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

• Label: 3520.1.i
• Level: $3520$
• Weight: $1$
• Character orbit: 3520.i
• Rep. character: $\chi_{3520}(769,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $5$
• Sturm bound: $576$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3520.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(576\)
Trace bound:			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	68	14	54
Cusp forms	44	10	34
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

\( 10 q - 4 q^{5} - 10 q^{9} + 4 q^{25} + 10 q^{45} - 10 q^{49} - 4 q^{69} + 2 q^{81}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3520.1.i.a	$3520$	$1$	3520.i	55.d	$2$	$1$	$1$	$1.757$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)	✓				55.1.d.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{5}+q^{9}-q^{11}+q^{25}+2q^{31}+\cdots\)
3520.1.i.b	$3520$	$1$	3520.i	55.d	$2$	$1$	$1$	$1.757$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)	✓				55.1.d.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{5}+q^{9}+q^{11}+q^{25}-2q^{31}+\cdots\)
3520.1.i.c	$3520$	$1$	3520.i	55.d	$2$	$2$	$2$	$1.757$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None					220.1.e.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+\zeta_{6}^{2}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots\)
3520.1.i.d	$3520$	$1$	3520.i	55.d	$2$	$2$	$2$	$1.757$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-11}) \)	None					220.1.e.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots\)
3520.1.i.e	$3520$	$1$	3520.i	55.d	$2$	$4$	$4$	$1.757$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{55}) \)			✓		1760.1.i.a	$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{5}-q^{9}+\zeta_{8}^{2}q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3520, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1760, [\chi])\)\(^{\oplus 2}\)