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

• Label: 3700.1.j
• Level: $3700$
• Weight: $1$
• Character orbit: 3700.j
• Rep. character: $\chi_{3700}(401,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $570$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3700.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(570\)
Trace bound:			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	48	6	42
Cusp forms	12	6	6
Eisenstein series	36	0	36

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	6	0

Trace form

\( 6 q + 2 q^{7} + 2 q^{17} + 2 q^{19} + 2 q^{23} - 2 q^{29} + 4 q^{31} - 2 q^{33} - 2 q^{47} + 2 q^{51} - 2 q^{53} + 2 q^{57} - 4 q^{61} + 2 q^{69} - 2 q^{71} - 6 q^{79} - 6 q^{81} + 2 q^{83} + 2 q^{87} + 2 q^{89}+O(q^{100}) \)

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.j.a	$3700$	$1$	3700.j	37.d	$4$	$2$	$1$	$1.847$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None					740.1.t.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-i q^{3}-q^{7}-i q^{11}+i q^{21}-i q^{27}+\cdots\)
3700.1.j.b	$3700$	$1$	3700.j	37.d	$4$	$2$	$1$	$1.847$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None					740.1.t.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+i q^{3}+q^{7}-i q^{11}+i q^{21}+i q^{27}+\cdots\)
3700.1.j.c	$3700$	$1$	3700.j	37.d	$4$	$2$	$1$	$1.847$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None					148.1.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-i q^{3}+q^{7}-i q^{11}+(i+1)q^{17}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3700, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)