Defining parameters
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.h (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(91, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 22 | 0 |
Cusp forms | 14 | 14 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(91, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
91.2.h.a | $2$ | $0.727$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(3\) | \(-3\) | \(4\) | \(q+q^{2}+3\zeta_{6}q^{3}-q^{4}-3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots\) |
91.2.h.b | $12$ | $0.727$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-4\) | \(1\) | \(1\) | \(-3\) | \(q+(\beta _{3}+\beta _{5}-\beta _{11})q^{2}+\beta _{11}q^{3}+(1+\cdots)q^{4}+\cdots\) |