Space of modular forms of level 3997, weight 1, and Character 3997.ce

• Label: 3997.1.ce
• Level: $3997$
• Weight: $1$
• Character orbit: 3997.ce
• Rep. character: $\chi_{3997}(258,\cdot)$
• Character field: $\Q(\zeta_{114})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $381$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3997 = 7 \cdot 571 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3997.ce (of order \(114\) and degree \(36\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3997 \)
Character field:			\(\Q(\zeta_{114})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(381\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3997, [\chi])\).

	Total	New	Old
Modular forms	108	108	0
Cusp forms	36	36	0
Eisenstein series	72	72	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	36	0	0	0

Trace form

\( 36 q - q^{2} - 2 q^{7} - 21 q^{8} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3997, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3997.1.ce.a	$3997$	$1$	3997.ce	3997.be	$114$	$36$	$1$	$1.995$	\(\Q(\zeta_{57})\)	$D_{57}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+(\zeta_{114}^{24}-\zeta_{114}^{47})q^{2}+(\zeta_{114}^{14}-\zeta_{114}^{37}+\cdots)q^{4}+\cdots\)