Defining parameters
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(15, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 18 | 0 |
Cusp forms | 14 | 14 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(15, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
15.9.d.a | $1$ | $6.111$ | \(\Q\) | \(\Q(\sqrt{-15}) \) | \(-17\) | \(-81\) | \(-625\) | \(0\) | \(q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots\) |
15.9.d.b | $1$ | $6.111$ | \(\Q\) | \(\Q(\sqrt{-15}) \) | \(17\) | \(81\) | \(625\) | \(0\) | \(q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots\) |
15.9.d.c | $12$ | $6.111$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots\) |