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

• Label: 3520.1.y
• Level: $3520$
• Weight: $1$
• Character orbit: 3520.y
• Rep. character: $\chi_{3520}(703,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3520.y (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 220 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	96	20	76
Cusp forms	48	12	36
Eisenstein series	48	8	40

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

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.y.a	$3520$	$1$	3520.y	220.i	$4$	$2$	$1$	$1.757$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(-1-i)q^{3}+iq^{5}+iq^{9}-iq^{11}+\cdots\)
3520.1.y.b	$3520$	$1$	3520.y	220.i	$4$	$2$	$1$	$1.757$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(1+i)q^{3}+iq^{5}+iq^{9}+iq^{11}+\cdots\)
3520.1.y.c	$3520$	$1$	3520.y	220.i	$4$	$4$	$2$	$1.757$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{12}^{4}-\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
3520.1.y.d	$3520$	$1$	3520.y	220.i	$4$	$4$	$2$	$1.757$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)