Space of modular forms of level 2760, weight 2, and Character 2760.k

• Label: 2760.2.k
• Level: $2760$
• Weight: $2$
• Character orbit: 2760.k
• Rep. character: $\chi_{2760}(2209,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $6$
• Sturm bound: $1152$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2760.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1152\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2760, [\chi])\).

	Total	New	Old
Modular forms	592	68	524
Cusp forms	560	68	492
Eisenstein series	32	0	32

Trace form

\( 68 q - 8 q^{5} - 68 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2760, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2760.2.k.a	$2760$	$2$	2760.k	5.b	$2$	$2$	$2$	$22.039$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2760.2.k.b	$2760$	$2$	2760.k	5.b	$2$	$2$	$2$	$22.039$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-1+2i)q^{5}-q^{9}+(2+i)q^{15}+\cdots\)
2760.2.k.c	$2760$	$2$	2760.k	5.b	$2$	$12$	$12$	$22.039$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}-\beta _{10}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots\)
2760.2.k.d	$2760$	$2$	2760.k	5.b	$2$	$14$	$14$	$22.039$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{12}q^{5}+(\beta _{2}+\beta _{10})q^{7}+\cdots\)
2760.2.k.e	$2760$	$2$	2760.k	5.b	$2$	$16$	$16$	$22.039$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{14}q^{11}+\cdots\)
2760.2.k.f	$2760$	$2$	2760.k	5.b	$2$	$22$	$22$	$22.039$		None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 2}\)