Space of modular forms of level 961, weight 1, and Character 961.f

• Label: 961.1.f
• Level: $961$
• Weight: $1$
• Character orbit: 961.f
• Rep. character: $\chi_{961}(333,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $82$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	961.f (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(82\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(961, [\chi])\).

	Total	New	Old
Modular forms	68	60	8
Cusp forms	4	4	0
Eisenstein series	64	56	8

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + q^{2} - 4 q^{5} + q^{7} - q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(961, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
961.1.f.a	$961$	$1$	961.f	31.f	$10$	$4$	$1$	$0.480$	\(\Q(\zeta_{10})\)	$D_{3}$	\(\Q(\sqrt{-31}) \)	None			✓	✓	31.1.b.a	$8$	$0$	\(1\)	\(0\)	\(-4\)	\(1\)	$1$		\(q+\zeta_{10}^{3}q^{2}-q^{5}+\zeta_{10}q^{7}+\zeta_{10}^{4}q^{8}+\cdots\)