Space of modular forms of level 1520, weight 1, and Character 1520.bh

• Label: 1520.1.bh
• Level: $1520$
• Weight: $1$
• Character orbit: 1520.bh
• Rep. character: $\chi_{1520}(189,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bh (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1520 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1520, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	8	0

Trace form

\( 24 q + 4 q^{5} - 8 q^{6} - 8 q^{16} - 4 q^{20} - 16 q^{24} - 8 q^{26} - 4 q^{30} + 4 q^{35} - 16 q^{49} - 8 q^{61} + 16 q^{66} + 12 q^{80} - 8 q^{81} - 4 q^{85} + 16 q^{95} + 24 q^{96} + 16 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1520, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1520.1.bh.a	$1520$	$1$	1520.bh	1520.ah	$4$	$4$	$2$	$0.759$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓			1520.1.bh.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+\cdots\)
1520.1.bh.b	$1520$	$1$	1520.bh	1520.ah	$4$	$4$	$2$	$0.759$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓			1520.1.bh.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$1$		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{5}+\cdots\)
1520.1.bh.c	$1520$	$1$	1520.bh	1520.ah	$4$	$16$	$8$	$0.759$	\(\Q(\zeta_{32})\)	$D_{16}$	\(\Q(\sqrt{-95}) \)	None		✓	✓		1520.1.bh.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{32}^{3}q^{2}+(\zeta_{32}-\zeta_{32}^{7})q^{3}+\zeta_{32}^{6}q^{4}+\cdots\)