Defining parameters
Level: | \( N \) | \(=\) | \( 333 = 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 333.i (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(114\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(333, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 160 | 64 | 96 |
Cusp forms | 144 | 60 | 84 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(333, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
333.3.i.a | $12$ | $9.074$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(6\) | \(0\) | \(6\) | \(-4\) | \(q+(1-\beta _{1}-\beta _{6})q^{2}+(1-\beta _{1}+\beta _{3}-3\beta _{6}+\cdots)q^{4}+\cdots\) |
333.3.i.b | $24$ | $9.074$ | None | \(-8\) | \(0\) | \(-20\) | \(0\) | ||
333.3.i.c | $24$ | $9.074$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(333, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(333, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)