Defining parameters
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.e (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(33, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 40 | 48 |
Cusp forms | 72 | 40 | 32 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(33, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
33.6.e.a | $20$ | $5.293$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-2\) | \(-45\) | \(-33\) | \(-335\) | \(q+(-\beta _{1}+\beta _{7})q^{2}-9\beta _{9}q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\) |
33.6.e.b | $20$ | $5.293$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(6\) | \(45\) | \(-11\) | \(-139\) | \(q+(-\beta _{5}+\beta _{6})q^{2}+9\beta _{7}q^{3}+(-12+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(33, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)