Space of modular forms of level 3700, weight 1, and Character 3700.cb

• Label: 3700.1.cb
• Level: $3700$
• Weight: $1$
• Character orbit: 3700.cb
• Rep. character: $\chi_{3700}(599,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $570$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3700.cb (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 740 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(570\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3700, [\chi])\).

	Total	New	Old
Modular forms	84	36	48
Cusp forms	12	12	0
Eisenstein series	72	24	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3700, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3700.1.cb.a	$3700$	$1$	3700.cb	740.as	$18$	$12$	$2$	$1.847$	\(\Q(\zeta_{36})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None			✓	✓	148.1.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{36}^{17}q^{2}-\zeta_{36}^{16}q^{4}-\zeta_{36}^{15}q^{8}+\cdots\)