Defining parameters
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.f (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(216\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(891, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 480 | 208 | 272 |
Cusp forms | 384 | 176 | 208 |
Eisenstein series | 96 | 32 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(891, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
891.2.f.a | $4$ | $7.115$ | \(\Q(\zeta_{10})\) | None | \(-4\) | \(0\) | \(6\) | \(1\) | \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\) |
891.2.f.b | $4$ | $7.115$ | \(\Q(\zeta_{10})\) | None | \(4\) | \(0\) | \(-6\) | \(1\) | \(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots\) |
891.2.f.c | $24$ | $7.115$ | None | \(-2\) | \(0\) | \(4\) | \(7\) | ||
891.2.f.d | $24$ | $7.115$ | None | \(2\) | \(0\) | \(-4\) | \(7\) | ||
891.2.f.e | $36$ | $7.115$ | None | \(-1\) | \(0\) | \(-8\) | \(2\) | ||
891.2.f.f | $36$ | $7.115$ | None | \(1\) | \(0\) | \(8\) | \(2\) | ||
891.2.f.g | $48$ | $7.115$ | None | \(0\) | \(0\) | \(0\) | \(-14\) |
Decomposition of \(S_{2}^{\mathrm{old}}(891, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(891, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 2}\)