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

• Label: 3751.1.bs
• Level: $3751$
• Weight: $1$
• Character orbit: 3751.bs
• Rep. character: $\chi_{3751}(606,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $8$
• 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.bs (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{30})\)
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	104	80	24
Cusp forms	8	8	0
Eisenstein series	96	72	24

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^4 - q^5 + q^9 - 5 * q^15 - 2 * q^16 + q^20 - 5 * q^23 - 5 * q^25 + 10 * q^27 + 4 * q^31 - 6 * q^36 + 12 * q^37 - 6 * q^45 + 3 * q^47 - 5 * q^48 - q^49 + 3 * q^53 - q^59 - 5 * q^60 + 2 * q^64 - q^67 + q^71 - 10 * q^75 + 9 * q^80 + 6 * q^81 + 3 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3751.1.bs.a	$3751$	$1$	3751.bs	31.h	$30$	$8$	$1$	$1.872$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-11}) \)	None		✓	✓	✓	3751.1.bs.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(\zeta_{30}^{8}+\zeta_{30}^{11})q^{3}-\zeta_{30}^{6}q^{4}+(\zeta_{30}^{2}+\cdots)q^{5}+\cdots\)