Defining parameters
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.n (of order \(15\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 77 \) |
Character field: | \(\Q(\zeta_{15})\) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(176\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(847, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 800 | 640 | 160 |
Cusp forms | 608 | 512 | 96 |
Eisenstein series | 192 | 128 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
847.2.n.a | $8$ | $6.763$ | \(\Q(\zeta_{15})\) | None | \(-3\) | \(1\) | \(5\) | \(5\) | \(q+(-1-\zeta_{15}^{5}+\zeta_{15}^{7})q^{2}+(-1+\zeta_{15}+\cdots)q^{3}+\cdots\) |
847.2.n.b | $8$ | $6.763$ | \(\Q(\zeta_{15})\) | None | \(2\) | \(1\) | \(-5\) | \(5\) | \(q+(1-\zeta_{15}+\zeta_{15}^{5}-\zeta_{15}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots\) |
847.2.n.c | $8$ | $6.763$ | \(\Q(\zeta_{15})\) | None | \(3\) | \(1\) | \(5\) | \(-5\) | \(q+(1+\zeta_{15}^{5}-\zeta_{15}^{7})q^{2}+(-1+\zeta_{15}+\cdots)q^{3}+\cdots\) |
847.2.n.d | $24$ | $6.763$ | None | \(0\) | \(-1\) | \(-2\) | \(2\) | ||
847.2.n.e | $24$ | $6.763$ | None | \(0\) | \(-1\) | \(-2\) | \(-2\) | ||
847.2.n.f | $24$ | $6.763$ | None | \(0\) | \(3\) | \(6\) | \(0\) | ||
847.2.n.g | $24$ | $6.763$ | None | \(0\) | \(3\) | \(6\) | \(0\) | ||
847.2.n.h | $40$ | $6.763$ | None | \(-2\) | \(1\) | \(-6\) | \(-13\) | ||
847.2.n.i | $40$ | $6.763$ | None | \(2\) | \(1\) | \(-6\) | \(13\) | ||
847.2.n.j | $40$ | $6.763$ | None | \(3\) | \(-4\) | \(4\) | \(2\) | ||
847.2.n.k | $48$ | $6.763$ | None | \(0\) | \(-2\) | \(-4\) | \(0\) | ||
847.2.n.l | $56$ | $6.763$ | None | \(0\) | \(3\) | \(4\) | \(2\) | ||
847.2.n.m | $56$ | $6.763$ | None | \(0\) | \(3\) | \(4\) | \(-2\) | ||
847.2.n.n | $112$ | $6.763$ | None | \(0\) | \(-6\) | \(-8\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(847, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(847, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)