Space of modular forms of level 2160, weight 4, and trivial character

• Label: 2160.4.a
• Level: $2160$
• Weight: $4$
• Character orbit: 2160.a
• Rep. character: $\chi_{2160}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $48$
• Sturm bound: $1728$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2160.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(1728\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2160))\).

	Total	New	Old
Modular forms	1332	96	1236
Cusp forms	1260	96	1164
Eisenstein series	72	0	72

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		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(172\)	\(11\)	\(161\)		\(163\)	\(11\)	\(152\)		\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)		\(161\)	\(11\)	\(150\)		\(152\)	\(11\)	\(141\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)		\(163\)	\(13\)	\(150\)		\(154\)	\(13\)	\(141\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)		\(170\)	\(13\)	\(157\)		\(161\)	\(13\)	\(148\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)		\(167\)	\(11\)	\(156\)		\(158\)	\(11\)	\(147\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)		\(166\)	\(13\)	\(153\)		\(157\)	\(13\)	\(144\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)		\(164\)	\(13\)	\(151\)		\(155\)	\(13\)	\(142\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)		\(169\)	\(11\)	\(158\)		\(160\)	\(11\)	\(149\)		\(9\)	\(0\)	\(9\)
Plus space			\(+\)		\(672\)	\(50\)	\(622\)		\(636\)	\(50\)	\(586\)		\(36\)	\(0\)	\(36\)
Minus space			\(-\)		\(660\)	\(46\)	\(614\)		\(624\)	\(46\)	\(578\)		\(36\)	\(0\)	\(36\)

