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

• Label: 3040.1.b
• Level: $3040$
• Weight: $1$
• Character orbit: 3040.b
• Rep. character: $\chi_{3040}(1329,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q\)
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	12	36
Cusp forms	32	8	24
Eisenstein series	16	4	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

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

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.b.a	$3040$	$1$	3040.b	760.b	$2$	$8$	$8$	$1.517$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-95}) \)	None			✓	✓	760.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$		\(q+(-\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{4}q^{5}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3040, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1520, [\chi])\)\(^{\oplus 2}\)