Space of modular forms of level 9408, weight 2, and trivial character

• Label: 9408.2.a
• Level: $9408$
• Weight: $2$
• Character orbit: 9408.a
• Rep. character: $\chi_{9408}(1,\cdot)$
• Character field: $\Q$
• Dimension: $164$
• Newform subspaces: $118$
• Sturm bound: $3584$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9408.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 118 \)
Sturm bound:			\(3584\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9408))\).

	Total	New	Old
Modular forms	1888	164	1724
Cusp forms	1697	164	1533
Eisenstein series	191	0	191

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	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(21\)
\(+\)	\(+\)	\(-\)	\(-\)	\(21\)
\(+\)	\(-\)	\(+\)	\(-\)	\(23\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(19\)
\(-\)	\(+\)	\(-\)	\(+\)	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	\(17\)
\(-\)	\(-\)	\(-\)	\(-\)	\(24\)
Plus space			\(+\)	\(77\)
Minus space			\(-\)	\(87\)

Trace form

\( 164 q + 164 q^{9} - 8 q^{13} - 8 q^{17} + 156 q^{25} + 16 q^{29} + 8 q^{37} - 8 q^{41} + 16 q^{53} - 24 q^{61} - 16 q^{69} + 8 q^{73} + 164 q^{81} - 64 q^{85} + 8 q^{89} - 8 q^{93} + 8 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9408))\) 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
9408.2.a.a	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.e	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots\)
9408.2.a.b	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				294.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots\)
9408.2.a.c	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9408.2.a.d	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.b	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.e	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.a	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots\)
9408.2.a.f	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.b	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots\)
9408.2.a.g	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9408.2.a.h	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				24.2.a.a	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.i	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.i.a	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots\)
9408.2.a.j	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				4704.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.k	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				21.2.e.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
9408.2.a.l	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				588.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
9408.2.a.m	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				21.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.n	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9408.2.a.o	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+q^{11}+q^{15}-8q^{17}+\cdots\)
9408.2.a.p	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.q	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+5q^{11}+q^{15}-4q^{17}+\cdots\)
9408.2.a.r	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-6q^{11}+2q^{13}+4q^{19}+\cdots\)
9408.2.a.s	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.t	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.u	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				1176.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-4q^{13}+4q^{17}+4q^{19}+\cdots\)
9408.2.a.v	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				1176.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+4q^{13}-4q^{17}+4q^{19}+\cdots\)
9408.2.a.w	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.x	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.d	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.y	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.z	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-5q^{11}-q^{15}+4q^{17}+\cdots\)
9408.2.a.ba	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.bb	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-q^{11}-q^{15}+8q^{17}+\cdots\)
9408.2.a.bc	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
9408.2.a.bd	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
9408.2.a.be	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+6q^{13}-2q^{15}+\cdots\)
9408.2.a.bf	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				588.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
9408.2.a.bg	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				21.2.e.a	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
9408.2.a.bh	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				4704.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bi	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.i.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots\)
9408.2.a.bj	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				96.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.bk	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.b	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots\)
9408.2.a.bl	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
9408.2.a.bm	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.b	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.bn	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9408.2.a.bo	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				294.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots\)
9408.2.a.bp	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.e	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots\)
9408.2.a.bq	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9408.2.a.br	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				294.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
9408.2.a.bs	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.e	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots\)
9408.2.a.bt	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
9408.2.a.bu	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.b	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.bv	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				21.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.bw	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9408.2.a.bx	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.i.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots\)
9408.2.a.by	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				4704.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bz	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				21.2.e.a	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
9408.2.a.ca	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				588.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
9408.2.a.cb	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9408.2.a.cc	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				24.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.cd	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.b	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots\)
9408.2.a.ce	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-5q^{11}-q^{15}-4q^{17}+\cdots\)
9408.2.a.cf	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.cg	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-q^{11}-q^{15}-8q^{17}+\cdots\)
