Space of modular forms of level 3744, weight 2, and Character 3744.g

• Label: 3744.2.g
• Level: $3744$
• Weight: $2$
• Character orbit: 3744.g
• Rep. character: $\chi_{3744}(1873,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $6$
• Sturm bound: $1344$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3744.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1344\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

	Total	New	Old
Modular forms	704	60	644
Cusp forms	640	60	580
Eisenstein series	64	0	64

Trace form

\( 60 q + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3744.2.g.a	$3744$	$2$	3744.g	8.b	$2$	$2$	$2$	$29.896$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{5}-3q^{7}-iq^{13}+7q^{17}-4iq^{19}+\cdots\)
3744.2.g.b	$3744$	$2$	3744.g	8.b	$2$	$4$	$4$	$29.896$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\zeta_{12}^{2}q^{5}+(3+\zeta_{12}^{3})q^{7}+(-3\zeta_{12}+\cdots)q^{11}+\cdots\)
3744.2.g.c	$3744$	$2$	3744.g	8.b	$2$	$6$	$6$	$29.896$	6.0.399424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{1}q^{7}+(2\beta _{2}-\beta _{3}+\beta _{5})q^{11}+\cdots\)
3744.2.g.d	$3744$	$2$	3744.g	8.b	$2$	$8$	$8$	$29.896$	\(\Q(\zeta_{20})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{20}+\zeta_{20}^{2})q^{5}+(-1-\zeta_{20}^{5}+\cdots)q^{7}+\cdots\)
3744.2.g.e	$3744$	$2$	3744.g	8.b	$2$	$16$	$16$	$29.896$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{12}q^{5}-\beta _{5}q^{7}+\beta _{10}q^{11}-\beta _{6}q^{13}+\cdots\)
3744.2.g.f	$3744$	$2$	3744.g	8.b	$2$	$24$	$24$	$29.896$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)