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

• Label: 961.1.h
• Level: $961$
• Weight: $1$
• Character orbit: 961.h
• Rep. character: $\chi_{961}(115,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $82$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	961.h (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{30})\)
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	136	120	16
Cusp forms	8	8	0
Eisenstein series	128	112	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

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

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.h.a	$961$	$1$	961.h	31.h	$30$	$8$	$1$	$0.480$	\(\Q(\zeta_{15})\)	$D_{3}$	\(\Q(\sqrt{-31}) \)	None			✓	✓	31.1.b.a	$16$	$0$	\(2\)	\(0\)	\(4\)	\(-1\)	$1$		\(q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{10}q^{5}+\zeta_{30}^{11}q^{7}+\cdots\)