Space of modular forms of level 2880, weight 2, and Character 2880.f

• Label: 2880.2.f
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.f
• Rep. character: $\chi_{2880}(1729,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $24$
• Sturm bound: $1152$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(1152\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).

	Total	New	Old
Modular forms	624	62	562
Cusp forms	528	58	470
Eisenstein series	96	4	92

Trace form

\( 58 q - 2 q^{5} + 2 q^{25} - 4 q^{29} - 4 q^{41} - 50 q^{49} - 12 q^{61} - 32 q^{85} + 12 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2880.2.f.a	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					480.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i-2)q^{5}+2 i q^{7}-6 q^{11}+\cdots\)
2880.2.f.b	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					360.2.f.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-2)q^{5}+4 i q^{7}-4 q^{11}+4 i q^{13}+\cdots\)
2880.2.f.c	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					30.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-2)q^{5}+2 i q^{7}-2 q^{11}-6 i q^{13}+\cdots\)
2880.2.f.d	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					1440.2.f.a	$4$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(i-2)q^{5}+4 i q^{13}-2 i q^{17}+(-4 i+3)q^{25}+\cdots\)
2880.2.f.e	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					30.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i-2)q^{5}+2 i q^{7}+2 q^{11}+\cdots\)
2880.2.f.f	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					360.2.f.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i-2)q^{5}+4 i q^{7}+4 q^{11}+\cdots\)
2880.2.f.g	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					480.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-2)q^{5}+2 i q^{7}+6 q^{11}+2 i q^{13}+\cdots\)
2880.2.f.h	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					40.2.c.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta-1)q^{5}+\beta q^{7}-4 q^{11}+2\beta q^{13}+\cdots\)
2880.2.f.i	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					40.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta-1)q^{5}+\beta q^{7}+4 q^{11}-2\beta q^{13}+\cdots\)
2880.2.f.j	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)					45.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{5}+2\beta q^{17}-4q^{19}+4\beta q^{23}+\cdots\)
2880.2.f.k	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)					45.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{5}+2\beta q^{17}+4q^{19}-4\beta q^{23}+\cdots\)
2880.2.f.l	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					60.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta+1)q^{5}+2\beta q^{7}-4 q^{11}+\cdots\)
2880.2.f.m	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					480.2.f.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta+1)q^{5}+2\beta q^{7}-2\beta q^{13}+\cdots\)
2880.2.f.n	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					160.2.c.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta+1)q^{5}+2\beta q^{13}-4\beta q^{17}+\cdots\)
2880.2.f.o	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					480.2.f.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta+1)q^{5}+2\beta q^{7}+2\beta q^{13}+8 q^{19}+\cdots\)
2880.2.f.p	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					60.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta+1)q^{5}+2\beta q^{7}+4 q^{11}+2\beta q^{17}+\cdots\)
2880.2.f.q	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					360.2.f.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+2)q^{5}+4 i q^{7}-4 q^{11}-4 i q^{13}+\cdots\)
2880.2.f.r	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					120.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+2)q^{5}+2 i q^{7}-2 q^{11}+2 i q^{13}+\cdots\)
2880.2.f.s	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					1440.2.f.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(i+2)q^{5}-4 i q^{13}-2 i q^{17}+(4 i+3)q^{25}+\cdots\)
2880.2.f.t	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					120.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+2)q^{5}+2 i q^{7}+2 q^{11}+\cdots\)
2880.2.f.u	$2880$	$2$	2880.f	5.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					360.2.f.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+2)q^{5}+4 i q^{7}+4 q^{11}+\cdots\)
2880.2.f.v	$2880$	$2$	2880.f	5.b	$2$	$4$	$4$	$22.997$	\(\Q(i, \sqrt{5})\)	None					480.2.f.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+2\beta _{1}q^{13}+\cdots\)
2880.2.f.w	$2880$	$2$	2880.f	5.b	$2$	$4$	$4$	$22.997$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)					160.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{5}-\beta _{1}q^{7}+(-\beta _{1}+2\beta _{2})q^{23}+\cdots\)
2880.2.f.x	$2880$	$2$	2880.f	5.b	$2$	$8$	$8$	$22.997$	\(\Q(\zeta_{24})\)	None			✓		1440.2.f.j	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{4} q^{5}+\beta_{5} q^{7}+\beta_{6} q^{11}+\beta_{7} q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)