Defining parameters
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(23, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9 | 9 | 0 |
Cusp forms | 7 | 7 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(23, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
23.5.b.a | $3$ | $2.378$ | 3.3.621.1 | \(\Q(\sqrt{-23}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\) |
23.5.b.b | $4$ | $2.378$ | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) | None | \(-8\) | \(-12\) | \(0\) | \(0\) | \(q+(-2-\beta _{3})q^{2}+(-3+3\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\) |