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

• Label: 3040.2.j
• Level: $3040$
• Weight: $2$
• Character orbit: 3040.j
• Rep. character: $\chi_{3040}(2431,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $960$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3040.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(960\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

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

Trace form

\( 80 q + 64 q^{9} + O(q^{10}) \)

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.j.a	$3040$	$2$	3040.j	76.d	$2$	$4$	$4$	$24.275$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}-3q^{9}+(\zeta_{8}+\cdots)q^{11}+\cdots\)
3040.2.j.b	$3040$	$2$	3040.j	76.d	$2$	$4$	$4$	$24.275$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{3}q^{3}+q^{5}+4\zeta_{8}q^{7}-q^{9}+4\zeta_{8}q^{11}+\cdots\)
3040.2.j.c	$3040$	$2$	3040.j	76.d	$2$	$4$	$4$	$24.275$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+q^{5}+(\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
3040.2.j.d	$3040$	$2$	3040.j	76.d	$2$	$8$	$8$	$24.275$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}q^{3}+q^{5}-\zeta_{24}^{7}q^{7}+(\zeta_{24}^{2}+\cdots)q^{11}+\cdots\)
3040.2.j.e	$3040$	$2$	3040.j	76.d	$2$	$20$	$20$	$24.275$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2^{32}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+q^{5}+\beta _{7}q^{7}+(1-\beta _{3})q^{9}+\cdots\)
3040.2.j.f	$3040$	$2$	3040.j	76.d	$2$	$40$	$40$	$24.275$		None		$4$	$0$	\(0\)	\(0\)	\(-40\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(3040, [\chi]) \cong \)