Space of modular forms of level 14400, weight 2, and trivial character

• Label: 14400.2.a
• Level: $14400$
• Weight: $2$
• Character orbit: 14400.a
• Rep. character: $\chi_{14400}(1,\cdot)$
• Character field: $\Q$
• Dimension: $187$
• Newform subspaces: $162$
• Sturm bound: $5760$

Defining parameters

Level:	\( N \)	\(=\)	\( 14400 = 2^{6} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	14400.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 162 \)
Sturm bound:			\(5760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(14400))\).

	Total	New	Old
Modular forms	3024	193	2831
Cusp forms	2737	187	2550
Eisenstein series	287	6	281

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

\(2\)	\(3\)	\(5\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(372\)	\(17\)	\(355\)		\(337\)	\(17\)	\(320\)		\(35\)	\(0\)	\(35\)
\(+\)	\(+\)	\(-\)	\(-\)		\(380\)	\(22\)	\(358\)		\(344\)	\(22\)	\(322\)		\(36\)	\(0\)	\(36\)
\(+\)	\(-\)	\(+\)	\(-\)		\(384\)	\(28\)	\(356\)		\(348\)	\(27\)	\(321\)		\(36\)	\(1\)	\(35\)
\(+\)	\(-\)	\(-\)	\(+\)		\(376\)	\(30\)	\(346\)		\(340\)	\(28\)	\(312\)		\(36\)	\(2\)	\(34\)
\(-\)	\(+\)	\(+\)	\(-\)		\(384\)	\(19\)	\(365\)		\(348\)	\(19\)	\(329\)		\(36\)	\(0\)	\(36\)
\(-\)	\(+\)	\(-\)	\(+\)		\(376\)	\(18\)	\(358\)		\(340\)	\(18\)	\(322\)		\(36\)	\(0\)	\(36\)
\(-\)	\(-\)	\(+\)	\(+\)		\(372\)	\(27\)	\(345\)		\(336\)	\(26\)	\(310\)		\(36\)	\(1\)	\(35\)
\(-\)	\(-\)	\(-\)	\(-\)		\(380\)	\(32\)	\(348\)		\(344\)	\(30\)	\(314\)		\(36\)	\(2\)	\(34\)
Plus space			\(+\)		\(1496\)	\(92\)	\(1404\)		\(1353\)	\(89\)	\(1264\)		\(143\)	\(3\)	\(140\)
Minus space			\(-\)		\(1528\)	\(101\)	\(1427\)		\(1384\)	\(98\)	\(1286\)		\(144\)	\(3\)	\(141\)

Trace form

\( 187 q + 6 q^{13} - 6 q^{17} + 10 q^{29} + 14 q^{37} - 6 q^{41} + 171 q^{49} - 14 q^{53} + 30 q^{61} + 6 q^{73} + 48 q^{77} + 18 q^{89} + 14 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(14400))\) 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	5
14400.2.a.a	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{7}-6q^{11}+3q^{13}+2q^{17}-q^{19}+\cdots\)
14400.2.a.b	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$1$		\(q-5q^{7}-5q^{13}-q^{19}+7q^{31}+10q^{37}+\cdots\)
14400.2.a.c	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-5\)		$+$	$+$	$+$	$+$	$1$		\(q-5q^{7}+5q^{13}+q^{19}-7q^{31}-10q^{37}+\cdots\)
14400.2.a.d	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{7}+6q^{11}-3q^{13}-2q^{17}+q^{19}+\cdots\)
14400.2.a.e	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{11}-4q^{13}-6q^{17}+4q^{19}+\cdots\)
14400.2.a.f	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{11}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
14400.2.a.g	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{11}-2q^{13}+2q^{17}+4q^{19}+\cdots\)
14400.2.a.h	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{11}+4q^{17}+4q^{23}-6q^{29}+\cdots\)
14400.2.a.i	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{11}+4q^{13}-6q^{17}-4q^{19}+\cdots\)
14400.2.a.j	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{11}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
14400.2.a.k	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-6q^{13}-2q^{17}-4q^{19}-8q^{23}+\cdots\)
14400.2.a.l	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{13}+8q^{19}-4q^{23}-6q^{29}+\cdots\)
14400.2.a.m	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-2q^{13}-6q^{17}+4q^{23}-2q^{29}+\cdots\)
14400.2.a.n	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$		\(q-4q^{7}+2q^{13}+8q^{19}+4q^{31}-10q^{37}+\cdots\)
14400.2.a.o	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+2q^{13}+6q^{17}-4q^{19}-6q^{29}+\cdots\)
14400.2.a.p	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{13}-8q^{19}-4q^{23}-6q^{29}+\cdots\)
