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

• Label: 560.2.cc
• Level: $560$
• Weight: $2$
• Character orbit: 560.cc
• Rep. character: $\chi_{560}(159,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $192$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(192\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(11\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	216	48	168
Cusp forms	168	48	120
Eisenstein series	48	0	48

Trace form

\( 48 q + 24 q^{9} + 12 q^{21} + 12 q^{25} + 24 q^{29} - 24 q^{65} - 84 q^{81} + 24 q^{85} + 36 q^{89}+O(q^{100}) \)

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.cc.a	$560$	$2$	560.cc	140.s	$6$	$4$	$2$	$4.472$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			560.2.cc.a	$2$	$1$	\(0\)	\(-3\)	\(-6\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{3})q^{3}+(-2+\beta _{1}-\beta _{3})q^{5}+\cdots\)
560.2.cc.b	$560$	$2$	560.cc	140.s	$6$	$4$	$2$	$4.472$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			560.2.cc.a	$2$	$0$	\(0\)	\(-3\)	\(-3\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{3})q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-3+\cdots)q^{7}+\cdots\)
560.2.cc.c	$560$	$2$	560.cc	140.s	$6$	$4$	$2$	$4.472$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			560.2.cc.a	$2$	$0$	\(0\)	\(3\)	\(-6\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1})q^{3}+(-2+\beta _{1}-\beta _{3})q^{5}+\cdots\)
560.2.cc.d	$560$	$2$	560.cc	140.s	$6$	$4$	$2$	$4.472$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			560.2.cc.a	$2$	$0$	\(0\)	\(3\)	\(-3\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
560.2.cc.e	$560$	$2$	560.cc	140.s	$6$	$8$	$4$	$4.472$	8.0.1731891456.1	None		✓			560.2.cc.e	$8$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{7})q^{3}+(-1-\beta _{2}-\beta _{5}+\cdots)q^{5}+\cdots\)
560.2.cc.f	$560$	$2$	560.cc	140.s	$6$	$8$	$4$	$4.472$	8.0.3317760000.8	\(\Q(\sqrt{-5}) \)		✓			560.2.cc.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$7$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\beta _{2}-\beta _{5}-\beta _{7})q^{3}-\beta _{1}q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots\)
560.2.cc.g	$560$	$2$	560.cc	140.s	$6$	$8$	$4$	$4.472$	8.0.3317760000.3	None		✓			560.2.cc.g	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{4}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.cc.h	$560$	$2$	560.cc	140.s	$6$	$8$	$4$	$4.472$	8.0.3317760000.3	None		✓			560.2.cc.g	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{4}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)