Space of modular forms of level 3040, weight 1, and Character 3040.cc

• Label: 3040.1.cc
• Level: $3040$
• Weight: $1$
• Character orbit: 3040.cc
• Rep. character: $\chi_{3040}(239,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3040.cc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3040, [\chi])\).

	Total	New	Old
Modular forms	48	12	36
Cusp forms	16	4	12
Eisenstein series	32	8	24

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 2 q^{9} + 4 q^{11} + 2 q^{19} - 2 q^{25} - 2 q^{35} + 2 q^{41} + 4 q^{59} + 8 q^{65} - 2 q^{81} + 2 q^{89} - 4 q^{91} - 2 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3040, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3040.1.cc.a	$3040$	$1$	3040.cc	760.am	$6$	$2$	$1$	$1.517$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None					760.1.bm.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)	$1$		\(q-\zeta_{6}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}+q^{11}+\zeta_{6}^{2}q^{13}+\cdots\)
3040.1.cc.b	$3040$	$1$	3040.cc	760.am	$6$	$2$	$1$	$1.517$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-10}) \)	None					760.1.bm.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$		\(q+\zeta_{6}q^{5}-q^{7}+\zeta_{6}^{2}q^{9}+q^{11}-\zeta_{6}^{2}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3040, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3040, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 3}\)