14400.2.a.q	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
14400.2.a.r	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}-4q^{17}+4q^{23}-6q^{29}+\cdots\)
14400.2.a.s	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}+4q^{13}+6q^{17}-4q^{19}+\cdots\)
14400.2.a.t	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}-4q^{11}-7q^{13}+4q^{17}-q^{19}+\cdots\)
14400.2.a.u	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}-2q^{11}+q^{13}+2q^{17}-5q^{19}+\cdots\)
14400.2.a.v	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}-2q^{11}+3q^{13}-6q^{17}-7q^{19}+\cdots\)
14400.2.a.w	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}-5q^{13}+5q^{19}-4q^{23}+4q^{29}+\cdots\)
14400.2.a.x	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+5q^{13}-5q^{19}-4q^{23}+4q^{29}+\cdots\)
14400.2.a.y	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+2q^{11}-3q^{13}+6q^{17}+7q^{19}+\cdots\)
14400.2.a.z	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+2q^{11}-q^{13}-2q^{17}+5q^{19}+\cdots\)
14400.2.a.ba	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+4q^{11}+7q^{13}-4q^{17}+q^{19}+\cdots\)
14400.2.a.bb	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-6q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
14400.2.a.bc	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-6q^{11}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
14400.2.a.bd	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-5q^{11}+5q^{17}+5q^{19}-6q^{23}+\cdots\)
14400.2.a.be	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-4q^{11}+4q^{13}+4q^{19}-2q^{23}+\cdots\)
14400.2.a.bf	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{11}-4q^{13}-3q^{17}-5q^{19}+\cdots\)
14400.2.a.bg	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{11}-6q^{13}-2q^{17}-4q^{23}+\cdots\)
14400.2.a.bh	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{11}+2q^{17}-4q^{19}-2q^{29}+\cdots\)
14400.2.a.bi	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{11}+2q^{13}+6q^{17}+8q^{19}+\cdots\)
14400.2.a.bj	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
14400.2.a.bk	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{11}-4q^{13}-5q^{17}+q^{19}+\cdots\)
14400.2.a.bl	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{13}-6q^{17}+4q^{19}+6q^{23}+\cdots\)
14400.2.a.bm	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}+4q^{13}+5q^{17}-q^{19}+\cdots\)
14400.2.a.bn	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{11}-2q^{13}-6q^{17}-8q^{19}+\cdots\)
14400.2.a.bo	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{11}-2q^{17}-4q^{19}+2q^{29}+\cdots\)
14400.2.a.bp	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{11}+4q^{13}-2q^{17}-4q^{19}+\cdots\)
14400.2.a.bq	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{11}+6q^{13}+2q^{17}-4q^{23}+\cdots\)
14400.2.a.br	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+3q^{11}+4q^{13}+3q^{17}+5q^{19}+\cdots\)
14400.2.a.bs	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+4q^{11}-6q^{13}+2q^{17}+8q^{19}+\cdots\)
14400.2.a.bt	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+4q^{11}-4q^{13}-4q^{19}-2q^{23}+\cdots\)
14400.2.a.bu	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+5q^{11}-5q^{17}-5q^{19}-6q^{23}+\cdots\)
14400.2.a.bv	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+6q^{11}-4q^{13}-6q^{17}+4q^{19}+\cdots\)
14400.2.a.bw	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+6q^{11}+2q^{13}+6q^{17}+4q^{19}+\cdots\)
14400.2.a.bx	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-6q^{11}+5q^{13}-6q^{17}+5q^{19}+\cdots\)
14400.2.a.by	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-4q^{11}-3q^{13}-4q^{17}+q^{19}+\cdots\)
14400.2.a.bz	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-4q^{11}-q^{13}-4q^{17}-q^{19}+\cdots\)
