Defining parameters
Level: | \( N \) | \(=\) | \( 96 = 2^{5} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 96.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(96, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 136 | 16 | 120 |
Cusp forms | 120 | 16 | 104 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(96, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
96.9.g.a | $8$ | $39.108$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(-1232\) | \(0\) | \(q+\beta _{1}q^{3}+(-154+\beta _{6})q^{5}+(17\beta _{1}+\cdots)q^{7}+\cdots\) |
96.9.g.b | $8$ | $39.108$ | 8.0.3468738816.6 | None | \(0\) | \(0\) | \(560\) | \(0\) | \(q+\beta _{2}q^{3}+(70+\beta _{4})q^{5}+(-7\beta _{1}-7\beta _{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{9}^{\mathrm{old}}(96, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)