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

• Label: 560.2.e
• Level: $560$
• Weight: $2$
• Character orbit: 560.e
• Rep. character: $\chi_{560}(559,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	108	24	84
Cusp forms	84	24	60
Eisenstein series	24	0	24

Trace form

\( 24 q - 24 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.2.e.a	$560$	$2$	560.e	140.c	$2$	$4$	$4$	$4.472$	\(\Q(\sqrt{5}, \sqrt{-7})\)	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-4q^{9}+\beta _{3}q^{11}+\cdots\)
560.2.e.b	$560$	$2$	560.e	140.c	$2$	$4$	$4$	$4.472$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}+q^{9}+\cdots\)
560.2.e.c	$560$	$2$	560.e	140.c	$2$	$8$	$8$	$4.472$	8.0.121550625.1	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{6}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots\)
560.2.e.d	$560$	$2$	560.e	140.c	$2$	$8$	$8$	$4.472$	8.0.\(\cdots\).5	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+2\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(560, [\chi]) \cong \)