14400.2.a.ca	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-4q^{11}+q^{13}-4q^{17}+q^{19}+\cdots\)
14400.2.a.cb	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$		\(q-q^{7}-7q^{13}-7q^{19}-11q^{31}-10q^{37}+\cdots\)
14400.2.a.cc	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-q^{13}+3q^{19}+4q^{23}+4q^{29}+\cdots\)
14400.2.a.cd	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+q^{13}-3q^{19}+4q^{23}+4q^{29}+\cdots\)
14400.2.a.ce	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$		\(q-q^{7}+7q^{13}+7q^{19}+11q^{31}+10q^{37}+\cdots\)
14400.2.a.cf	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+4q^{11}-q^{13}+4q^{17}-q^{19}+\cdots\)
14400.2.a.cg	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+4q^{11}+q^{13}+4q^{17}+q^{19}+\cdots\)
14400.2.a.ch	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+4q^{11}+3q^{13}+4q^{17}-q^{19}+\cdots\)
14400.2.a.ci	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+6q^{11}-5q^{13}+6q^{17}-5q^{19}+\cdots\)
14400.2.a.cj	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{11}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
14400.2.a.ck	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{11}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
14400.2.a.cl	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{11}+2q^{13}-2q^{17}+8q^{19}+\cdots\)
14400.2.a.cm	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{11}+6q^{13}-6q^{17}+4q^{19}+\cdots\)
14400.2.a.cn	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$		\(q-6q^{13}-8q^{17}+4q^{29}-2q^{37}+\cdots\)
14400.2.a.co	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$		\(q-6q^{13}+8q^{17}-4q^{29}-2q^{37}+\cdots\)
14400.2.a.cp	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$		\(q-4q^{13}-8q^{17}+10q^{29}-12q^{37}+\cdots\)
14400.2.a.cq	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$		\(q-4q^{13}-2q^{17}+4q^{29}+12q^{37}+\cdots\)
14400.2.a.cr	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$		\(q-4q^{13}+2q^{17}-4q^{29}+12q^{37}+\cdots\)
14400.2.a.cs	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{13}+6q^{17}-4q^{19}-8q^{23}+\cdots\)
14400.2.a.ct	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{13}+6q^{17}+4q^{19}+8q^{23}+\cdots\)
14400.2.a.cu	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$		\(q+4q^{13}-2q^{17}-4q^{29}-12q^{37}+\cdots\)
14400.2.a.cv	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$		\(q+4q^{13}+2q^{17}+4q^{29}-12q^{37}+\cdots\)
14400.2.a.cw	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$		\(q+4q^{13}+8q^{17}+10q^{29}+12q^{37}+\cdots\)
14400.2.a.cx	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$		\(q+6q^{13}+2q^{17}-10q^{29}-2q^{37}+\cdots\)
14400.2.a.cy	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{11}-2q^{13}+2q^{17}+4q^{19}+\cdots\)
14400.2.a.cz	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{11}-2q^{13}+2q^{17}+4q^{19}+\cdots\)
14400.2.a.da	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{11}+2q^{13}-2q^{17}-8q^{19}+\cdots\)
14400.2.a.db	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{11}+6q^{13}-6q^{17}-4q^{19}+\cdots\)
14400.2.a.dc	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-6q^{11}-5q^{13}+6q^{17}+5q^{19}+\cdots\)
14400.2.a.dd	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-4q^{11}-q^{13}+4q^{17}+q^{19}+\cdots\)
14400.2.a.de	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-4q^{11}+q^{13}+4q^{17}-q^{19}+\cdots\)
14400.2.a.df	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-4q^{11}+3q^{13}+4q^{17}+q^{19}+\cdots\)
14400.2.a.dg	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$		\(q+q^{7}-7q^{13}+7q^{19}+11q^{31}-10q^{37}+\cdots\)
14400.2.a.dh	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-q^{13}-3q^{19}-4q^{23}+4q^{29}+\cdots\)
14400.2.a.di	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+q^{13}+3q^{19}-4q^{23}+4q^{29}+\cdots\)
