Space of modular forms of level 3648, weight 2, and Character 3648.g

• Label: 3648.2.g
• Level: $3648$
• Weight: $2$
• Character orbit: 3648.g
• Rep. character: $\chi_{3648}(1825,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $10$
• Sturm bound: $1280$
• Trace bound: $33$

Defining parameters

Level:	\( N \)	\(=\)	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3648.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1280\)
Trace bound:			\(33\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3648, [\chi])\).

	Total	New	Old
Modular forms	664	72	592
Cusp forms	616	72	544
Eisenstein series	48	0	48

Trace form

\( 72 q - 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3648, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3648.2.g.a	$3648$	$2$	3648.g	8.b	$2$	$4$	$4$	$29.129$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}-2\beta _{3}q^{7}-q^{9}+\beta _{2}q^{13}+\cdots\)
3648.2.g.b	$3648$	$2$	3648.g	8.b	$2$	$4$	$4$	$29.129$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-2\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3648.2.g.c	$3648$	$2$	3648.g	8.b	$2$	$4$	$4$	$29.129$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3648.2.g.d	$3648$	$2$	3648.g	8.b	$2$	$4$	$4$	$29.129$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}-q^{9}+\cdots\)
3648.2.g.e	$3648$	$2$	3648.g	8.b	$2$	$4$	$4$	$29.129$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-q^{9}+\cdots\)
3648.2.g.f	$3648$	$2$	3648.g	8.b	$2$	$8$	$8$	$29.129$	8.0.\(\cdots\).8	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}-q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
3648.2.g.g	$3648$	$2$	3648.g	8.b	$2$	$8$	$8$	$29.129$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{1}q^{5}-\beta _{5}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
3648.2.g.h	$3648$	$2$	3648.g	8.b	$2$	$8$	$8$	$29.129$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{1}q^{5}-\beta _{5}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
3648.2.g.i	$3648$	$2$	3648.g	8.b	$2$	$12$	$12$	$29.129$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}-q^{9}+(2\beta _{6}+\cdots)q^{11}+\cdots\)
3648.2.g.j	$3648$	$2$	3648.g	8.b	$2$	$16$	$16$	$29.129$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}-q^{9}+(-2\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \)