Defining parameters
Level: | \( N \) | \(=\) | \( 925 = 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 925.f (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 185 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(190\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(925, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 202 | 118 | 84 |
Cusp forms | 178 | 110 | 68 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(925, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
925.2.f.a | $2$ | $7.386$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+i q^{2}+(-2 i-2)q^{3}+q^{4}+(-2 i+2)q^{6}+\cdots\) |
925.2.f.b | $2$ | $7.386$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(0\) | \(6\) | \(q+i q^{2}+(i+1)q^{3}+q^{4}+(i-1)q^{6}+\cdots\) |
925.2.f.c | $6$ | $7.386$ | 6.0.350464.1 | None | \(0\) | \(2\) | \(0\) | \(4\) | \(q-\beta _{5}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\) |
925.2.f.d | $24$ | $7.386$ | None | \(0\) | \(-4\) | \(0\) | \(-6\) | ||
925.2.f.e | $28$ | $7.386$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
925.2.f.f | $48$ | $7.386$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(925, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(925, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)