Defining parameters
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(351, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 24 | 72 |
Cusp forms | 72 | 24 | 48 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(351, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
351.2.e.a | $2$ | $2.803$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(4\) | \(-2\) | \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots\) |
351.2.e.b | $10$ | $2.803$ | 10.0.\(\cdots\).1 | None | \(2\) | \(0\) | \(1\) | \(2\) | \(q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{9})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\) |
351.2.e.c | $12$ | $2.803$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-2\) | \(0\) | \(-3\) | \(0\) | \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(351, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(351, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)