Space of modular forms of level 3736, weight 1, and Character 3736.l

• Label: 3736.1.l
• Level: $3736$
• Weight: $1$
• Character orbit: 3736.l
• Rep. character: $\chi_{3736}(3,\cdot)$
• Character field: $\Q(\zeta_{466})$
• Dimension: $232$
• Newform subspaces: $1$
• Sturm bound: $468$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3736 = 2^{3} \cdot 467 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3736.l (of order \(466\) and degree \(232\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3736 \)
Character field:			\(\Q(\zeta_{466})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(468\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3736, [\chi])\).

	Total	New	Old
Modular forms	696	696	0
Cusp forms	232	232	0
Eisenstein series	464	464	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	232	0	0	0

Trace form

\( 232 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3736, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3736.1.l.a	$3736$	$1$	3736.l	3736.l	$466$	$232$	$1$	$1.865$	\(\Q(\zeta_{466})\)	$D_{233}$	\(\Q(\sqrt{-2}) \)	None		✓	3736.1.l.a	$4$	$0$	\(-1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{466}^{229}q^{2}+(\zeta_{466}^{180}-\zeta_{466}^{181})q^{3}+\cdots\)