Defining parameters
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(46\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(91, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38 | 38 | 0 |
Cusp forms | 34 | 34 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(91, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
91.5.b.a | $1$ | $9.407$ | \(\Q\) | \(\Q(\sqrt{-91}) \) | \(0\) | \(0\) | \(-41\) | \(49\) | \(q+2^{4}q^{4}-41q^{5}+7^{2}q^{7}+3^{4}q^{9}+\cdots\) |
91.5.b.b | $1$ | $9.407$ | \(\Q\) | \(\Q(\sqrt{-91}) \) | \(0\) | \(0\) | \(41\) | \(-49\) | \(q+2^{4}q^{4}+41q^{5}-7^{2}q^{7}+3^{4}q^{9}+\cdots\) |
91.5.b.c | $32$ | $9.407$ | None | \(0\) | \(0\) | \(0\) | \(0\) |