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

• Label: 2640.2.k
• Level: $2640$
• Weight: $2$
• Character orbit: 2640.k
• Rep. character: $\chi_{2640}(1871,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $8$
• Sturm bound: $1152$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2640.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1152\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(7\), \(23\), \(47\)

Dimensions

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

	Total	New	Old
Modular forms	600	80	520
Cusp forms	552	80	472
Eisenstein series	48	0	48

Trace form

\( 80 q + O(q^{10}) \)

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.k.a	$2640$	$2$	2640.k	12.b	$2$	$4$	$4$	$21.081$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots\)
2640.2.k.b	$2640$	$2$	2640.k	12.b	$2$	$4$	$4$	$21.081$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots\)
2640.2.k.c	$2640$	$2$	2640.k	12.b	$2$	$8$	$8$	$21.081$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}-\beta _{1}q^{5}+\beta _{7}q^{7}+(-1-2\beta _{1}+\cdots)q^{9}+\cdots\)
2640.2.k.d	$2640$	$2$	2640.k	12.b	$2$	$8$	$8$	$21.081$	8.0.195105024.2	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{3}+\beta _{7}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2640.2.k.e	$2640$	$2$	2640.k	12.b	$2$	$8$	$8$	$21.081$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}-\beta _{7}q^{7}+(-1-2\beta _{1}+\cdots)q^{9}+\cdots\)
2640.2.k.f	$2640$	$2$	2640.k	12.b	$2$	$8$	$8$	$21.081$	8.0.195105024.2	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{7}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2640.2.k.g	$2640$	$2$	2640.k	12.b	$2$	$20$	$20$	$21.081$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{2}+\beta _{11})q^{7}+\cdots\)
2640.2.k.h	$2640$	$2$	2640.k	12.b	$2$	$20$	$20$	$21.081$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}+\beta _{2}q^{5}+(-\beta _{2}+\beta _{11})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2640, [\chi]) \cong \)