Space of modular forms of level 1560, weight 2, and Character 1560.r

• Label: 1560.2.r
• Level: $1560$
• Weight: $2$
• Character orbit: 1560.r
• Rep. character: $\chi_{1560}(649,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $8$
• Sturm bound: $672$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.r (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(672\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

	Total	New	Old
Modular forms	352	44	308
Cusp forms	320	44	276
Eisenstein series	32	0	32

Trace form

\( 44 q - 44 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1560.2.r.a	$1560$	$2$	1560.r	65.d	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-2-i)q^{5}-q^{7}-q^{9}+3iq^{11}+\cdots\)
1560.2.r.b	$1560$	$2$	1560.r	65.d	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1-2i)q^{5}+4q^{7}-q^{9}+\cdots\)
1560.2.r.c	$1560$	$2$	1560.r	65.d	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(1+2i)q^{5}-4q^{7}-q^{9}+(-3+\cdots)q^{13}+\cdots\)
1560.2.r.d	$1560$	$2$	1560.r	65.d	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(2+i)q^{5}+q^{7}-q^{9}-3iq^{11}+\cdots\)
1560.2.r.e	$1560$	$2$	1560.r	65.d	$2$	$8$	$8$	$12.457$	8.0.\(\cdots\).2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{7}-q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1560.2.r.f	$1560$	$2$	1560.r	65.d	$2$	$8$	$8$	$12.457$	8.0.\(\cdots\).2	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}-q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1560.2.r.g	$1560$	$2$	1560.r	65.d	$2$	$10$	$10$	$12.457$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-12\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(-1-\beta _{4})q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots\)
1560.2.r.h	$1560$	$2$	1560.r	65.d	$2$	$10$	$10$	$12.457$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(12\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(1+\beta _{4})q^{5}+(1-\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \)