Defining parameters
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.h (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 33 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(12\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(33, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 40 | 0 |
Cusp forms | 24 | 24 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(33, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
33.3.h.a | $8$ | $0.899$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(4\) | \(0\) | \(-4\) | \(q+\zeta_{20}q^{2}+(2+2\zeta_{20}-2\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{3}+\cdots\) |
33.3.h.b | $16$ | $0.899$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-10\) | \(0\) | \(6\) | \(q+\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\) |