Space of modular forms of level 3520, weight 1, and Character 3520.cg

• Label: 3520.1.cg
• Level: $3520$
• Weight: $1$
• Character orbit: 3520.cg
• Rep. character: $\chi_{3520}(1249,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3520.cg (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 440 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3520, [\chi])\).

	Total	New	Old
Modular forms	112	16	96
Cusp forms	16	16	0
Eisenstein series	96	0	96

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3520.1.cg.a	$3520$	$1$	3520.cg	440.aa	$10$	$8$	$2$	$1.757$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-10}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{3}+\zeta_{20}^{5})q^{7}+\zeta_{20}^{2}q^{9}+\cdots\)
3520.1.cg.b	$3520$	$1$	3520.cg	440.aa	$10$	$8$	$2$	$1.757$	\(\Q(\zeta_{20})\)	$D_{10}$	\(\Q(\sqrt{-10}) \)	None		$8$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{20}^{8}q^{5}+(\zeta_{20}^{3}+\zeta_{20}^{5})q^{7}+\zeta_{20}^{2}q^{9}+\cdots\)