Defining parameters
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 112 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 480 | 336 | 144 |
Cusp forms | 416 | 304 | 112 |
Eisenstein series | 64 | 32 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(784, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
784.2.w.a | $4$ | $6.260$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(-6\) | \(-6\) | \(0\) | \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\) |
784.2.w.b | $4$ | $6.260$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(6\) | \(6\) | \(0\) | \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\cdots)q^{3}+\cdots\) |
784.2.w.c | $8$ | $6.260$ | 8.0.49787136.1 | \(\Q(\sqrt{-7}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots\) |
784.2.w.d | $8$ | $6.260$ | \(\Q(\zeta_{24})\) | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+(1+\zeta_{24}-\zeta_{24}^{2})q^{2}+(2\zeta_{24}-2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\) |
784.2.w.e | $32$ | $6.260$ | None | \(4\) | \(0\) | \(0\) | \(0\) | ||
784.2.w.f | $56$ | $6.260$ | None | \(-2\) | \(6\) | \(6\) | \(0\) | ||
784.2.w.g | $192$ | $6.260$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(784, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)