Space of modular forms of level 9744, weight 2, and trivial character

• Label: 9744.2.a
• Level: $9744$
• Weight: $2$
• Character orbit: 9744.a
• Rep. character: $\chi_{9744}(1,\cdot)$
• Character field: $\Q$
• Dimension: $168$
• Newform subspaces: $61$
• Sturm bound: $3840$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 9744 = 2^{4} \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9744.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 61 \)
Sturm bound:			\(3840\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9744))\).

	Total	New	Old
Modular forms	1944	168	1776
Cusp forms	1897	168	1729
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.

\(2\)	\(3\)	\(7\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(10\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(12\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(9\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(11\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(10\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(12\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(11\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(10\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(10\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(12\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(11\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(9\)
Plus space				\(+\)	\(76\)
Minus space				\(-\)	\(92\)

Trace form

\( 168 q + 168 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9744))\) 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	7	29
9744.2.a.a	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-4\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{7}+q^{9}-4q^{11}+4q^{15}+\cdots\)
9744.2.a.b	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9744.2.a.c	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9744.2.a.d	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots\)
9744.2.a.e	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9744.2.a.f	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9744.2.a.g	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9744.2.a.h	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
9744.2.a.i	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
9744.2.a.j	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}+5q^{11}+3q^{13}+\cdots\)
9744.2.a.k	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9744.2.a.l	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9744.2.a.m	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
9744.2.a.n	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
9744.2.a.o	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+6q^{13}-2q^{15}+\cdots\)
9744.2.a.p	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9744.2.a.q	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9744.2.a.r	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9744.2.a.s	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-4q^{11}+q^{21}-5q^{25}+\cdots\)
9744.2.a.t	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
9744.2.a.u	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
9744.2.a.v	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
9744.2.a.w	$9744$	$2$	9744.a	1.a	$1$	$1$	$1$	$77.806$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{7}+q^{9}+2q^{13}+4q^{15}+\cdots\)
9744.2.a.x	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}-q^{7}+q^{9}-2\beta q^{11}+\cdots\)
9744.2.a.y	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
9744.2.a.z	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+2q^{11}+(-2+\cdots)q^{13}+\cdots\)
9744.2.a.ba	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}-q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
9744.2.a.bb	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
9744.2.a.bc	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots\)
9744.2.a.bd	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}-2\beta q^{13}+\cdots\)
9744.2.a.be	$9744$	$2$	9744.a	1.a	$1$	$2$	$2$	$77.806$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
9744.2.a.bf	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-6\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta _{2})q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
9744.2.a.bg	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.564.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
9744.2.a.bh	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(\beta _{1}-\beta _{2})q^{5}+q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bi	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+(3-\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bj	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.2920.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+\beta _{2}q^{11}+\cdots\)
9744.2.a.bk	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.1304.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}-q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bl	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.404.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{2})q^{5}-q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bm	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bn	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.892.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bo	$9744$	$2$	9744.a	1.a	$1$	$3$	$3$	$77.806$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(3+\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bp	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.16448.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{3}q^{5}-q^{7}+q^{9}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bq	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.11344.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.br	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.14656.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
9744.2.a.bs	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.6224.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{3}q^{5}+q^{7}+q^{9}+(1-2\beta _{1}+\cdots)q^{11}+\cdots\)
9744.2.a.bt	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.6224.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
9744.2.a.bu	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.4352.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+q^{7}+q^{9}+\cdots\)
9744.2.a.bv	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.14656.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{3}q^{5}-q^{7}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
9744.2.a.bw	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.18688.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(0\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(-\beta _{1}-\beta _{3})q^{11}+\cdots\)
9744.2.a.bx	$9744$	$2$	9744.a	1.a	$1$	$4$	$4$	$77.806$	4.4.33428.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{2})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
9744.2.a.by	$9744$	$2$	9744.a	1.a	$1$	$5$	$5$	$77.806$	5.5.51621840.1	None	✓	$1$	$0$	\(0\)	\(-5\)	\(2\)	\(5\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{3}q^{5}+q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)
9744.2.a.bz	$9744$	$2$	9744.a	1.a	$1$	$5$	$5$	$77.806$	5.5.1280720.1	None	✓	$1$	$1$	\(0\)	\(5\)	\(-4\)	\(5\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{4})q^{5}+q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
9744.2.a.ca	$9744$	$2$	9744.a	1.a	$1$	$5$	$5$	$77.806$	5.5.1401440.1	None	✓	$1$	$1$	\(0\)	\(5\)	\(-2\)	\(-5\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
9744.2.a.cb	$9744$	$2$	9744.a	1.a	$1$	$5$	$5$	$77.806$	5.5.15122768.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(2\)	\(-5\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
9744.2.a.cc	$9744$	$2$	9744.a	1.a	$1$	$5$	$5$	$77.806$	5.5.6520400.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(4\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
9744.2.a.cd	$9744$	$2$	9744.a	1.a	$1$	$5$	$5$	$77.806$	5.5.16295936.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(6\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
9744.2.a.ce	$9744$	$2$	9744.a	1.a	$1$	$6$	$6$	$77.806$	6.6.34846148.1	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-2\)	\(6\)		$+$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{3}q^{5}+q^{7}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
9744.2.a.cf	$9744$	$2$	9744.a	1.a	$1$	$6$	$6$	$77.806$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(-4\)	\(-6\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{4})q^{5}-q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
9744.2.a.cg	$9744$	$2$	9744.a	1.a	$1$	$6$	$6$	$77.806$	6.6.89122816.1	None	✓	$1$	$0$	\(0\)	\(6\)	\(2\)	\(6\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{4}q^{5}+q^{7}+q^{9}+(1-\beta _{3}+\cdots)q^{11}+\cdots\)
9744.2.a.ch	$9744$	$2$	9744.a	1.a	$1$	$7$	$7$	$77.806$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(4\)	\(-7\)		$+$	$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{3})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
9744.2.a.ci	$9744$	$2$	9744.a	1.a	$1$	$8$	$8$	$77.806$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-8\)	\(2\)	\(-8\)		$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}-\beta _{4}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9744))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(203))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(348))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(406))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(609))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(696))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(812))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1218))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2436))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4872))\)\(^{\oplus 2}\)