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

• Label: 3762.2.g
• Level: $3762$
• Weight: $2$
• Character orbit: 3762.g
• Rep. character: $\chi_{3762}(2089,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $12$
• Sturm bound: $1440$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3762.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1440\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(13\), \(23\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	736	100	636
Cusp forms	704	100	604
Eisenstein series	32	0	32

Trace form

\( 100 q + 100 q^{4} - 4 q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3762.2.g.a	$3762$	$2$	3762.g	209.d	$2$	$2$	$2$	$30.040$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-q^{8}+(-3+\beta )q^{11}+4q^{13}+\cdots\)
3762.2.g.b	$3762$	$2$	3762.g	209.d	$2$	$2$	$2$	$30.040$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-q^{8}+(3+\beta )q^{11}-4q^{13}+\cdots\)
3762.2.g.c	$3762$	$2$	3762.g	209.d	$2$	$2$	$2$	$30.040$	\(\Q(\sqrt{-10}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+2q^{5}-\beta q^{7}-q^{8}-2q^{10}+\cdots\)
3762.2.g.d	$3762$	$2$	3762.g	209.d	$2$	$2$	$2$	$30.040$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+q^{8}+(-3+\beta )q^{11}-4q^{13}+\cdots\)
3762.2.g.e	$3762$	$2$	3762.g	209.d	$2$	$2$	$2$	$30.040$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+q^{8}+(3+\beta )q^{11}+4q^{13}+\cdots\)
3762.2.g.f	$3762$	$2$	3762.g	209.d	$2$	$2$	$2$	$30.040$	\(\Q(\sqrt{-10}) \)	None		$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+2q^{5}-\beta q^{7}+q^{8}+2q^{10}+\cdots\)
3762.2.g.g	$3762$	$2$	3762.g	209.d	$2$	$8$	$8$	$30.040$	8.0.\(\cdots\).1	None		$2$	$0$	\(-8\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{2}q^{5}+(\beta _{3}+\beta _{5})q^{7}+\cdots\)
3762.2.g.h	$3762$	$2$	3762.g	209.d	$2$	$8$	$8$	$30.040$	8.0.\(\cdots\).1	None		$2$	$0$	\(8\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{2}q^{5}+(-\beta _{3}-\beta _{5})q^{7}+\cdots\)
3762.2.g.i	$3762$	$2$	3762.g	209.d	$2$	$16$	$16$	$30.040$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{6}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots\)
3762.2.g.j	$3762$	$2$	3762.g	209.d	$2$	$16$	$16$	$30.040$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{6}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)
3762.2.g.k	$3762$	$2$	3762.g	209.d	$2$	$20$	$20$	$30.040$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-20\)	\(0\)	\(-4\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{5}q^{5}+\beta _{4}q^{7}-q^{8}+\cdots\)
3762.2.g.l	$3762$	$2$	3762.g	209.d	$2$	$20$	$20$	$30.040$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(20\)	\(0\)	\(-4\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{5}q^{5}-\beta _{4}q^{7}+q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3762, [\chi]) \cong \)