Defining parameters
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(77, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 12 | 8 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 8 | 0 | 8 |
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.e.a | $6$ | $0.615$ | \(\Q(\zeta_{18})\) | None | \(0\) | \(-3\) | \(-6\) | \(0\) | \(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\) |
77.2.e.b | $6$ | $0.615$ | 6.0.1783323.2 | None | \(0\) | \(1\) | \(2\) | \(2\) | \(q+(-\beta _{3}+\beta _{5})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\) |