Defining parameters
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(26\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{13}(23, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 25 | 25 | 0 |
Cusp forms | 23 | 23 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{13}^{\mathrm{new}}(23, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
23.13.b.a | $1$ | $21.022$ | \(\Q\) | \(\Q(\sqrt{-23}) \) | \(-79\) | \(-14\) | \(0\) | \(0\) | \(q-79q^{2}-14q^{3}+2145q^{4}+1106q^{6}+\cdots\) |
23.13.b.b | $2$ | $21.022$ | \(\Q(\sqrt{69}) \) | \(\Q(\sqrt{-23}) \) | \(79\) | \(14\) | \(0\) | \(0\) | \(q+(29+21\beta )q^{2}+(159-304\beta )q^{3}+\cdots\) |
23.13.b.c | $20$ | $21.022$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(88\) | \(318\) | \(0\) | \(0\) | \(q+(4+\beta _{1})q^{2}+(15+2\beta _{1}-\beta _{3})q^{3}+\cdots\) |