Space of modular forms of level 1170, weight 2, and Character 1170.v

• Label: 1170.2.v
• Level: $1170$
• Weight: $2$
• Character orbit: 1170.v
• Rep. character: $\chi_{1170}(233,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $504$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(504\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

	Total	New	Old
Modular forms	536	56	480
Cusp forms	472	56	416
Eisenstein series	64	0	64

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1170.2.v.a	$1170$	$2$	1170.v	195.s	$4$	$4$	$2$	$9.342$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
1170.2.v.b	$1170$	$2$	1170.v	195.s	$4$	$4$	$2$	$9.342$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
1170.2.v.c	$1170$	$2$	1170.v	195.s	$4$	$24$	$12$	$9.342$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1170.2.v.d	$1170$	$2$	1170.v	195.s	$4$	$24$	$12$	$9.342$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \)