Space of modular forms of level 9240, weight 2, and trivial character

• Label: 9240.2.a
• Level: $9240$
• Weight: $2$
• Character orbit: 9240.a
• Rep. character: $\chi_{9240}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $63$
• Sturm bound: $4608$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 9240 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9240.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 63 \)
Sturm bound:			\(4608\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(13\), \(17\), \(19\), \(23\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9240))\).

	Total	New	Old
Modular forms	2336	120	2216
Cusp forms	2273	120	2153
Eisenstein series	63	0	63

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

\(2\)	\(3\)	\(5\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	$+$	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
Plus space					\(+\)	\(52\)
Minus space					\(-\)	\(68\)

Trace form

\( 120 q + 120 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9240))\) 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	5	7	11
9240.2.a.a	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.b	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.c	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.d	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.e	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.f	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.g	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.h	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.i	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.j	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
9240.2.a.k	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.l	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
9240.2.a.m	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
9240.2.a.n	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-q^{15}+\cdots\)
9240.2.a.o	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
9240.2.a.p	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
9240.2.a.q	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.r	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.s	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.t	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
9240.2.a.u	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.v	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.w	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.x	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.y	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
9240.2.a.z	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{15}+\cdots\)
9240.2.a.ba	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
9240.2.a.bb	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
9240.2.a.bc	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.bd	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
9240.2.a.be	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
9240.2.a.bf	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.bg	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
9240.2.a.bh	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
9240.2.a.bi	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
9240.2.a.bj	$9240$	$2$	9240.a	1.a	$1$	$1$	$1$	$73.782$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.bk	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
9240.2.a.bl	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.bm	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2\beta q^{13}+\cdots\)
9240.2.a.bn	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-2\beta q^{13}+\cdots\)
9240.2.a.bo	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(-3+\cdots)q^{13}+\cdots\)
9240.2.a.bp	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
9240.2.a.bq	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-\beta q^{13}+\cdots\)
9240.2.a.br	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-q^{15}+\cdots\)
9240.2.a.bs	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-2\beta q^{13}+\cdots\)
9240.2.a.bt	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(2+\beta )q^{13}+\cdots\)
9240.2.a.bu	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
9240.2.a.bv	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
9240.2.a.bw	$9240$	$2$	9240.a	1.a	$1$	$2$	$2$	$73.782$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
9240.2.a.bx	$9240$	$2$	9240.a	1.a	$1$	$3$	$3$	$73.782$	3.3.2300.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(3\)		$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
9240.2.a.by	$9240$	$2$	9240.a	1.a	$1$	$3$	$3$	$73.782$	3.3.6616.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(3\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
9240.2.a.bz	$9240$	$2$	9240.a	1.a	$1$	$3$	$3$	$73.782$	3.3.4860.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)
9240.2.a.ca	$9240$	$2$	9240.a	1.a	$1$	$4$	$4$	$73.782$	4.4.13968.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(-4\)		$-$	$+$	$-$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
9240.2.a.cb	$9240$	$2$	9240.a	1.a	$1$	$4$	$4$	$73.782$	4.4.16448.2	None	✓	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-\beta _{2}q^{13}+\cdots\)
9240.2.a.cc	$9240$	$2$	9240.a	1.a	$1$	$4$	$4$	$73.782$	4.4.40864.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
9240.2.a.cd	$9240$	$2$	9240.a	1.a	$1$	$4$	$4$	$73.782$	4.4.30056.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-\beta _{2}q^{13}+\cdots\)
9240.2.a.ce	$9240$	$2$	9240.a	1.a	$1$	$4$	$4$	$73.782$	4.4.19664.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(4\)		$+$	$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+\beta _{1}q^{13}+\cdots\)
9240.2.a.cf	$9240$	$2$	9240.a	1.a	$1$	$4$	$4$	$73.782$	4.4.19664.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(4\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
9240.2.a.cg	$9240$	$2$	9240.a	1.a	$1$	$4$	$4$	$73.782$	4.4.11324.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(-4\)		$-$	$-$	$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(1+\beta _{2}+\cdots)q^{13}+\cdots\)
9240.2.a.ch	$9240$	$2$	9240.a	1.a	$1$	$5$	$5$	$73.782$	5.5.2245192.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-5\)	\(-5\)		$+$	$+$	$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+\beta _{2}q^{13}+\cdots\)
9240.2.a.ci	$9240$	$2$	9240.a	1.a	$1$	$5$	$5$	$73.782$	5.5.1457888.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(-5\)	\(-5\)		$-$	$+$	$+$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+(1-\beta _{4})q^{13}+\cdots\)
9240.2.a.cj	$9240$	$2$	9240.a	1.a	$1$	$5$	$5$	$73.782$	5.5.9229792.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(-5\)	\(5\)		$-$	$+$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
9240.2.a.ck	$9240$	$2$	9240.a	1.a	$1$	$6$	$6$	$73.782$	6.6.235324384.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(6\)	\(6\)		$-$	$-$	$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+(1-\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1848))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4620))\)\(^{\oplus 2}\)