Defining parameters
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(304, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 86 | 18 | 68 |
Cusp forms | 74 | 18 | 56 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(304, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
304.3.d.a | $6$ | $8.283$ | 6.0.210056875.1 | None | \(0\) | \(0\) | \(14\) | \(0\) | \(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\) |
304.3.d.b | $12$ | $8.283$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(304, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)