Defining parameters
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(56, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 4 | 20 |
Cusp forms | 8 | 4 | 4 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(56, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
56.2.i.a | $2$ | $0.447$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-3\) | \(1\) | \(4\) | \(q-3\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\) |
56.2.i.b | $2$ | $0.447$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(1\) | \(-4\) | \(q+\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(56, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(56, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)