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

• Label: 1520.1.cr
• Level: $1520$
• Weight: $1$
• Character orbit: 1520.cr
• Rep. character: $\chi_{1520}(273,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1520.cr (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	76	16	60
Cusp forms	28	8	20
Eisenstein series	48	8	40

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

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

Trace form

8 * q + 2 * q^5 - 8 * q^11 - 2 * q^13 - 2 * q^17 + 2 * q^23 + 8 * q^31 - 4 * q^37 + 2 * q^43 - 4 * q^45 + 2 * q^47 + 4 * q^51 + 4 * q^53 - 2 * q^55 - 8 * q^57 - 4 * q^65 - 2 * q^67 + 4 * q^71 + 2 * q^73 - 8 * q^75 - 4 * q^81 + 4 * q^83 + 2 * q^85 - 8 * q^87 - 4 * q^95 + 2 * q^97

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.cr.a	$1520$	$1$	1520.cr	95.m	$12$	$4$	$1$	$0.759$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None					760.1.bt.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{12}+\zeta_{12}^{4})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}+\cdots\)
1520.1.cr.b	$1520$	$1$	1520.cr	95.m	$12$	$4$	$1$	$0.759$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None					380.1.x.a	$4$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$		\(q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{4}q^{5}-\zeta_{12}^{5}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1520, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)