9408.2.a.ch	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.ci	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.cj	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.ck	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				1176.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-4q^{13}+4q^{17}-4q^{19}+\cdots\)
9408.2.a.cl	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				1176.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+4q^{13}-4q^{17}-4q^{19}+\cdots\)
9408.2.a.cm	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.cn	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.co	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+6q^{11}+2q^{13}-4q^{19}+\cdots\)
9408.2.a.cp	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+q^{11}+q^{15}+8q^{17}+\cdots\)
9408.2.a.cq	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.cr	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+5q^{11}+q^{15}+4q^{17}+\cdots\)
9408.2.a.cs	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.q.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots\)
9408.2.a.ct	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				96.2.a.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.cu	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				588.2.a.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
9408.2.a.cv	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				21.2.e.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}-q^{13}+\cdots\)
9408.2.a.cw	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				4704.2.a.d	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.cx	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.i.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots\)
9408.2.a.cy	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.a.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
9408.2.a.cz	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.a.d	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
9408.2.a.da	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				168.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots\)
9408.2.a.db	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				42.2.e.b	$1$	$1$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.dc	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
9408.2.a.dd	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				672.2.q.e	$1$	$1$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots\)
9408.2.a.de	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				294.2.a.b	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots\)
9408.2.a.df	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	\(\Q\)	None	✓				84.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9408.2.a.dg	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.j	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.dh	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.l	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.di	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				147.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots\)
9408.2.a.dj	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	✓				168.2.q.c	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dk	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bi	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots\)
9408.2.a.dl	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bj	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.dm	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bk	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+\beta q^{17}+\cdots\)
9408.2.a.dn	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bl	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.do	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{3}) \)	None	✓				672.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}+(2-\beta )q^{11}+2q^{13}+\cdots\)
9408.2.a.dp	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	✓				168.2.q.c	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.dq	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				147.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+q^{9}-2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.dr	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.l	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.ds	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.j	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dt	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				147.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}-2q^{11}+\cdots\)
9408.2.a.du	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.j	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.dv	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.l	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dw	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	✓				168.2.q.c	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dx	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{3}) \)	None	✓				672.2.a.i	$1$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9408.2.a.dy	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bl	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.dz	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bk	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+\beta q^{11}+\beta q^{13}-\beta q^{17}+\cdots\)
9408.2.a.ea	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bj	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.eb	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				4704.2.a.bi	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots\)
9408.2.a.ec	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	✓				168.2.q.c	$1$	$0$	\(0\)	\(2\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.ed	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.l	$1$	$1$	\(0\)	\(2\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.ee	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.j	$1$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.ef	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	✓				147.2.a.d	$1$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.eg	$9408$	$2$	9408.a	1.a	$1$	$3$	$3$	$75.123$	3.3.621.1	None	✓		✓		672.2.q.k	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.eh	$9408$	$2$	9408.a	1.a	$1$	$3$	$3$	$75.123$	3.3.621.1	None	✓				672.2.q.k	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ei	$9408$	$2$	9408.a	1.a	$1$	$3$	$3$	$75.123$	3.3.621.1	None	✓		✓		672.2.q.k	$1$	$1$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ej	$9408$	$2$	9408.a	1.a	$1$	$3$	$3$	$75.123$	3.3.621.1	None	✓				672.2.q.k	$1$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.ek	$9408$	$2$	9408.a	1.a	$1$	$4$	$4$	$75.123$	4.4.2624.1	None	✓				4704.2.a.bw	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.el	$9408$	$2$	9408.a	1.a	$1$	$4$	$4$	$75.123$	4.4.2624.1	None	✓				4704.2.a.bw	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
9408.2.a.em	$9408$	$2$	9408.a	1.a	$1$	$4$	$4$	$75.123$	4.4.2624.1	None	✓				4704.2.a.bw	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.en	$9408$	$2$	9408.a	1.a	$1$	$4$	$4$	$75.123$	4.4.2624.1	None	✓				4704.2.a.bw	$1$	$0$	\(0\)	\(4\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9408))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9408)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4704))\)\(^{\oplus 2}\)