Defining parameters
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 136 | 20 | 116 |
Cusp forms | 88 | 20 | 68 |
Eisenstein series | 48 | 0 | 48 |
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.f.a | $2$ | $6.260$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-q^{3}+\zeta_{6}q^{5}-2q^{9}-\zeta_{6}q^{11}-\zeta_{6}q^{15}+\cdots\) |
784.2.f.b | $2$ | $6.260$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+q^{3}+\zeta_{6}q^{5}-2q^{9}+\zeta_{6}q^{11}+\zeta_{6}q^{15}+\cdots\) |
784.2.f.c | $4$ | $6.260$ | 4.0.2048.2 | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{5}-3q^{9}+(\beta _{1}+\beta _{2})q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\) |
784.2.f.d | $4$ | $6.260$ | \(\Q(\sqrt{-3}, \sqrt{7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+4q^{9}+\beta _{3}q^{11}+\cdots\) |
784.2.f.e | $8$ | $6.260$ | 8.0.339738624.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(3-3\beta _{1})q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(784, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(784, [\chi]) \cong \)