Defining parameters
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.u (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
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.u.a | $2$ | $0.727$ | \(\Q(\sqrt{-3}) \) | None | \(-3\) | \(-2\) | \(-3\) | \(-5\) | \(q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots\) |
91.2.u.b | $12$ | $0.727$ | 12.0.\(\cdots\).1 | None | \(0\) | \(6\) | \(3\) | \(3\) | \(q-\beta _{10}q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{8})q^{3}+\cdots\) |