Space of modular forms of level 9024, weight 2, and trivial character

• Label: 9024.2.a
• Level: $9024$
• Weight: $2$
• Character orbit: 9024.a
• Rep. character: $\chi_{9024}(1,\cdot)$
• Character field: $\Q$
• Dimension: $184$
• Newform subspaces: $88$
• Sturm bound: $3072$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 9024 = 2^{6} \cdot 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9024.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 88 \)
Sturm bound:			\(3072\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9024))\).

	Total	New	Old
Modular forms	1560	184	1376
Cusp forms	1513	184	1329
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(21\)
\(+\)	\(+\)	\(-\)	$-$	\(25\)
\(+\)	\(-\)	\(+\)	$-$	\(24\)
\(+\)	\(-\)	\(-\)	$+$	\(20\)
\(-\)	\(+\)	\(+\)	$-$	\(25\)
\(-\)	\(+\)	\(-\)	$+$	\(21\)
\(-\)	\(-\)	\(+\)	$+$	\(22\)
\(-\)	\(-\)	\(-\)	$-$	\(26\)
Plus space			\(+\)	\(84\)
Minus space			\(-\)	\(100\)

Trace form

\( 184 q + 184 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9024))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	47
9024.2.a.a	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
9024.2.a.b	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+5q^{7}+q^{9}+3q^{11}+\cdots\)
9024.2.a.c	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-6q^{11}+2q^{15}+\cdots\)
9024.2.a.d	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
9024.2.a.e	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
9024.2.a.f	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
9024.2.a.g	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9024.2.a.h	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+6q^{13}+\cdots\)
9024.2.a.i	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}-6q^{13}-6q^{17}+\cdots\)
9024.2.a.j	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9024.2.a.k	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}+4q^{13}-2q^{17}+\cdots\)
9024.2.a.l	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{13}+2q^{17}+6q^{19}+\cdots\)
9024.2.a.m	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
9024.2.a.n	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9024.2.a.o	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
9024.2.a.p	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots\)
9024.2.a.q	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
9024.2.a.r	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9024.2.a.s	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
9024.2.a.t	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
9024.2.a.u	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots\)
9024.2.a.v	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9024.2.a.w	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9024.2.a.x	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
9024.2.a.y	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots\)
9024.2.a.z	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-5q^{7}+q^{9}-3q^{11}+\cdots\)
9024.2.a.ba	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
9024.2.a.bb	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(1\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
9024.2.a.bc	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
9024.2.a.bd	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9024.2.a.be	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+6q^{11}-2q^{15}+\cdots\)
9024.2.a.bf	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+6q^{13}+\cdots\)
9024.2.a.bg	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9024.2.a.bh	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{13}+2q^{17}-6q^{19}+\cdots\)
9024.2.a.bi	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
9024.2.a.bj	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9024.2.a.bk	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-6q^{13}-6q^{17}+\cdots\)
9024.2.a.bl	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9024.2.a.bm	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
9024.2.a.bn	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
9024.2.a.bo	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
9024.2.a.bp	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9024.2.a.bq	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9024.2.a.br	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
9024.2.a.bs	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9024.2.a.bt	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9024.2.a.bu	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
9024.2.a.bv	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
9024.2.a.bw	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(4\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{13}+\cdots\)
9024.2.a.bx	$9024$	$2$	9024.a	1.a	$1$	$1$	$1$	$72.057$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
9024.2.a.by	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$2$	\(0\)	\(-2\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}-2q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
9024.2.a.bz	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
9024.2.a.ca	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
9024.2.a.cb	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+2q^{7}+q^{9}-\beta q^{11}+\cdots\)
9024.2.a.cc	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
9024.2.a.cd	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+2q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
9024.2.a.ce	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
9024.2.a.cf	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
9024.2.a.cg	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-2q^{7}+q^{9}+\beta q^{11}+\cdots\)
9024.2.a.ch	$9024$	$2$	9024.a	1.a	$1$	$2$	$2$	$72.057$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+2\beta q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
9024.2.a.ci	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(1\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
9024.2.a.cj	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
9024.2.a.ck	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9024.2.a.cl	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.2700.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
9024.2.a.cm	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9024.2.a.cn	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots\)
9024.2.a.co	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots\)
9024.2.a.cp	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9024.2.a.cq	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
9024.2.a.cr	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-1\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots\)
9024.2.a.cs	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9024.2.a.ct	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.2700.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
9024.2.a.cu	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9024.2.a.cv	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
9024.2.a.cw	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
9024.2.a.cx	$9024$	$2$	9024.a	1.a	$1$	$3$	$3$	$72.057$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(5\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)
9024.2.a.cy	$9024$	$2$	9024.a	1.a	$1$	$4$	$4$	$72.057$	4.4.11348.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-1\)	\(7\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
9024.2.a.cz	$9024$	$2$	9024.a	1.a	$1$	$4$	$4$	$72.057$	4.4.2777.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(3\)	\(1\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
9024.2.a.da	$9024$	$2$	9024.a	1.a	$1$	$4$	$4$	$72.057$	4.4.11348.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(-1\)	\(-7\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+q^{9}+\cdots\)
9024.2.a.db	$9024$	$2$	9024.a	1.a	$1$	$4$	$4$	$72.057$	4.4.2777.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9024.2.a.dc	$9024$	$2$	9024.a	1.a	$1$	$5$	$5$	$72.057$	5.5.2324776.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{3})q^{5}-\beta _{4}q^{7}+q^{9}+\cdots\)
9024.2.a.dd	$9024$	$2$	9024.a	1.a	$1$	$5$	$5$	$72.057$	5.5.2324776.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{3})q^{5}+\beta _{4}q^{7}+q^{9}+\cdots\)
9024.2.a.de	$9024$	$2$	9024.a	1.a	$1$	$6$	$6$	$72.057$	6.6.6697472.1	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-2\)	\(6\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+(1-\beta _{5})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
9024.2.a.df	$9024$	$2$	9024.a	1.a	$1$	$6$	$6$	$72.057$	6.6.262900480.1	None	✓	$1$	$0$	\(0\)	\(-6\)	\(2\)	\(6\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)
9024.2.a.dg	$9024$	$2$	9024.a	1.a	$1$	$6$	$6$	$72.057$	6.6.6697472.1	None	✓	$1$	$1$	\(0\)	\(6\)	\(-2\)	\(-6\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{5})q^{7}+q^{9}+\cdots\)
9024.2.a.dh	$9024$	$2$	9024.a	1.a	$1$	$6$	$6$	$72.057$	6.6.262900480.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(2\)	\(-6\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots\)
9024.2.a.di	$9024$	$2$	9024.a	1.a	$1$	$8$	$8$	$72.057$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-8\)	\(6\)	\(2\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}-\beta _{6}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
9024.2.a.dj	$9024$	$2$	9024.a	1.a	$1$	$8$	$8$	$72.057$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(6\)	\(-2\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2})q^{5}+\beta _{6}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(141))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(282))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(564))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2256))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4512))\)\(^{\oplus 2}\)