Defining parameters
Level: | \( N \) | = | \( 894 = 2 \cdot 3 \cdot 149 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(88800\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(894))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22792 | 5551 | 17241 |
Cusp forms | 21609 | 5551 | 16058 |
Eisenstein series | 1183 | 0 | 1183 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(894))\)
We only show spaces with even 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 |
---|---|---|---|---|
894.2.a | \(\chi_{894}(1, \cdot)\) | 894.2.a.a | 1 | 1 |
894.2.a.b | 1 | |||
894.2.a.c | 1 | |||
894.2.a.d | 1 | |||
894.2.a.e | 1 | |||
894.2.a.f | 1 | |||
894.2.a.g | 1 | |||
894.2.a.h | 2 | |||
894.2.a.i | 3 | |||
894.2.a.j | 4 | |||
894.2.a.k | 4 | |||
894.2.a.l | 5 | |||
894.2.d | \(\chi_{894}(595, \cdot)\) | 894.2.d.a | 2 | 1 |
894.2.d.b | 2 | |||
894.2.d.c | 10 | |||
894.2.d.d | 12 | |||
894.2.e | \(\chi_{894}(491, \cdot)\) | 894.2.e.a | 4 | 2 |
894.2.e.b | 4 | |||
894.2.e.c | 4 | |||
894.2.e.d | 4 | |||
894.2.e.e | 4 | |||
894.2.e.f | 8 | |||
894.2.e.g | 72 | |||
894.2.g | \(\chi_{894}(19, \cdot)\) | 894.2.g.a | 180 | 36 |
894.2.g.b | 216 | |||
894.2.g.c | 216 | |||
894.2.g.d | 252 | |||
894.2.h | \(\chi_{894}(7, \cdot)\) | 894.2.h.a | 432 | 36 |
894.2.h.b | 504 | |||
894.2.l | \(\chi_{894}(11, \cdot)\) | 894.2.l.a | 3600 | 72 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(894))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(894)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(149))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(298))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(447))\)\(^{\oplus 2}\)