Space of modular forms of level 3751, weight 1, and Character 3751.s

• Label: 3751.1.s
• Level: $3751$
• Weight: $1$
• Character orbit: 3751.s
• Rep. character: $\chi_{3751}(511,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $352$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3751.s (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 341 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(352\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3751, [\chi])\).

	Total	New	Old
Modular forms	52	36	16
Cusp forms	4	4	0
Eisenstein series	48	32	16

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

\( 4 q + 5 q^{3} + q^{4} - 2 q^{5} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3751, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3751.1.s.a	$3751$	$1$	3751.s	341.s	$10$	$4$	$1$	$1.872$	\(\Q(\zeta_{10})\)	$D_{10}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(5\)	\(-2\)	\(0\)	$1$		\(q+(1-\zeta_{10}^{2})q^{3}+\zeta_{10}q^{4}+(-\zeta_{10}+\cdots)q^{5}+\cdots\)