Defining parameters
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
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: | \(74\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{37}(23, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 73 | 73 | 0 |
Cusp forms | 71 | 71 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{37}^{\mathrm{new}}(23, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
23.37.b.a | $1$ | $188.810$ | \(\Q\) | \(\Q(\sqrt{-23}) \) | \(477713\) | \(22317778\) | \(0\) | \(0\) | \(q+477713q^{2}+22317778q^{3}+159490233633q^{4}+\cdots\) |
23.37.b.b | $2$ | $188.810$ | \(\Q(\sqrt{69}) \) | \(\Q(\sqrt{-23}) \) | \(-477713\) | \(-22317778\) | \(0\) | \(0\) | \(q+(-239266-819\beta )q^{2}+(-12627057+\cdots)q^{3}+\cdots\) |
23.37.b.c | $68$ | $188.810$ | None | \(-169832\) | \(420071358\) | \(0\) | \(0\) |