Defining parameters
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(76, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 18 | 4 |
Cusp forms | 18 | 18 | 0 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(76, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
76.3.b.a | $4$ | $2.071$ | \(\Q(\sqrt{-3}, \sqrt{-19})\) | None | \(-4\) | \(0\) | \(-4\) | \(0\) | \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\) |
76.3.b.b | $14$ | $2.071$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots\) |