Space of modular forms of level 560, weight 4, and Character 560.g

• Label: 560.4.g
• Level: $560$
• Weight: $4$
• Character orbit: 560.g
• Rep. character: $\chi_{560}(449,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	560.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(560, [\chi])\).

	Total	New	Old
Modular forms	300	54	246
Cusp forms	276	54	222
Eisenstein series	24	0	24

Trace form

\( 54 q - 2 q^{5} - 486 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(560, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.4.g.a	$560$	$4$	560.g	5.b	$2$	$2$	$2$	$33.041$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{3}+(-10+5i)q^{5}-7iq^{7}+\cdots\)
560.4.g.b	$560$	$4$	560.g	5.b	$2$	$2$	$2$	$33.041$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+7iq^{3}+(-2-11i)q^{5}+7iq^{7}+\cdots\)
560.4.g.c	$560$	$4$	560.g	5.b	$2$	$2$	$2$	$33.041$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+7iq^{3}+(10-5i)q^{5}+7iq^{7}-22q^{9}+\cdots\)
560.4.g.d	$560$	$4$	560.g	5.b	$2$	$4$	$4$	$33.041$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{5}-\beta _{1}q^{7}+\cdots\)
560.4.g.e	$560$	$4$	560.g	5.b	$2$	$6$	$6$	$33.041$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{3}-\beta _{5})q^{3}+(-3+\beta _{2}+3\beta _{3}+\cdots)q^{5}+\cdots\)
560.4.g.f	$560$	$4$	560.g	5.b	$2$	$10$	$10$	$33.041$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{7}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(1+\beta _{6})q^{5}+\beta _{4}q^{7}+(-5+\cdots)q^{9}+\cdots\)
560.4.g.g	$560$	$4$	560.g	5.b	$2$	$12$	$12$	$33.041$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}+(-1-\beta _{2}+\beta _{4})q^{5}-7\beta _{2}q^{7}+\cdots\)
560.4.g.h	$560$	$4$	560.g	5.b	$2$	$16$	$16$	$33.041$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(22\)	\(0\)	$2^{12}\cdot 5^{2}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(1+\beta _{3}-\beta _{4})q^{5}-7\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)