Defining parameters
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(108\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(230, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 16 | 60 |
Cusp forms | 68 | 16 | 52 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(230, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
230.3.d.a | $16$ | $6.267$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{6}q^{2}-\beta _{5}q^{3}+2q^{4}+\beta _{2}q^{5}-\beta _{10}q^{6}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(230, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)