Trace form

\( 96 q + 36 q^{7} + 192 q^{19} + 2400 q^{25} + 348 q^{31} - 672 q^{43} + 4344 q^{49} - 456 q^{61} - 2508 q^{67} + 216 q^{73} - 1920 q^{79} + 120 q^{85} - 3588 q^{91} + 792 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2160))\) 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
2160.4.a.a	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				540.4.a.b	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-17\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}-17q^{7}-30q^{11}-61q^{13}+\cdots\)
2160.4.a.b	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.f	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-14\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}-14q^{7}+3q^{11}+47q^{13}+\cdots\)
2160.4.a.c	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.b	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}-8q^{7}+18q^{11}+8q^{13}-15q^{17}+\cdots\)
2160.4.a.d	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				135.4.a.a	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+10q^{11}-80q^{13}-7q^{17}+\cdots\)
2160.4.a.e	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.e	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+4q^{7}-42q^{11}+20q^{13}+\cdots\)
2160.4.a.f	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				135.4.a.b	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+6q^{7}-47q^{11}-5q^{13}+131q^{17}+\cdots\)
2160.4.a.g	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.d	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(13\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+13q^{7}+30q^{11}-61q^{13}+\cdots\)
2160.4.a.h	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				540.4.a.a	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(22\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+22q^{7}+9q^{11}+17q^{13}+\cdots\)
2160.4.a.i	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.c	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(22\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+22q^{7}+12q^{11}+38q^{13}+\cdots\)
2160.4.a.j	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.a	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(34\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+34q^{7}-48q^{11}-70q^{13}+\cdots\)
2160.4.a.k	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				540.4.a.b	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-17\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}-17q^{7}+30q^{11}-61q^{13}+\cdots\)
2160.4.a.l	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.f	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-14\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}-14q^{7}-3q^{11}+47q^{13}+\cdots\)
2160.4.a.m	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.b	$1$	$1$	\(0\)	\(0\)	\(5\)	\(-8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}-8q^{7}-18q^{11}+8q^{13}+15q^{17}+\cdots\)
2160.4.a.n	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				135.4.a.a	$1$	$1$	\(0\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}-10q^{11}-80q^{13}+7q^{17}+\cdots\)
2160.4.a.o	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.e	$1$	$1$	\(0\)	\(0\)	\(5\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+4q^{7}+42q^{11}+20q^{13}+\cdots\)
2160.4.a.p	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				135.4.a.b	$1$	$1$	\(0\)	\(0\)	\(5\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+6q^{7}+47q^{11}-5q^{13}-131q^{17}+\cdots\)
2160.4.a.q	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.d	$1$	$1$	\(0\)	\(0\)	\(5\)	\(13\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+13q^{7}-30q^{11}-61q^{13}+\cdots\)
2160.4.a.r	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.c	$1$	$0$	\(0\)	\(0\)	\(5\)	\(22\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+22q^{7}-12q^{11}+38q^{13}+\cdots\)
2160.4.a.s	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				540.4.a.a	$1$	$0$	\(0\)	\(0\)	\(5\)	\(22\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+22q^{7}-9q^{11}+17q^{13}+\cdots\)
2160.4.a.t	$2160$	$4$	2160.a	1.a	$1$	$1$	$1$	$127.444$	\(\Q\)	None	✓				270.4.a.a	$1$	$0$	\(0\)	\(0\)	\(5\)	\(34\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+34q^{7}+48q^{11}-70q^{13}+\cdots\)
2160.4.a.u	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{41}) \)	None	✓				540.4.a.g	$1$	$0$	\(0\)	\(0\)	\(-10\)	\(-13\)		$-$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-5q^{5}+(-7-\beta )q^{7}+(10+5\beta )q^{11}+\cdots\)
2160.4.a.v	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{69}) \)	None	✓				540.4.a.f	$1$	$1$	\(0\)	\(0\)	\(-10\)	\(-10\)		$-$	$+$	$+$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-5q^{5}+(-5-\beta )q^{7}+(9-\beta )q^{11}+\cdots\)
2160.4.a.w	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{401}) \)	None	✓				270.4.a.m	$1$	$0$	\(0\)	\(0\)	\(-10\)	\(-1\)		$-$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-5q^{5}+(-1-\beta )q^{7}+(2^{4}-\beta )q^{11}+\cdots\)
2160.4.a.x	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{21}) \)	None	✓				540.4.a.e	$1$	$0$	\(0\)	\(0\)	\(-10\)	\(2\)		$-$	$-$	$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-5q^{5}+(1+\beta )q^{7}+(-21+\beta )q^{11}+\cdots\)
2160.4.a.y	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{241}) \)	None	✓				1080.4.a.a	$1$	$0$	\(0\)	\(0\)	\(-10\)	\(5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}+(3-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
2160.4.a.z	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{41}) \)	None	✓				540.4.a.g	$1$	$1$	\(0\)	\(0\)	\(10\)	\(-13\)		$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+5q^{5}+(-7-\beta )q^{7}+(-10-5\beta )q^{11}+\cdots\)
2160.4.a.ba	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{69}) \)	None	✓				540.4.a.f	$1$	$1$	\(0\)	\(0\)	\(10\)	\(-10\)		$-$	$-$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+5q^{5}+(-5-\beta )q^{7}+(-9+\beta )q^{11}+\cdots\)
