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

• Label: 3520.2.g
• Level: $3520$
• Weight: $2$
• Character orbit: 3520.g
• Rep. character: $\chi_{3520}(1761,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $16$
• Sturm bound: $1152$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3520.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1152\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	600	80	520
Cusp forms	552	80	472
Eisenstein series	48	0	48

Trace form

\( 80 q - 80 q^{9} + O(q^{10}) \)

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.g.a	$3520$	$2$	3520.g	8.b	$2$	$2$	$2$	$28.107$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+iq^{5}-3q^{7}-6q^{9}-iq^{11}+\cdots\)
3520.2.g.b	$3520$	$2$	3520.g	8.b	$2$	$2$	$2$	$28.107$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}-3q^{7}+2q^{9}+iq^{11}+\cdots\)
3520.2.g.c	$3520$	$2$	3520.g	8.b	$2$	$2$	$2$	$28.107$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}-q^{7}+2q^{9}-iq^{11}+\cdots\)
3520.2.g.d	$3520$	$2$	3520.g	8.b	$2$	$2$	$2$	$28.107$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}+q^{7}+2q^{9}-iq^{11}+\cdots\)
3520.2.g.e	$3520$	$2$	3520.g	8.b	$2$	$2$	$2$	$28.107$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-iq^{5}+3q^{7}-6q^{9}-iq^{11}+\cdots\)
3520.2.g.f	$3520$	$2$	3520.g	8.b	$2$	$2$	$2$	$28.107$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}+3q^{7}+2q^{9}+iq^{11}+\cdots\)
3520.2.g.g	$3520$	$2$	3520.g	8.b	$2$	$4$	$4$	$28.107$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}-3q^{7}-\zeta_{12}q^{11}+\cdots\)
3520.2.g.h	$3520$	$2$	3520.g	8.b	$2$	$4$	$4$	$28.107$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{3}+\beta _{1}q^{5}+(-2-\beta _{3})q^{7}+\cdots\)
3520.2.g.i	$3520$	$2$	3520.g	8.b	$2$	$4$	$4$	$28.107$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{3}-\beta _{1}q^{5}+(2+\beta _{3})q^{7}-q^{9}+\cdots\)
3520.2.g.j	$3520$	$2$	3520.g	8.b	$2$	$4$	$4$	$28.107$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+3q^{7}-\zeta_{12}q^{11}+\cdots\)
3520.2.g.k	$3520$	$2$	3520.g	8.b	$2$	$6$	$6$	$28.107$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+\beta _{3}q^{5}-\beta _{2}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.g.l	$3520$	$2$	3520.g	8.b	$2$	$6$	$6$	$28.107$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.g.m	$3520$	$2$	3520.g	8.b	$2$	$8$	$8$	$28.107$	8.0.22581504.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{5}q^{5}+(-1-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.g.n	$3520$	$2$	3520.g	8.b	$2$	$8$	$8$	$28.107$	8.0.22581504.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{5}q^{5}+(1+\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.g.o	$3520$	$2$	3520.g	8.b	$2$	$12$	$12$	$28.107$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{9}q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)
3520.2.g.p	$3520$	$2$	3520.g	8.b	$2$	$12$	$12$	$28.107$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{9}q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)