Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(108\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(99, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 100 | 41 | 59 |
Cusp forms | 92 | 39 | 53 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(99, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
99.9.c.a | $1$ | $40.330$ | \(\Q\) | \(\Q(\sqrt{-11}) \) | \(0\) | \(0\) | \(-1151\) | \(0\) | \(q+2^{8}q^{4}-1151q^{5}-11^{4}q^{11}+2^{16}q^{16}+\cdots\) |
99.9.c.b | $6$ | $40.330$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(0\) | \(0\) | \(448\) | \(0\) | \(q+\beta _{1}q^{2}+(-203+3\beta _{3}-2\beta _{4})q^{4}+\cdots\) |
99.9.c.c | $16$ | $40.330$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-151-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\) |
99.9.c.d | $16$ | $40.330$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(1116\) | \(0\) | \(q+\beta _{1}q^{2}+(-105+\beta _{2})q^{4}+(70-\beta _{4}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{9}^{\mathrm{old}}(99, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)