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

• Label: 3751.1.n
• Level: $3751$
• Weight: $1$
• Character orbit: 3751.n
• Rep. character: $\chi_{3751}(243,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• 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.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{6})\)
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	26	20	6
Cusp forms	2	2	0
Eisenstein series	24	18	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

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

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.n.a	$3751$	$1$	3751.n	31.e	$6$	$2$	$1$	$1.872$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+q^{16}+\zeta_{6}^{2}q^{20}+\cdots\)