Space of modular forms of level 9072, weight 2, and trivial character

• Label: 9072.2.a
• Level: $9072$
• Weight: $2$
• Character orbit: 9072.a
• Rep. character: $\chi_{9072}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $66$
• Sturm bound: $3456$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9072 = 2^{4} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9072.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 66 \)
Sturm bound:			\(3456\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9072))\).

	Total	New	Old
Modular forms	1800	144	1656
Cusp forms	1657	144	1513
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.

\(2\)	\(3\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(216\)	\(19\)	\(197\)		\(199\)	\(19\)	\(180\)		\(17\)	\(0\)	\(17\)
\(+\)	\(+\)	\(-\)	\(-\)		\(234\)	\(19\)	\(215\)		\(216\)	\(19\)	\(197\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)		\(234\)	\(17\)	\(217\)		\(216\)	\(17\)	\(199\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(-\)	\(+\)		\(216\)	\(17\)	\(199\)		\(198\)	\(17\)	\(181\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)		\(222\)	\(19\)	\(203\)		\(204\)	\(19\)	\(185\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)	\(+\)		\(228\)	\(15\)	\(213\)		\(210\)	\(15\)	\(195\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)	\(+\)		\(228\)	\(17\)	\(211\)		\(210\)	\(17\)	\(193\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)		\(222\)	\(21\)	\(201\)		\(204\)	\(21\)	\(183\)		\(18\)	\(0\)	\(18\)
Plus space			\(+\)		\(888\)	\(68\)	\(820\)		\(817\)	\(68\)	\(749\)		\(71\)	\(0\)	\(71\)
Minus space			\(-\)		\(912\)	\(76\)	\(836\)		\(840\)	\(76\)	\(764\)		\(72\)	\(0\)	\(72\)

