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

• Label: 1560.2.l
• Level: $1560$
• Weight: $2$
• Character orbit: 1560.l
• Rep. character: $\chi_{1560}(1249,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $6$
• 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.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
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	36	316
Cusp forms	320	36	284
Eisenstein series	32	0	32

Trace form

\( 36 q - 36 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1560.2.l.a	$1560$	$2$	1560.l	5.b	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		✓			1560.2.l.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1+2i)q^{5}+5iq^{7}-q^{9}+\cdots\)
1560.2.l.b	$1560$	$2$	1560.l	5.b	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		✓			1560.2.l.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+3q^{11}+\cdots\)
1560.2.l.c	$1560$	$2$	1560.l	5.b	$2$	$6$	$6$	$12.457$	6.0.5161984.1	None		✓			1560.2.l.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(-2+\beta _{4}+\cdots)q^{11}+\cdots\)
1560.2.l.d	$1560$	$2$	1560.l	5.b	$2$	$8$	$8$	$12.457$	8.0.\(\cdots\).2	None		✓			1560.2.l.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
1560.2.l.e	$1560$	$2$	1560.l	5.b	$2$	$8$	$8$	$12.457$	8.0.1698758656.6	None		✓			1560.2.l.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}-\beta _{4}q^{7}+\cdots\)
1560.2.l.f	$1560$	$2$	1560.l	5.b	$2$	$10$	$10$	$12.457$	10.0.\(\cdots\).1	None		✓	✓		1560.2.l.f	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)