Defining parameters
Level: | \( N \) | \(=\) | \( 925 = 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 925.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(190\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(925, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 200 | 126 | 74 |
Cusp forms | 176 | 114 | 62 |
Eisenstein series | 24 | 12 | 12 |
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.e.a | $2$ | $7.386$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(0\) | \(0\) | \(2\) | \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{7}+3q^{8}+\cdots\) |
925.2.e.b | $14$ | $7.386$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(-2\) | \(2\) | \(0\) | \(-2\) | \(q-\beta _{8}q^{2}-\beta _{6}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\) |
925.2.e.c | $14$ | $7.386$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{2}+\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots\) |
925.2.e.d | $24$ | $7.386$ | None | \(-1\) | \(-2\) | \(0\) | \(-6\) | ||
925.2.e.e | $24$ | $7.386$ | None | \(1\) | \(2\) | \(0\) | \(6\) | ||
925.2.e.f | $36$ | $7.386$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(925, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(925, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 3}\)