Defining parameters
Level: | \( N \) | \(=\) | \( 234 = 2 \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 234.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(234, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 50 | 4 | 46 |
Cusp forms | 34 | 4 | 30 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(234, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
234.2.b.a | $2$ | $1.868$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}-q^{4}+2 i q^{5}+2 i q^{7}-i q^{8}+\cdots\) |
234.2.b.b | $2$ | $1.868$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}-q^{4}-3 i q^{5}-3 i q^{7}-i q^{8}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(234, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)