2160.4.a.bb	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{401}) \)	None	✓				270.4.a.m	$1$	$1$	\(0\)	\(0\)	\(10\)	\(-1\)		$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+5q^{5}+(-1-\beta )q^{7}+(-2^{4}+\beta )q^{11}+\cdots\)
2160.4.a.bc	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{21}) \)	None	✓				540.4.a.e	$1$	$0$	\(0\)	\(0\)	\(10\)	\(2\)		$-$	$+$	$-$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+5q^{5}+(1+\beta )q^{7}+(21-\beta )q^{11}+(-7+\cdots)q^{13}+\cdots\)
2160.4.a.bd	$2160$	$4$	2160.a	1.a	$1$	$2$	$2$	$127.444$	\(\Q(\sqrt{241}) \)	None	✓				1080.4.a.a	$1$	$1$	\(0\)	\(0\)	\(10\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+(3-\beta )q^{7}+(2+\beta )q^{11}+(-9+\cdots)q^{13}+\cdots\)
2160.4.a.be	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.5637.1	None	✓		✓		135.4.a.f	$1$	$0$	\(0\)	\(0\)	\(-15\)	\(-44\)		$-$	$-$	$+$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q-5q^{5}+(-15-\beta _{1})q^{7}+(12-\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.bf	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.47977.1	None	✓				1080.4.a.h	$1$	$0$	\(0\)	\(0\)	\(-15\)	\(-9\)		$+$	$+$	$+$	$+$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-5q^{5}+(-3-\beta _{2})q^{7}+(6+\beta _{1}-\beta _{2})q^{11}+\cdots\)
2160.4.a.bg	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.985.1	None	✓				1080.4.a.g	$1$	$1$	\(0\)	\(0\)	\(-15\)	\(-6\)		$+$	$-$	$+$	$-$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-5q^{5}+(-2+\beta _{2})q^{7}+(4-\beta _{1}-\beta _{2})q^{11}+\cdots\)
2160.4.a.bh	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.1765.1	None	✓				1080.4.a.f	$1$	$1$	\(0\)	\(0\)	\(-15\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-5q^{5}+\beta _{1}q^{7}+(-9-\beta _{1}+2\beta _{2})q^{11}+\cdots\)
2160.4.a.bi	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.1772.1	None	✓		✓		135.4.a.e	$1$	$1$	\(0\)	\(0\)	\(-15\)	\(4\)		$-$	$+$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q-5q^{5}+(3\beta _{1}+\beta _{2})q^{7}+(3-5\beta _{1}+\beta _{2})q^{11}+\cdots\)
2160.4.a.bj	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.4281.1	None	✓				1080.4.a.e	$1$	$0$	\(0\)	\(0\)	\(-15\)	\(8\)		$+$	$+$	$+$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-5q^{5}+(3-\beta _{1})q^{7}+(-4+\beta _{1}-\beta _{2})q^{11}+\cdots\)
2160.4.a.bk	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.1257.1	None	✓				1080.4.a.d	$1$	$1$	\(0\)	\(0\)	\(-15\)	\(10\)		$+$	$-$	$+$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q-5q^{5}+(4-\beta _{1}-\beta _{2})q^{7}+(11-5\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.bl	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.697.1	None	✓				1080.4.a.c	$1$	$0$	\(0\)	\(0\)	\(-15\)	\(24\)		$+$	$+$	$+$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-5q^{5}+(8+\beta _{2})q^{7}+(2-\beta _{1}+3\beta _{2})q^{11}+\cdots\)
2160.4.a.bm	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.5637.1	None	✓				135.4.a.f	$1$	$0$	\(0\)	\(0\)	\(15\)	\(-44\)		$-$	$+$	$-$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+5q^{5}+(-15-\beta _{1})q^{7}+(-12+\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.bn	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.47977.1	None	✓				1080.4.a.h	$1$	$1$	\(0\)	\(0\)	\(15\)	\(-9\)		$+$	$+$	$-$	$-$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+5q^{5}+(-3-\beta _{2})q^{7}+(-6-\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.bo	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.985.1	None	✓				1080.4.a.g	$1$	$1$	\(0\)	\(0\)	\(15\)	\(-6\)		$+$	$+$	$-$	$-$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+5q^{5}+(-2+\beta _{2})q^{7}+(-4+\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.bp	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.1765.1	None	✓				1080.4.a.f	$1$	$0$	\(0\)	\(0\)	\(15\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+5q^{5}+\beta _{1}q^{7}+(9+\beta _{1}-2\beta _{2})q^{11}+\cdots\)
2160.4.a.bq	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.1772.1	None	✓				135.4.a.e	$1$	$0$	\(0\)	\(0\)	\(15\)	\(4\)		$-$	$+$	$-$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+5q^{5}+(3\beta _{1}+\beta _{2})q^{7}+(-3+5\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.br	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.4281.1	None	✓				1080.4.a.e	$1$	$0$	\(0\)	\(0\)	\(15\)	\(8\)		$+$	$-$	$-$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+5q^{5}+(3-\beta _{1})q^{7}+(4-\beta _{1}+\beta _{2})q^{11}+\cdots\)
2160.4.a.bs	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.1257.1	None	✓				1080.4.a.d	$1$	$1$	\(0\)	\(0\)	\(15\)	\(10\)		$+$	$+$	$-$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+5q^{5}+(4-\beta _{1}-\beta _{2})q^{7}+(-11+5\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.bt	$2160$	$4$	2160.a	1.a	$1$	$3$	$3$	$127.444$	3.3.697.1	None	✓				1080.4.a.c	$1$	$0$	\(0\)	\(0\)	\(15\)	\(24\)		$+$	$-$	$-$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+5q^{5}+(8+\beta _{2})q^{7}+(-2+\beta _{1}-3\beta _{2})q^{11}+\cdots\)
2160.4.a.bu	$2160$	$4$	2160.a	1.a	$1$	$4$	$4$	$127.444$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		1080.4.a.o	$1$	$1$	\(0\)	\(0\)	\(-20\)	\(-14\)		$+$	$-$	$+$	$-$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-5q^{5}+(-3+\beta _{2})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2160.4.a.bv	$2160$	$4$	2160.a	1.a	$1$	$4$	$4$	$127.444$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		1080.4.a.o	$1$	$0$	\(0\)	\(0\)	\(20\)	\(-14\)		$+$	$-$	$-$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+5q^{5}+(-3+\beta _{2})q^{7}+(1-\beta _{1})q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2160))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2160)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 2}\)