Trace form

\( 144 q + 144 q^{25} - 24 q^{37} + 144 q^{49} - 24 q^{61} - 24 q^{67} + 24 q^{73} - 24 q^{79} - 24 q^{85} + 24 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9072))\) 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	7
9072.2.a.a	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				4536.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+q^{7}+3q^{11}+4q^{13}-6q^{17}+\cdots\)
9072.2.a.b	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				1134.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}+6q^{11}-q^{13}+3q^{17}+\cdots\)
9072.2.a.c	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				126.2.f.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}+6q^{11}+2q^{13}+6q^{17}+\cdots\)
9072.2.a.d	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				504.2.r.b	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-3q^{11}-6q^{13}-7q^{17}+\cdots\)
9072.2.a.e	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				4536.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+3q^{11}+2q^{17}+2q^{19}+\cdots\)
9072.2.a.f	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				126.2.f.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+q^{11}-6q^{13}+5q^{17}+\cdots\)
9072.2.a.g	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				2268.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+q^{11}+2q^{17}-2q^{19}+\cdots\)
9072.2.a.h	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				4536.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+3q^{13}+7q^{17}-4q^{19}+\cdots\)
9072.2.a.i	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				504.2.r.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+6q^{11}+6q^{13}-2q^{17}+\cdots\)
9072.2.a.j	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				567.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-2q^{11}-5q^{13}-3q^{17}+\cdots\)
9072.2.a.k	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				1134.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+2q^{11}+3q^{13}+q^{17}+\cdots\)
9072.2.a.l	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				2268.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{11}-4q^{13}-6q^{17}+4q^{19}+\cdots\)
9072.2.a.m	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				2268.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+3q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
9072.2.a.n	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				504.2.r.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-6q^{11}+6q^{13}+2q^{17}+\cdots\)
9072.2.a.o	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				4536.2.a.e	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+3q^{13}-7q^{17}-4q^{19}+\cdots\)
9072.2.a.p	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				1134.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-2q^{11}+3q^{13}-q^{17}+\cdots\)
9072.2.a.q	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				567.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+2q^{11}-5q^{13}+3q^{17}+\cdots\)
9072.2.a.r	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				4536.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{11}-2q^{17}+2q^{19}+\cdots\)
9072.2.a.s	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				504.2.r.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+3q^{11}-6q^{13}+7q^{17}+\cdots\)
9072.2.a.t	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				126.2.f.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-q^{11}-6q^{13}-5q^{17}+\cdots\)
9072.2.a.u	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				2268.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-q^{11}-2q^{17}-2q^{19}+\cdots\)
9072.2.a.v	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				1134.2.a.d	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-6q^{11}-q^{13}-3q^{17}+\cdots\)
9072.2.a.w	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				126.2.f.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-6q^{11}+2q^{13}-6q^{17}+\cdots\)
9072.2.a.x	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	\(\Q\)	None	✓				4536.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+q^{7}-3q^{11}+4q^{13}+6q^{17}+\cdots\)
9072.2.a.y	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.l	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{5}+q^{7}+(1+3\beta )q^{11}+\cdots\)
9072.2.a.z	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				4536.2.a.l	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+(2+\beta )q^{11}-4q^{13}+\cdots\)
9072.2.a.ba	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				4536.2.a.k	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{5}+q^{7}+(3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
9072.2.a.bb	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{33}) \)	None	✓				126.2.f.d	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}+(2-\beta )q^{11}+2q^{13}+\cdots\)
9072.2.a.bc	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{21}) \)	None	✓				4536.2.a.m	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+(1-\beta )q^{11}-q^{13}-\beta q^{17}+\cdots\)
9072.2.a.bd	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{6}) \)	None	✓				126.2.f.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+q^{7}+2q^{11}+2\beta q^{13}+\cdots\)
9072.2.a.be	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{33}) \)	None	✓				4536.2.a.n	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+q^{7}+(1-\beta )q^{11}+(4-\beta )q^{13}+\cdots\)
9072.2.a.bf	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.j	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+(-3+\beta )q^{11}-q^{13}+\cdots\)
9072.2.a.bg	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				2268.2.a.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}-q^{7}-\beta q^{11}-4q^{13}+2\beta q^{17}+\cdots\)
9072.2.a.bh	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				2268.2.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}-2\beta q^{11}+5q^{13}+\beta q^{17}+\cdots\)
9072.2.a.bi	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.j	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}+(3+\beta )q^{11}-q^{13}+(-3+\cdots)q^{17}+\cdots\)
9072.2.a.bj	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{33}) \)	None	✓				4536.2.a.n	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+q^{7}+(-1+\beta )q^{11}+(4-\beta )q^{13}+\cdots\)
9072.2.a.bk	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{6}) \)	None	✓				126.2.f.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}-2q^{11}-2\beta q^{13}+\cdots\)
9072.2.a.bl	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{21}) \)	None	✓				4536.2.a.m	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+(-1-\beta )q^{11}-q^{13}+\cdots\)
9072.2.a.bm	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{33}) \)	None	✓				126.2.f.d	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(-2+\beta )q^{11}+2q^{13}+\cdots\)
9072.2.a.bn	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				4536.2.a.k	$1$	$1$	\(0\)	\(0\)	\(4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+q^{7}+(-3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
9072.2.a.bo	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				4536.2.a.l	$1$	$1$	\(0\)	\(0\)	\(4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+(-2+\beta )q^{11}-4q^{13}+\cdots\)
9072.2.a.bp	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	\(\Q(\sqrt{3}) \)	None	✓				1134.2.a.l	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+q^{7}+(-1+3\beta )q^{11}+\cdots\)
9072.2.a.bq	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓				63.2.f.b	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{5}+q^{7}+(1-2\beta _{1}-\beta _{2})q^{11}+\cdots\)
9072.2.a.br	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	\(\Q(\zeta_{18})^+\)	None	✓				504.2.r.c	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{5}-q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots\)
9072.2.a.bs	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	\(\Q(\zeta_{18})^+\)	None	✓				63.2.f.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}-q^{7}+(2+\beta _{1})q^{11}+\cdots\)
9072.2.a.bt	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓				252.2.j.b	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}-q^{7}+(2+\beta _{1})q^{11}+\cdots\)
9072.2.a.bu	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.621.1	None	✓				567.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}-q^{7}+(2-\beta _{2})q^{11}+\cdots\)
9072.2.a.bv	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓				252.2.j.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+q^{7}+(1+\beta _{1}+2\beta _{2})q^{11}+\cdots\)
9072.2.a.bw	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.837.1	None	✓				4536.2.a.t	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}-q^{7}+(-1+\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots\)
9072.2.a.bx	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.837.1	None	✓				4536.2.a.t	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}-q^{7}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots\)
9072.2.a.by	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓				252.2.j.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+q^{7}+(-1-\beta _{1}-2\beta _{2})q^{11}+\cdots\)
9072.2.a.bz	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓				252.2.j.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}-q^{7}+(-2-\beta _{1})q^{11}+\cdots\)
9072.2.a.ca	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	\(\Q(\zeta_{18})^+\)	None	✓				63.2.f.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}-q^{7}+(-2-\beta _{1})q^{11}+\cdots\)
9072.2.a.cb	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.621.1	None	✓				567.2.a.e	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}-q^{7}+(-2+\beta _{2})q^{11}+\cdots\)
9072.2.a.cc	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	\(\Q(\zeta_{18})^+\)	None	✓				504.2.r.c	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}-q^{7}+(\beta _{1}-2\beta _{2})q^{11}+\cdots\)
9072.2.a.cd	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓				63.2.f.b	$1$	$0$	\(0\)	\(0\)	\(5\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta _{2})q^{5}+q^{7}+(-1+2\beta _{1}+\beta _{2})q^{11}+\cdots\)
9072.2.a.ce	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	4.4.22545.1	None	✓		✓		504.2.r.d	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{3})q^{5}-q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
9072.2.a.cf	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	\(\Q(\sqrt{15 +4 \sqrt{3}})\)	None	✓				4536.2.a.w	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1}+\beta _{2})q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
9072.2.a.cg	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	4.4.45729.1	None	✓				504.2.r.e	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+q^{7}+(-2+\beta _{1})q^{11}+\cdots\)
9072.2.a.ch	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	\(\Q(\sqrt{3}, \sqrt{19})\)	None	✓				2268.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
9072.2.a.ci	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				567.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{5}+q^{7}+\beta _{2}q^{11}+4q^{13}+\cdots\)
9072.2.a.cj	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	4.4.45729.1	None	✓				504.2.r.e	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+q^{7}+(2-\beta _{1})q^{11}+(-1+\cdots)q^{13}+\cdots\)
9072.2.a.ck	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	\(\Q(\sqrt{15 +4 \sqrt{3}})\)	None	✓				4536.2.a.w	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}-\beta _{2})q^{5}-q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
9072.2.a.cl	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	4.4.22545.1	None	✓				504.2.r.d	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{3})q^{5}-q^{7}+(2-\beta _{1}+\beta _{3})q^{11}+\cdots\)
9072.2.a.cm	$9072$	$2$	9072.a	1.a	$1$	$5$	$5$	$72.440$	5.5.1425384.1	None	✓		✓		504.2.r.f	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(5\)		$+$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}+q^{7}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
9072.2.a.cn	$9072$	$2$	9072.a	1.a	$1$	$5$	$5$	$72.440$	5.5.1425384.1	None	✓		✓		504.2.r.f	$1$	$0$	\(0\)	\(0\)	\(3\)	\(5\)		$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{5}+q^{7}+(1-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9072))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9072)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(567))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(756))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2268))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4536))\)\(^{\oplus 2}\)