Space of modular forms of level 4800, weight 2, and Character 4800.f

• Label: 4800.2.f
• Level: $4800$
• Weight: $2$
• Character orbit: 4800.f
• Rep. character: $\chi_{4800}(3649,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $36$
• Sturm bound: $1920$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 4800 = 2^{6} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4800.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 36 \)
Sturm bound:			\(1920\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4800, [\chi])\).

	Total	New	Old
Modular forms	1032	72	960
Cusp forms	888	72	816
Eisenstein series	144	0	144

Trace form

\( 72 q - 72 q^{9} - 16 q^{41} - 72 q^{49} + 32 q^{61} - 32 q^{69} + 72 q^{81} - 16 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4800, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4800.2.f.a	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					600.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+5 i q^{7}-q^{9}-6 q^{11}-3 i q^{13}+\cdots\)
4800.2.f.b	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					300.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{7}-q^{9}-6 q^{11}-5 i q^{13}+\cdots\)
4800.2.f.c	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					15.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-q^{9}-4 q^{11}+2 i q^{13}-2 i q^{17}+\cdots\)
4800.2.f.d	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					24.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-q^{9}-4 q^{11}+2 i q^{13}-2 i q^{17}+\cdots\)
4800.2.f.e	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					96.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+4 i q^{7}-q^{9}-4 q^{11}+2 i q^{13}+\cdots\)
4800.2.f.f	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+3 i q^{7}-q^{9}-4 q^{11}+7 i q^{13}+\cdots\)
4800.2.f.g	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{7}-q^{9}-4 q^{11}+3 i q^{13}+\cdots\)
4800.2.f.h	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+4 i q^{7}-q^{9}-4 q^{11}-6 i q^{13}+\cdots\)
4800.2.f.i	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					120.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-q^{9}-4 q^{11}+6 i q^{13}-6 i q^{17}+\cdots\)
4800.2.f.j	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-q^{9}-4 q^{11}-2 i q^{13}+2 i q^{17}+\cdots\)
4800.2.f.k	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					600.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{7}-q^{9}-2 q^{11}-3 i q^{13}+\cdots\)
4800.2.f.l	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					75.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{7}-q^{9}-2 q^{11}-i q^{13}+\cdots\)
4800.2.f.m	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+3 i q^{7}-q^{9}-5 i q^{13}+\cdots\)
4800.2.f.n	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					120.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+4 i q^{7}-q^{9}+6 i q^{13}+\cdots\)
4800.2.f.o	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-q^{9}-2 i q^{13}-6 i q^{17}+\cdots\)
4800.2.f.p	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					30.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+4 i q^{7}-q^{9}-2 i q^{13}+\cdots\)
4800.2.f.q	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{7}-q^{9}-i q^{13}-3 q^{19}+\cdots\)
4800.2.f.r	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+4 i q^{7}-q^{9}+2 i q^{13}+\cdots\)
4800.2.f.s	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+4 i q^{7}-q^{9}-2 i q^{13}+\cdots\)
4800.2.f.t	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{7}-q^{9}+i q^{13}+3 q^{19}+\cdots\)
4800.2.f.u	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					120.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+4 i q^{7}-q^{9}-6 i q^{13}+\cdots\)
4800.2.f.v	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-q^{9}+2 i q^{13}+6 i q^{17}+\cdots\)
4800.2.f.w	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					30.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+4 i q^{7}-q^{9}+2 i q^{13}+\cdots\)
4800.2.f.x	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+3 i q^{7}-q^{9}+5 i q^{13}+\cdots\)
4800.2.f.y	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					75.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{7}-q^{9}+2 q^{11}+i q^{13}+\cdots\)
4800.2.f.z	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					600.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{7}-q^{9}+2 q^{11}+3 i q^{13}+\cdots\)
4800.2.f.ba	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-q^{9}+4 q^{11}+2 i q^{13}-2 i q^{17}+\cdots\)
4800.2.f.bb	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					480.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+4 i q^{7}-q^{9}+4 q^{11}+6 i q^{13}+\cdots\)
4800.2.f.bc	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					120.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-q^{9}+4 q^{11}-6 i q^{13}+6 i q^{17}+\cdots\)
4800.2.f.bd	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{7}-q^{9}+4 q^{11}-3 i q^{13}+\cdots\)
4800.2.f.be	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					2400.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+3 i q^{7}-q^{9}+4 q^{11}-7 i q^{13}+\cdots\)
4800.2.f.bf	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					15.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-q^{9}+4 q^{11}+2 i q^{13}-2 i q^{17}+\cdots\)
4800.2.f.bg	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					24.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-q^{9}+4 q^{11}+2 i q^{13}-2 i q^{17}+\cdots\)
4800.2.f.bh	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					96.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+4 i q^{7}-q^{9}+4 q^{11}-2 i q^{13}+\cdots\)
4800.2.f.bi	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					300.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{7}-q^{9}+6 q^{11}+5 i q^{13}+\cdots\)
4800.2.f.bj	$4800$	$2$	4800.f	5.b	$2$	$2$	$2$	$38.328$	\(\Q(\sqrt{-1}) \)	None					600.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+5 i q^{7}-q^{9}+6 q^{11}+3 i q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4800, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2400, [\chi])\)\(^{\oplus 2}\)