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

• Label: 1560.2.g
• Level: $1560$
• Weight: $2$
• Character orbit: 1560.g
• Rep. character: $\chi_{1560}(961,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $9$
• Sturm bound: $672$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(672\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	352	28	324
Cusp forms	320	28	292
Eisenstein series	32	0	32

Trace form

28 * q - 4 * q^3 + 28 * q^9 - 4 * q^13 + 8 * q^17 - 16 * q^23 - 28 * q^25 - 4 * q^27 - 8 * q^29 - 8 * q^35 + 8 * q^39 + 48 * q^43 - 36 * q^49 - 16 * q^51 + 24 * q^53 + 8 * q^55 + 16 * q^61 + 12 * q^65 + 4 * q^75 - 16 * q^77 + 24 * q^79 + 28 * q^81 - 8 * q^87 + 16 * q^91

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.g.a	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		✓			1560.2.g.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+i q^{5}+2 i q^{7}+q^{9}+(2 i-3)q^{13}+\cdots\)
1560.2.g.b	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		✓			1560.2.g.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-i q^{5}+2 i q^{7}+q^{9}-4 i q^{11}+\cdots\)
1560.2.g.c	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		✓			1560.2.g.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-i q^{5}+4 i q^{7}+q^{9}+4 i q^{11}+\cdots\)
1560.2.g.d	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		✓			1560.2.g.d	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-i q^{5}+3 i q^{7}+q^{9}-3 i q^{11}+\cdots\)
1560.2.g.e	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	\(\Q(\sqrt{-1}) \)	None		✓			1560.2.g.e	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-i q^{5}+q^{9}+6 i q^{11}+(3 i-2)q^{13}+\cdots\)
1560.2.g.f	$1560$	$2$	1560.g	13.b	$2$	$4$	$4$	$12.457$	\(\Q(i, \sqrt{41})\)	None		✓			1560.2.g.f	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1560.2.g.g	$1560$	$2$	1560.g	13.b	$2$	$4$	$4$	$12.457$	\(\Q(\zeta_{12})\)	None		✓			1560.2.g.g	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta_1 q^{5}+\beta_{2} q^{7}+q^{9}+(\beta_{2}+1)q^{13}+\cdots\)
1560.2.g.h	$1560$	$2$	1560.g	13.b	$2$	$4$	$4$	$12.457$	\(\Q(i, \sqrt{17})\)	None		✓			1560.2.g.h	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1560.2.g.i	$1560$	$2$	1560.g	13.b	$2$	$6$	$6$	$12.457$	6.0.3356224.1	None		✓	✓		1560.2.g.i	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}+(-2\beta _{1}+\beta _{4})q^{7}+q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)