Space of modular forms of level 560, weight 5, and Character 560.p

• Label: 560.5.p
• Level: $560$
• Weight: $5$
• Character orbit: 560.p
• Rep. character: $\chi_{560}(209,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $10$
• Sturm bound: $480$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	560.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(480\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(560, [\chi])\).

	Total	New	Old
Modular forms	396	98	298
Cusp forms	372	94	278
Eisenstein series	24	4	20

Trace form

\( 94 q + 2426 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.5.p.a	$560$	$5$	560.p	35.c	$2$	$1$	$1$	$57.887$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(-17\)	\(-25\)	\(49\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-17q^{3}-5^{2}q^{5}+7^{2}q^{7}+208q^{9}+\cdots\)
560.5.p.b	$560$	$5$	560.p	35.c	$2$	$1$	$1$	$57.887$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(17\)	\(25\)	\(-49\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+17q^{3}+5^{2}q^{5}-7^{2}q^{7}+208q^{9}+\cdots\)
560.5.p.c	$560$	$5$	560.p	35.c	$2$	$2$	$2$	$57.887$	\(\Q(\sqrt{105}) \)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(-17\)	\(50\)	\(-98\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-8-\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(9+\cdots)q^{9}+\cdots\)
560.5.p.d	$560$	$5$	560.p	35.c	$2$	$2$	$2$	$57.887$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(-10\)	\(10\)	\(-70\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-5q^{3}+(5+5\beta )q^{5}+(-35+7\beta )q^{7}+\cdots\)
560.5.p.e	$560$	$5$	560.p	35.c	$2$	$2$	$2$	$57.887$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(10\)	\(-10\)	\(70\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+5q^{3}+(-5-5\beta )q^{5}+(35+7\beta )q^{7}+\cdots\)
560.5.p.f	$560$	$5$	560.p	35.c	$2$	$2$	$2$	$57.887$	\(\Q(\sqrt{105}) \)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(17\)	\(-50\)	\(98\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(9-\beta )q^{3}-5^{2}q^{5}+7^{2}q^{7}+(26-17\beta )q^{9}+\cdots\)
560.5.p.g	$560$	$5$	560.p	35.c	$2$	$8$	$8$	$57.887$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{2}q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
560.5.p.h	$560$	$5$	560.p	35.c	$2$	$12$	$12$	$57.887$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{7})q^{5}+(\beta _{1}+\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots\)
560.5.p.i	$560$	$5$	560.p	35.c	$2$	$16$	$16$	$57.887$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}-\beta _{6}q^{5}+\beta _{8}q^{7}+(29-\beta _{10}+\cdots)q^{9}+\cdots\)
560.5.p.j	$560$	$5$	560.p	35.c	$2$	$48$	$48$	$57.887$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

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