Defining parameters
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bw (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(560, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 52 | 164 |
Cusp forms | 168 | 44 | 124 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(560, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
560.2.bw.a | $4$ | $4.472$ | \(\Q(\sqrt{-3}, \sqrt{-19})\) | None | \(0\) | \(-6\) | \(-2\) | \(-3\) | \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\) |
560.2.bw.b | $4$ | $4.472$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots\) |
560.2.bw.c | $4$ | $4.472$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+3\zeta_{12}q^{3}+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\) |
560.2.bw.d | $4$ | $4.472$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots\) |
560.2.bw.e | $4$ | $4.472$ | \(\Q(\sqrt{-3}, \sqrt{-19})\) | None | \(0\) | \(6\) | \(1\) | \(3\) | \(q+(1+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots\) |
560.2.bw.f | $24$ | $4.472$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(560, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)