Space of modular forms of level 3762, weight 2, and Character 3762.d

• Label: 3762.2.d
• Level: $3762$
• Weight: $2$
• Character orbit: 3762.d
• Rep. character: $\chi_{3762}(683,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $1440$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3762.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1440\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3762, [\chi])\).

	Total	New	Old
Modular forms	736	72	664
Cusp forms	704	72	632
Eisenstein series	32	0	32

Trace form

\( 72 q + 72 q^{4} - 16 q^{7} + 72 q^{16} - 24 q^{19} - 104 q^{25} - 16 q^{28} + 48 q^{43} + 136 q^{49} + 16 q^{58} - 48 q^{61} + 72 q^{64} + 80 q^{73} - 24 q^{76} + 48 q^{82} - 64 q^{85}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3762, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3762.2.d.a	$3762$	$2$	3762.d	57.d	$2$	$36$	$36$	$30.040$		None		✓			3762.2.d.a	$2$	$0$	\(-36\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$
3762.2.d.b	$3762$	$2$	3762.d	57.d	$2$	$36$	$36$	$30.040$		None		✓			3762.2.d.a	$2$	$0$	\(36\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3762, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3762, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(627, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1254, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1881, [\chi])\)\(^{\oplus 2}\)