Defining parameters
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.k (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 104 | 64 | 40 |
Cusp forms | 88 | 64 | 24 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
315.2.k.a | $4$ | $2.515$ | \(\Q(\sqrt{-3}, \sqrt{13})\) | None | \(1\) | \(0\) | \(-4\) | \(-8\) | \(q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\) |
315.2.k.b | $24$ | $2.515$ | None | \(-1\) | \(1\) | \(-24\) | \(7\) | ||
315.2.k.c | $36$ | $2.515$ | None | \(0\) | \(-1\) | \(36\) | \(-1\) |
Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)