Defining parameters
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.p (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 44 | 68 |
Cusp forms | 80 | 36 | 44 |
Eisenstein series | 32 | 8 | 24 |
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.p.a | $4$ | $2.515$ | \(\Q(i, \sqrt{10})\) | None | \(0\) | \(0\) | \(-8\) | \(4\) | \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(-2+\beta _{2})q^{5}+\cdots\) |
315.2.p.b | $4$ | $2.515$ | \(\Q(i, \sqrt{10})\) | None | \(0\) | \(0\) | \(8\) | \(4\) | \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(2-\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\) |
315.2.p.c | $4$ | $2.515$ | \(\Q(i, \sqrt{10})\) | None | \(4\) | \(0\) | \(0\) | \(4\) | \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\) |
315.2.p.d | $8$ | $2.515$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\beta _{1}q^{2}-\beta _{3}q^{4}+\beta _{5}q^{5}+(-1-\beta _{3}+\cdots)q^{7}+\cdots\) |
315.2.p.e | $16$ | $2.515$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\beta _{2}q^{2}+(-\beta _{6}-\beta _{7}+\beta _{13})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)