Defining parameters
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.ci (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(560, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 432 | 104 | 328 |
Cusp forms | 336 | 88 | 248 |
Eisenstein series | 96 | 16 | 80 |
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.ci.a | $4$ | $4.472$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(2\) | \(-4\) | \(0\) | \(q+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\) |
560.2.ci.b | $4$ | $4.472$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(4\) | \(4\) | \(10\) | \(q+(1+\zeta_{12}-\zeta_{12}^{3})q^{3}+(\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\) |
560.2.ci.c | $16$ | $4.472$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(-12\) | \(-8\) | \(q+(\beta _{3}-\beta _{7}-\beta _{15})q^{3}+(-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\) |
560.2.ci.d | $16$ | $4.472$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(6\) | \(-2\) | \(q+(-2\beta _{1}-\beta _{2}-\beta _{10}+\beta _{11}-\beta _{13}+\cdots)q^{3}+\cdots\) |
560.2.ci.e | $48$ | $4.472$ | None | \(0\) | \(0\) | \(0\) | \(4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(560, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)