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

• Label: 1520.1.bu
• Level: $1520$
• Weight: $1$
• Character orbit: 1520.bu
• Rep. character: $\chi_{1520}(159,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bu (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(19\)

Dimensions

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

	Total	New	Old
Modular forms	28	4	24
Cusp forms	4	4	0
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{5} + 2 q^{9} - 2 q^{25} + 2 q^{29} + 4 q^{41} + 4 q^{45} - 4 q^{49} - 2 q^{61} - 2 q^{81} + 2 q^{89}+O(q^{100}) \)

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.bu.a	$1520$	$1$	1520.bu	380.p	$6$	$2$	$1$	$0.759$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{5}) \)		✓			1520.1.bu.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+\cdots\)
1520.1.bu.b	$1520$	$1$	1520.bu	380.p	$6$	$2$	$1$	$0.759$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{5}) \)		✓			1520.1.bu.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+(-\zeta_{6}-\zeta_{6}^{2})q^{11}+\cdots\)