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

• Label: 560.2.ci
• Level: $560$
• Weight: $2$
• Character orbit: 560.ci
• Rep. character: $\chi_{560}(17,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $88$
• Newform subspaces: $5$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	432	104	328
Cusp forms	336	88	248
Eisenstein series	96	16	80

Trace form

\( 88 q + 6 q^{3} - 6 q^{5} + 4 q^{7} + O(q^{10}) \)

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.ci.a	$560$	$2$	560.ci	35.k	$12$	$4$	$1$	$4.472$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
560.2.ci.b	$560$	$2$	560.ci	35.k	$12$	$4$	$1$	$4.472$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(4\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{3})q^{3}+(\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
560.2.ci.c	$560$	$2$	560.ci	35.k	$12$	$16$	$4$	$4.472$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{3}-\beta _{7}-\beta _{15})q^{3}+(-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
560.2.ci.d	$560$	$2$	560.ci	35.k	$12$	$16$	$4$	$4.472$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2\beta _{1}-\beta _{2}-\beta _{10}+\beta _{11}-\beta _{13}+\cdots)q^{3}+\cdots\)
560.2.ci.e	$560$	$2$	560.ci	35.k	$12$	$48$	$12$	$4.472$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{12}]$

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

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