14400.2.a.dj	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$		\(q+q^{7}+7q^{13}-7q^{19}-11q^{31}+10q^{37}+\cdots\)
14400.2.a.dk	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+4q^{11}-3q^{13}-4q^{17}-q^{19}+\cdots\)
14400.2.a.dl	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+4q^{11}-q^{13}-4q^{17}+q^{19}+\cdots\)
14400.2.a.dm	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+4q^{11}+q^{13}-4q^{17}-q^{19}+\cdots\)
14400.2.a.dn	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+6q^{11}+5q^{13}-6q^{17}-5q^{19}+\cdots\)
14400.2.a.do	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-6q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots\)
14400.2.a.dp	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-6q^{11}+2q^{13}+6q^{17}-4q^{19}+\cdots\)
14400.2.a.dq	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-5q^{11}-5q^{17}+5q^{19}+6q^{23}+\cdots\)
14400.2.a.dr	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-4q^{11}-6q^{13}+2q^{17}-8q^{19}+\cdots\)
14400.2.a.ds	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-4q^{11}-4q^{13}+4q^{19}+2q^{23}+\cdots\)
14400.2.a.dt	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{11}+4q^{13}+3q^{17}-5q^{19}+\cdots\)
14400.2.a.du	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-2q^{11}-2q^{13}-6q^{17}+8q^{19}+\cdots\)
14400.2.a.dv	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-2q^{11}-2q^{17}+4q^{19}+2q^{29}+\cdots\)
14400.2.a.dw	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-2q^{11}+4q^{13}-2q^{17}+4q^{19}+\cdots\)
14400.2.a.dx	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-2q^{11}+6q^{13}+2q^{17}+4q^{23}+\cdots\)
14400.2.a.dy	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{11}+4q^{13}+5q^{17}+q^{19}+\cdots\)
14400.2.a.dz	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{13}-6q^{17}-4q^{19}-6q^{23}+\cdots\)
14400.2.a.ea	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}-4q^{13}-5q^{17}-q^{19}+\cdots\)
14400.2.a.eb	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{11}-6q^{13}-2q^{17}+4q^{23}+\cdots\)
14400.2.a.ec	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{11}+2q^{17}+4q^{19}-2q^{29}+\cdots\)
14400.2.a.ed	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{11}+2q^{13}+6q^{17}-8q^{19}+\cdots\)
14400.2.a.ee	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
14400.2.a.ef	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+3q^{11}-4q^{13}-3q^{17}+5q^{19}+\cdots\)
14400.2.a.eg	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+4q^{11}+4q^{13}-4q^{19}+2q^{23}+\cdots\)
14400.2.a.eh	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+5q^{11}+5q^{17}-5q^{19}+6q^{23}+\cdots\)
14400.2.a.ei	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+6q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
14400.2.a.ej	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+6q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
14400.2.a.ek	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}-4q^{11}+7q^{13}-4q^{17}-q^{19}+\cdots\)
14400.2.a.el	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}-2q^{11}-3q^{13}+6q^{17}-7q^{19}+\cdots\)
14400.2.a.em	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}-2q^{11}-q^{13}-2q^{17}-5q^{19}+\cdots\)
14400.2.a.en	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}-5q^{13}-5q^{19}+4q^{23}+4q^{29}+\cdots\)
14400.2.a.eo	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}+5q^{13}+5q^{19}+4q^{23}+4q^{29}+\cdots\)
14400.2.a.ep	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}+2q^{11}+q^{13}+2q^{17}+5q^{19}+\cdots\)
14400.2.a.eq	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}+2q^{11}+3q^{13}-6q^{17}+7q^{19}+\cdots\)
14400.2.a.er	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}+4q^{11}-7q^{13}+4q^{17}+q^{19}+\cdots\)
