Space of modular forms of level 5040, weight 2, and Character 5040.v

• Label: 5040.2.v
• Level: $5040$
• Weight: $2$
• Character orbit: 5040.v
• Rep. character: $\chi_{5040}(3599,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $2304$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5040.v (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(2304\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(11\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5040, [\chi])\).

	Total	New	Old
Modular forms	1200	72	1128
Cusp forms	1104	72	1032
Eisenstein series	96	0	96

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(5040, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5040.2.v.a	$5040$	$2$	5040.v	60.h	$2$	$12$	$12$	$40.245$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-q^{7}+(\beta _{1}-\beta _{2}+\beta _{5})q^{11}+\cdots\)
5040.2.v.b	$5040$	$2$	5040.v	60.h	$2$	$12$	$12$	$40.245$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+q^{7}+(\beta _{1}-\beta _{2}+\beta _{5})q^{11}+\cdots\)
5040.2.v.c	$5040$	$2$	5040.v	60.h	$2$	$24$	$24$	$40.245$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{2}]$
5040.2.v.d	$5040$	$2$	5040.v	60.h	$2$	$24$	$24$	$40.245$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)