Space of modular forms of level 5760, weight 2, and Character 5760.k

• Label: 5760.2.k
• Level: $5760$
• Weight: $2$
• Character orbit: 5760.k
• Rep. character: $\chi_{5760}(2881,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $25$
• Sturm bound: $2304$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5760.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(2304\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5760, [\chi])\).

	Total	New	Old
Modular forms	1216	80	1136
Cusp forms	1088	80	1008
Eisenstein series	128	0	128

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5760, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5760.2.k.a	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None		✓			5760.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{5}-4 q^{7}-4 q^{17}-4 i q^{19}+\cdots\)
5760.2.k.b	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None		✓			5760.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{5}-4 q^{7}+4 q^{17}+4 i q^{19}+\cdots\)
5760.2.k.c	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}-2 q^{7}-6 i q^{11}-6 i q^{13}+\cdots\)
5760.2.k.d	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}-2 q^{7}+2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.e	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}-2 q^{7}-2 i q^{11}-2 i q^{13}+\cdots\)
5760.2.k.f	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{5}-2 q^{7}+2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.g	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+2 q^{7}-2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.h	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+2 q^{7}+6 i q^{11}-6 i q^{13}+\cdots\)
5760.2.k.i	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{5}+2 q^{7}-2 i q^{11}+2 i q^{13}+\cdots\)
5760.2.k.j	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None					1920.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+2 q^{7}+2 i q^{11}-2 i q^{13}+\cdots\)
5760.2.k.k	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None		✓			5760.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+4 q^{7}-4 q^{17}-4 i q^{19}+\cdots\)
5760.2.k.l	$5760$	$2$	5760.k	8.b	$2$	$2$	$2$	$45.994$	\(\Q(\sqrt{-1}) \)	None		✓			5760.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{5}+4 q^{7}+4 q^{17}-4 i q^{19}+\cdots\)
5760.2.k.m	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None					1920.2.k.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{5}-2 q^{7}+(-\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.n	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None					1920.2.k.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{5}+(\beta_{3}-2)q^{7}+(-\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.o	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None					640.2.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}-3\beta_{3} q^{7}+4\beta_{2} q^{11}-2\beta_1 q^{13}+\cdots\)
5760.2.k.p	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None		✓			5760.2.k.p	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{5}+\beta_{3} q^{7}+\beta_{2} q^{11}-4\beta_1 q^{13}+\cdots\)
5760.2.k.q	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None					640.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}-\beta_{3} q^{7}-2\beta_{2} q^{11}+2\beta_1 q^{13}+\cdots\)
5760.2.k.r	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None		✓			5760.2.k.r	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}-\beta_{2} q^{11}-4\beta_1 q^{13}+\beta_{2} q^{19}+\cdots\)
5760.2.k.s	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None		✓			5760.2.k.r	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}-\beta_{2} q^{11}+4\beta_1 q^{13}-\beta_{2} q^{19}+\cdots\)
5760.2.k.t	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(i, \sqrt{10})\)	None					640.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{3}q^{7}+6\beta _{1}q^{13}+2q^{17}+\cdots\)
5760.2.k.u	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None		✓			5760.2.k.p	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{5}+\beta_{3} q^{7}+\beta_{2} q^{11}+4\beta_1 q^{13}+\cdots\)
5760.2.k.v	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None					640.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{5}+3\beta_{3} q^{7}-2\beta_{2} q^{11}+6\beta_1 q^{13}+\cdots\)
5760.2.k.w	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None					1920.2.k.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}+(\beta_{3}+2)q^{7}+(\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.x	$5760$	$2$	5760.k	8.b	$2$	$4$	$4$	$45.994$	\(\Q(\zeta_{8})\)	None					1920.2.k.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}+2 q^{7}+(\beta_{2}-2\beta_1)q^{11}+\cdots\)
5760.2.k.y	$5760$	$2$	5760.k	8.b	$2$	$8$	$8$	$45.994$	\(\Q(\zeta_{24})\)	None		✓	✓		5760.2.k.y	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{5}-\beta_{2} q^{11}+\beta_{5} q^{13}-\beta_{3} q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5760, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2880, [\chi])\)\(^{\oplus 2}\)