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

• Label: 3700.1.dd
• Level: $3700$
• Weight: $1$
• Character orbit: 3700.dd
• Rep. character: $\chi_{3700}(143,\cdot)$
• Character field: $\Q(\zeta_{36})$
• 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.dd (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 740 \)
Character field:			\(\Q(\zeta_{36})\)
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	180	60	120
Cusp forms	36	12	24
Eisenstein series	144	48	96

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

\( 12 q - 6 q^{8} - 6 q^{41} - 12 q^{61} - 6 q^{64} + 6 q^{73} - 6 q^{74}+O(q^{100}) \)

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.dd.a	$3700$	$1$	3700.dd	740.bb	$36$	$12$	$1$	$1.847$	\(\Q(\zeta_{36})\)	$D_{36}$	\(\Q(\sqrt{-1}) \)	None			✓	✓	740.1.bw.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{36}^{16}q^{2}-\zeta_{36}^{14}q^{4}+\zeta_{36}^{12}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3700, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3700, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(740, [\chi])\)\(^{\oplus 2}\)