_{275}(139, \cdot)\) | None | 0 | 4 |
275.1.be | \(\chi_{275}(42, \cdot)\) | None | 0 | 8 |
275.1.bh | \(\chi_{275}(37, \cdot)\) | None | 0 | 8 |
275.1.bi | \(\chi_{275}(12, \cdot)\) | None | 0 | 8 |
275.1.bj | \(\chi_{275}(38, \cdot)\) | None | 0 | 8 |
275.1.bk | \(\chi_{275}(82, \cdot)\) | None | 0 | 8 |
275.1.bp | \(\chi_{275}(3, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(275)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)