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

• Label: 3040.1.cn
• Level: $3040$
• Weight: $1$
• Character orbit: 3040.cn
• Rep. character: $\chi_{3040}(189,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $480$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3040.cn (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3040 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(480\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	48	48	0
Cusp forms	32	32	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q + O(q^{10}) \)

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.cn.a	$3040$	$1$	3040.cn	3040.bn	$8$	$32$	$8$	$1.517$	\(\Q(\zeta_{64})\)	$D_{32}$	\(\Q(\sqrt{-95}) \)	None		✓	✓	✓	3040.1.cn.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{64}^{27}q^{2}+(-\zeta_{64}^{25}-\zeta_{64}^{31}+\cdots)q^{3}+\cdots\)