Space of modular forms of level 4800, weight 2, and trivial character

• Label: 4800.2.a
• Level: $4800$
• Weight: $2$
• Character orbit: 4800.a
• Rep. character: $\chi_{4800}(1,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $74$
• Sturm bound: $1920$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4800 = 2^{6} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4800.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 74 \)
Sturm bound:			\(1920\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4800))\).

	Total	New	Old
Modular forms	1032	76	956
Cusp forms	889	76	813
Eisenstein series	143	0	143

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(5\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)	\(11\)
\(+\)	\(-\)	\(-\)	\(+\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	\(10\)
\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(12\)
Plus space			\(+\)	\(33\)
Minus space			\(-\)	\(43\)

Trace form

\( 76 q + 76 q^{9} + 8 q^{13} + 8 q^{17} + 8 q^{21} - 16 q^{29} - 8 q^{37} + 8 q^{41} + 76 q^{49} - 16 q^{53} + 24 q^{61} + 16 q^{69} - 8 q^{73} - 64 q^{77} + 76 q^{81} - 8 q^{89} + 8 q^{93} + 24 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4800))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5
4800.2.a.a	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-5q^{7}+q^{9}-6q^{11}-3q^{13}+\cdots\)
4800.2.a.b	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-5q^{7}+q^{9}+6q^{11}+3q^{13}+\cdots\)
4800.2.a.c	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}-4q^{13}+8q^{19}+\cdots\)
4800.2.a.d	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				30.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots\)
4800.2.a.e	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+4q^{13}-8q^{19}+\cdots\)
4800.2.a.f	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				96.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4800.2.a.g	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.k	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}-4q^{11}+7q^{13}+\cdots\)
4800.2.a.h	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.l	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}-5q^{13}+5q^{19}+\cdots\)
4800.2.a.i	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.l	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}+5q^{13}-5q^{19}+\cdots\)
4800.2.a.j	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.k	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}+q^{9}+4q^{11}-7q^{13}+\cdots\)
4800.2.a.k	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.f.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
4800.2.a.l	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				30.2.c.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
4800.2.a.m	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				30.2.c.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
4800.2.a.n	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.f.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
4800.2.a.o	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				300.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-6q^{11}-5q^{13}+\cdots\)
4800.2.a.p	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				300.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots\)
4800.2.a.q	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				24.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.r	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-4q^{11}+6q^{13}+6q^{17}+\cdots\)
4800.2.a.s	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
4800.2.a.t	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				15.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.u	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
4800.2.a.v	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-4q^{11}-3q^{13}+\cdots\)
4800.2.a.w	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-q^{13}-3q^{19}-q^{21}+\cdots\)
4800.2.a.x	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+q^{13}+3q^{19}-q^{21}+\cdots\)
4800.2.a.y	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+4q^{11}+3q^{13}+\cdots\)
4800.2.a.z	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
4800.2.a.ba	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
4800.2.a.bb	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				75.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
4800.2.a.bc	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots\)
4800.2.a.bd	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots\)
4800.2.a.be	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				75.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4800.2.a.bf	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				60.2.d.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots\)
4800.2.a.bg	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
4800.2.a.bh	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
4800.2.a.bi	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
4800.2.a.bj	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				60.2.d.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}+4q^{11}+4q^{17}+\cdots\)
4800.2.a.bk	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				60.2.d.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots\)
4800.2.a.bl	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
4800.2.a.bm	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
4800.2.a.bn	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				60.2.d.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+4q^{11}-4q^{17}+\cdots\)
4800.2.a.bo	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4800.2.a.bp	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots\)
4800.2.a.bq	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				75.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
4800.2.a.br	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				75.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
4800.2.a.bs	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots\)
4800.2.a.bt	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
4800.2.a.bu	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
4800.2.a.bv	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-4q^{11}+3q^{13}+\cdots\)
4800.2.a.bw	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.f	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-q^{13}+3q^{19}-q^{21}+\cdots\)
4800.2.a.bx	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.f	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+q^{13}-3q^{19}-q^{21}+\cdots\)
4800.2.a.by	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+4q^{11}-3q^{13}+\cdots\)
4800.2.a.bz	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				15.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.ca	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
4800.2.a.cb	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.a.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
4800.2.a.cc	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				24.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
4800.2.a.cd	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+4q^{11}+6q^{13}+6q^{17}+\cdots\)
4800.2.a.ce	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				300.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-6q^{11}+5q^{13}+\cdots\)
4800.2.a.cf	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				300.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\)
4800.2.a.cg	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				30.2.c.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
4800.2.a.ch	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.f.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
4800.2.a.ci	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				120.2.f.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
4800.2.a.cj	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				30.2.c.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
4800.2.a.ck	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.k	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-4q^{11}-7q^{13}+\cdots\)
4800.2.a.cl	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.l	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}-5q^{13}-5q^{19}+\cdots\)
4800.2.a.cm	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.l	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}+5q^{13}+5q^{19}+\cdots\)
4800.2.a.cn	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				2400.2.a.k	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}+4q^{11}+7q^{13}+\cdots\)
4800.2.a.co	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				96.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4800.2.a.cp	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-4q^{13}-8q^{19}+\cdots\)
4800.2.a.cq	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				30.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots\)
4800.2.a.cr	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				480.2.f.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}+4q^{13}+8q^{19}+\cdots\)
4800.2.a.cs	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+5q^{7}+q^{9}-6q^{11}+3q^{13}+\cdots\)
4800.2.a.ct	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	\(\Q\)	None	✓				600.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+5q^{7}+q^{9}+6q^{11}-3q^{13}+\cdots\)
4800.2.a.cu	$4800$	$2$	4800.a	1.a	$1$	$2$	$2$	$38.328$	\(\Q(\sqrt{5}) \)	None	✓		✓		480.2.f.e	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
4800.2.a.cv	$4800$	$2$	4800.a	1.a	$1$	$2$	$2$	$38.328$	\(\Q(\sqrt{5}) \)	None	✓		✓		480.2.f.e	$2$	$1$	\(0\)	\(2\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-\beta q^{11}+\beta q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4800)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 2}\)