Space of modular forms of level 520, weight 2, and Character 520.bh

• Label: 520.2.bh
• Level: $520$
• Weight: $2$
• Character orbit: 520.bh
• Rep. character: $\chi_{520}(177,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $42$
• Newform subspaces: $6$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.bh (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(520, [\chi])\).

	Total	New	Old
Modular forms	184	42	142
Cusp forms	152	42	110
Eisenstein series	32	0	32

Trace form

\( 42 q + 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(520, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
520.2.bh.a	$520$	$2$	520.bh	65.f	$4$	$2$	$1$	$4.152$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{3}+(-1-2i)q^{5}+iq^{9}+\cdots\)
520.2.bh.b	$520$	$2$	520.bh	65.f	$4$	$2$	$1$	$4.152$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}-4q^{7}+3iq^{9}+(4+\cdots)q^{11}+\cdots\)
520.2.bh.c	$520$	$2$	520.bh	65.f	$4$	$2$	$1$	$4.152$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-i)q^{3}+(-2+i)q^{5}+2q^{7}+iq^{9}+\cdots\)
520.2.bh.d	$520$	$2$	520.bh	65.f	$4$	$4$	$2$	$4.152$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(8\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(2+\zeta_{8}^{2})q^{5}+\cdots\)
520.2.bh.e	$520$	$2$	520.bh	65.f	$4$	$12$	$6$	$4.152$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(2\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+\beta _{2}q^{7}+\cdots\)
520.2.bh.f	$520$	$2$	520.bh	65.f	$4$	$20$	$10$	$4.152$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}-\beta _{15}q^{5}+\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(520, [\chi]) \cong \)