Defining parameters
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.f (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(70\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(325, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 82 | 46 | 36 |
Cusp forms | 58 | 38 | 20 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(325, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
325.2.f.a | $2$ | $2.595$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(0\) | \(4\) | \(q-iq^{2}+(-1+i)q^{3}+q^{4}+(1+i)q^{6}+\cdots\) |
325.2.f.b | $8$ | $2.595$ | 8.0.619810816.2 | None | \(0\) | \(6\) | \(0\) | \(0\) | \(q-\beta _{6}q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\) |
325.2.f.c | $12$ | $2.595$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{7}q^{2}-\beta _{4}q^{3}+(-2+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\) |
325.2.f.d | $16$ | $2.595$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{13}q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(1+\beta _{4}+\cdots)q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(325, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)