Defining parameters
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.e (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(33, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 24 | 32 |
Cusp forms | 40 | 24 | 16 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(33, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
33.4.e.a | $4$ | $1.947$ | \(\Q(\zeta_{10})\) | None | \(10\) | \(-3\) | \(-21\) | \(37\) | \(q+(4-2\zeta_{10}+4\zeta_{10}^{2})q^{2}-3\zeta_{10}^{3}q^{3}+\cdots\) |
33.4.e.b | $8$ | $1.947$ | 8.0.682515625.5 | None | \(-6\) | \(-6\) | \(9\) | \(3\) | \(q+(-\beta _{1}-2\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+\cdots\) |
33.4.e.c | $12$ | $1.947$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(9\) | \(28\) | \(12\) | \(q+(-1-\beta _{3}-\beta _{5}-\beta _{6}-\beta _{7})q^{2}-3\beta _{6}q^{3}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(33, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)