Defining parameters
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(45\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{15}(22, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 14 | 30 |
Cusp forms | 40 | 14 | 26 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{15}^{\mathrm{new}}(22, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
22.15.b.a | $14$ | $27.352$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(0\) | \(4394\) | \(69758\) | \(0\) | \(q+\beta _{2}q^{2}+(314+\beta _{1})q^{3}-2^{13}q^{4}+\cdots\) |
Decomposition of \(S_{15}^{\mathrm{old}}(22, [\chi])\) into lower level spaces
\( S_{15}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)