Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.k (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(99, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 44 | 68 |
Cusp forms | 80 | 36 | 44 |
Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(99, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
99.3.k.a | $4$ | $2.698$ | \(\Q(\zeta_{10})\) | None | \(5\) | \(0\) | \(4\) | \(10\) | \(q+(2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-4+\cdots)q^{4}+\cdots\) |
99.3.k.b | $16$ | $2.698$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(30\) | \(q+\beta _{5}q^{2}+(-1-3\beta _{2}-\beta _{4}-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\) |
99.3.k.c | $16$ | $2.698$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(4\) | \(-30\) | \(q+(-1-\beta _{2}+\beta _{5}-\beta _{7}-\beta _{8})q^{2}+(-\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(99, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)