Space of modular forms of level 3040, weight 2, and Character 3040.f

• Label: 3040.2.f
• Level: $3040$
• Weight: $2$
• Character orbit: 3040.f
• Rep. character: $\chi_{3040}(1521,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $960$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3040.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(960\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3040, [\chi])\).

	Total	New	Old
Modular forms	496	72	424
Cusp forms	464	72	392
Eisenstein series	32	0	32

Trace form

\( 72 q - 8 q^{7} - 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3040, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3040.2.f.a	$3040$	$2$	3040.f	8.b	$2$	$28$	$28$	$24.275$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$
3040.2.f.b	$3040$	$2$	3040.f	8.b	$2$	$44$	$44$	$24.275$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)