Defining parameters
Level: | \( N \) | = | \( 944 = 2^{4} \cdot 59 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(55680\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(944))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 894 | 265 | 629 |
Cusp forms | 82 | 8 | 74 |
Eisenstein series | 812 | 257 | 555 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(944))\)
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 |
---|---|---|---|---|
944.1.c | \(\chi_{944}(825, \cdot)\) | None | 0 | 1 |
944.1.d | \(\chi_{944}(591, \cdot)\) | None | 0 | 1 |
944.1.g | \(\chi_{944}(119, \cdot)\) | None | 0 | 1 |
944.1.h | \(\chi_{944}(353, \cdot)\) | 944.1.h.a | 1 | 1 |
944.1.h.b | 3 | |||
944.1.j | \(\chi_{944}(117, \cdot)\) | 944.1.j.a | 4 | 2 |
944.1.l | \(\chi_{944}(355, \cdot)\) | None | 0 | 2 |
944.1.n | \(\chi_{944}(33, \cdot)\) | None | 0 | 28 |
944.1.o | \(\chi_{944}(7, \cdot)\) | None | 0 | 28 |
944.1.r | \(\chi_{944}(15, \cdot)\) | None | 0 | 28 |
944.1.s | \(\chi_{944}(73, \cdot)\) | None | 0 | 28 |
944.1.u | \(\chi_{944}(3, \cdot)\) | None | 0 | 56 |
944.1.w | \(\chi_{944}(13, \cdot)\) | None | 0 | 56 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(944))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(944)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(472))\)\(^{\oplus 2}\)