Defining parameters
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{33}(4, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 17 | 17 | 0 |
Cusp forms | 15 | 15 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{33}^{\mathrm{new}}(4, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
4.33.b.a | $1$ | $25.947$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(65536\) | \(0\) | \(-196496109694\) | \(0\) | \(q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots\) |
4.33.b.b | $14$ | $25.947$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(-23780\) | \(0\) | \(138121491740\) | \(0\) | \(q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\) |