Space of modular forms of level 560, weight 2, and Character 560.q

• Label: 560.2.q
• Level: $560$
• Weight: $2$
• Character orbit: 560.q
• Rep. character: $\chi_{560}(81,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $12$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(560, [\chi])\).

	Total	New	Old
Modular forms	216	32	184
Cusp forms	168	32	136
Eisenstein series	48	0	48

Trace form

32 * q - 4 * q^3 - 4 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^19 + 4 * q^21 + 4 * q^23 - 16 * q^25 + 32 * q^27 + 24 * q^29 + 16 * q^31 - 8 * q^37 - 8 * q^39 + 8 * q^41 - 40 * q^43 - 4 * q^45 + 20 * q^47 - 16 * q^49 - 32 * q^51 - 16 * q^53 - 16 * q^55 - 16 * q^57 - 8 * q^59 - 8 * q^61 - 56 * q^63 - 4 * q^65 + 24 * q^67 + 16 * q^69 + 32 * q^71 + 8 * q^73 - 4 * q^75 - 24 * q^77 + 24 * q^79 - 12 * q^81 + 112 * q^83 + 60 * q^87 + 12 * q^89 + 24 * q^91 - 16 * q^93 + 32 * q^97 - 88 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.2.q.a	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					140.2.i.b	$2$	$1$	\(0\)	\(-3\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.b	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					70.2.e.d	$2$	$0$	\(0\)	\(-2\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
560.2.q.c	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					280.2.q.c	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
560.2.q.d	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					70.2.e.b	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
560.2.q.e	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					280.2.q.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.f	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					140.2.i.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
560.2.q.g	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					70.2.e.c	$2$	$0$	\(0\)	\(1\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
560.2.q.h	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					280.2.q.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
560.2.q.i	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	\(\Q(\sqrt{-3}) \)	None					70.2.e.a	$2$	$0$	\(0\)	\(3\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.j	$560$	$2$	560.q	7.c	$3$	$4$	$2$	$4.472$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					280.2.q.d	$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.k	$560$	$2$	560.q	7.c	$3$	$4$	$2$	$4.472$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					35.2.e.a	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.l	$560$	$2$	560.q	7.c	$3$	$6$	$3$	$4.472$	6.0.11337408.1	None			✓		280.2.q.e	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)