Space of modular forms of level 2640, weight 2, and Character 2640.q

• Label: 2640.2.q
• Level: $2640$
• Weight: $2$
• Character orbit: 2640.q
• Rep. character: $\chi_{2640}(1759,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $1152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2640.q (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 220 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1152\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2640, [\chi])\).

	Total	New	Old
Modular forms	600	72	528
Cusp forms	552	72	480
Eisenstein series	48	0	48

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(2640, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2640.2.q.a	$2640$	$2$	2640.q	220.g	$2$	$12$	$12$	$21.081$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(-12\)	\(-4\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
2640.2.q.b	$2640$	$2$	2640.q	220.g	$2$	$12$	$12$	$21.081$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(12\)	\(-4\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
2640.2.q.c	$2640$	$2$	2640.q	220.g	$2$	$24$	$24$	$21.081$		None		$4$	$0$	\(0\)	\(-24\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2640.2.q.d	$2640$	$2$	2640.q	220.g	$2$	$24$	$24$	$21.081$		None		$4$	$0$	\(0\)	\(24\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)