Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 33 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(99, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 4 | 12 |
Cusp forms | 8 | 4 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(99, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
99.2.d.a | $4$ | $0.791$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{8}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(99, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(99, [\chi]) \cong \)