14400.2.a.es	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
14400.2.a.et	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{11}-4q^{17}-4q^{23}-6q^{29}+\cdots\)
14400.2.a.eu	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots\)
14400.2.a.ev	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-6q^{13}-2q^{17}+4q^{19}+8q^{23}+\cdots\)
14400.2.a.ew	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{13}-8q^{19}+4q^{23}-6q^{29}+\cdots\)
14400.2.a.ex	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-2q^{13}-6q^{17}-4q^{23}-2q^{29}+\cdots\)
14400.2.a.ey	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$1$		\(q+4q^{7}+2q^{13}-8q^{19}-4q^{31}-10q^{37}+\cdots\)
14400.2.a.ez	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+2q^{13}+6q^{17}+4q^{19}-6q^{29}+\cdots\)
14400.2.a.fa	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{13}+8q^{19}+4q^{23}-6q^{29}+\cdots\)
14400.2.a.fb	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots\)
14400.2.a.fc	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
14400.2.a.fd	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
14400.2.a.fe	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}+4q^{17}-4q^{23}-6q^{29}+\cdots\)
14400.2.a.ff	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}+4q^{13}-6q^{17}+4q^{19}+\cdots\)
14400.2.a.fg	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{11}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
14400.2.a.fh	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{7}-6q^{11}-3q^{13}-2q^{17}-q^{19}+\cdots\)
14400.2.a.fi	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(5\)		$+$	$+$	$-$	$-$	$1$		\(q+5q^{7}-5q^{13}+q^{19}-7q^{31}+10q^{37}+\cdots\)
14400.2.a.fj	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$+$	$-$	$1$		\(q+5q^{7}+5q^{13}-q^{19}+7q^{31}-10q^{37}+\cdots\)
14400.2.a.fk	$14400$	$2$	14400.a	1.a	$1$	$1$	$1$	$114.985$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{7}+6q^{11}+3q^{13}+2q^{17}+q^{19}+\cdots\)
14400.2.a.fl	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-6\)		$+$	$-$	$-$	$+$
14400.2.a.fm	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$
14400.2.a.fn	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
14400.2.a.fo	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
14400.2.a.fp	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$
14400.2.a.fq	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$
14400.2.a.fr	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$
14400.2.a.fs	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$
14400.2.a.ft	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$
14400.2.a.fu	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$
14400.2.a.fv	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
14400.2.a.fw	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
14400.2.a.fx	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$
14400.2.a.fy	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
14400.2.a.fz	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
14400.2.a.ga	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
14400.2.a.gb	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
14400.2.a.gc	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$
14400.2.a.gd	$14400$	$2$	14400.a	1.a	$1$	$2$	$2$	$114.985$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(6\)		$+$	$-$	$-$	$+$
14400.2.a.ge	$14400$	$2$	14400.a	1.a	$1$	$4$	$4$	$114.985$	\(\Q(\zeta_{24})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$
14400.2.a.gf	$14400$	$2$	14400.a	1.a	$1$	$4$	$4$	$114.985$	\(\Q(\zeta_{24})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(14400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(14400)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(7200))\)\(^{\oplus 2}\)