Space of modular forms of level 2280, weight 2, and Character 2280.r

• Label: 2280.2.r
• Level: $2280$
• Weight: $2$
• Character orbit: 2280.r
• Rep. character: $\chi_{2280}(1481,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $960$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2280.r (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(960\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2280, [\chi])\).

	Total	New	Old
Modular forms	496	80	416
Cusp forms	464	80	384
Eisenstein series	32	0	32

Trace form

\( 80 q + 8 q^{7} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2280, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2280.2.r.a	$2280$	$2$	2280.r	57.d	$2$	$40$	$40$	$18.206$		None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$
2280.2.r.b	$2280$	$2$	2280.r	57.d	$2$	$40$	$40$	$18.206$		None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2280, [\chi]) \cong \)