Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 65 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(21\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{65}(3, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 22 | 0 |
Cusp forms | 20 | 20 | 0 |
Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{65}^{\mathrm{new}}(3, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3.65.b.a | $20$ | $77.821$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(-14\!\cdots\!92\) | \(0\) | \(68\!\cdots\!76\) | \(q+\beta _{1}q^{2}+(-71037898477915+13312\beta _{1}+\cdots)q^{3}+\cdots\) |