Defining parameters
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.l (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 77 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(77, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 40 | 0 |
Cusp forms | 24 | 24 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(77, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
77.2.l.a | $8$ | $0.615$ | 8.0.37515625.1 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(1-\beta _{1}+\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6})q^{2}+\cdots\) |
77.2.l.b | $16$ | $0.615$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(-10\) | \(0\) | \(0\) | \(-10\) | \(q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\) |