Space of modular forms of level 3520, weight 2, and Character 3520.p

• Label: 3520.2.p
• Level: $3520$
• Weight: $2$
• Character orbit: 3520.p
• Rep. character: $\chi_{3520}(351,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3520.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(59\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3520, [\chi])\).

	Total	New	Old
Modular forms	600	96	504
Cusp forms	552	96	456
Eisenstein series	48	0	48

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3520.2.p.a	$3520$	$2$	3520.p	88.g	$2$	$4$	$4$	$28.107$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{5}-3\zeta_{8}^{3}q^{7}-3q^{9}+(-3-\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
3520.2.p.b	$3520$	$2$	3520.p	88.g	$2$	$4$	$4$	$28.107$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{5}+3\zeta_{8}^{3}q^{7}-3q^{9}+(3-\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
3520.2.p.c	$3520$	$2$	3520.p	88.g	$2$	$12$	$12$	$28.107$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{8})q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(2+\cdots)q^{9}+\cdots\)
3520.2.p.d	$3520$	$2$	3520.p	88.g	$2$	$12$	$12$	$28.107$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{8})q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
3520.2.p.e	$3520$	$2$	3520.p	88.g	$2$	$32$	$32$	$28.107$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
3520.2.p.f	$3520$	$2$	3520.p	88.g	$2$	$32$	$32$	$28.107$		None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1760, [\chi])\)\(^{\oplus 2}\)