Defining parameters
Level: | \( N \) | \(=\) | \( 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 61.e (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 61 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(10\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(61, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 20 | 0 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(61, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
61.2.e.a | $12$ | $0.487$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-2\) | \(-1\) | \(-5\) | \(-10\) | \(q-\beta _{5}q^{2}+(\beta _{8}+\beta _{10})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\) |