Space of modular forms of level 34848, weight 2, and trivial character

• Label: 34848.2.a
• Level: $34848$
• Weight: $2$
• Character orbit: 34848.a
• Rep. character: $\chi_{34848}(1,\cdot)$
• Character field: $\Q$
• Dimension: $545$
• Newform subspaces: $191$
• Sturm bound: $12672$

Defining parameters

Level:	\( N \)	\(=\)	\( 34848 = 2^{5} \cdot 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	34848.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 191 \)
Sturm bound:			\(12672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(34848))\).

	Total	New	Old
Modular forms	6528	545	5983
Cusp forms	6145	545	5600
Eisenstein series	383	0	383

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

\(2\)	\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(804\)	\(54\)	\(750\)		\(757\)	\(54\)	\(703\)		\(47\)	\(0\)	\(47\)
\(+\)	\(+\)	\(-\)	\(-\)		\(824\)	\(55\)	\(769\)		\(776\)	\(55\)	\(721\)		\(48\)	\(0\)	\(48\)
\(+\)	\(-\)	\(+\)	\(-\)		\(816\)	\(83\)	\(733\)		\(768\)	\(83\)	\(685\)		\(48\)	\(0\)	\(48\)
\(+\)	\(-\)	\(-\)	\(+\)		\(816\)	\(80\)	\(736\)		\(768\)	\(80\)	\(688\)		\(48\)	\(0\)	\(48\)
\(-\)	\(+\)	\(+\)	\(-\)		\(828\)	\(54\)	\(774\)		\(780\)	\(54\)	\(726\)		\(48\)	\(0\)	\(48\)
\(-\)	\(+\)	\(-\)	\(+\)		\(808\)	\(55\)	\(753\)		\(760\)	\(55\)	\(705\)		\(48\)	\(0\)	\(48\)
\(-\)	\(-\)	\(+\)	\(+\)		\(816\)	\(79\)	\(737\)		\(768\)	\(79\)	\(689\)		\(48\)	\(0\)	\(48\)
\(-\)	\(-\)	\(-\)	\(-\)		\(816\)	\(85\)	\(731\)		\(768\)	\(85\)	\(683\)		\(48\)	\(0\)	\(48\)
Plus space			\(+\)		\(3244\)	\(268\)	\(2976\)		\(3053\)	\(268\)	\(2785\)		\(191\)	\(0\)	\(191\)
Minus space			\(-\)		\(3284\)	\(277\)	\(3007\)		\(3092\)	\(277\)	\(2815\)		\(192\)	\(0\)	\(192\)

Trace form

\( 545 q - 2 q^{5} - 10 q^{13} + 2 q^{17} + 543 q^{25} + 6 q^{29} - 10 q^{37} + 26 q^{41} + 537 q^{49} + 30 q^{53} - 2 q^{61} + 36 q^{65} + 2 q^{73} - 44 q^{85} - 6 q^{89} + 42 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(34848))\) 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	11
34848.2.a.a	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$		\(q-4q^{5}-4q^{13}+2q^{17}+11q^{25}+\cdots\)
34848.2.a.b	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$		\(q-4q^{5}+4q^{13}-2q^{17}+11q^{25}+\cdots\)
34848.2.a.c	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$		\(q-4q^{5}+6q^{13}+8q^{17}+11q^{25}+\cdots\)
34848.2.a.d	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}-q^{13}+q^{17}-2q^{23}+\cdots\)
34848.2.a.e	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}+q^{13}-q^{17}+2q^{23}+\cdots\)
34848.2.a.f	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}-q^{13}+q^{17}+2q^{23}+\cdots\)
34848.2.a.g	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}+q^{13}-q^{17}-2q^{23}+\cdots\)
34848.2.a.h	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-4q^{13}-6q^{17}+2q^{19}+\cdots\)
34848.2.a.i	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
34848.2.a.j	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
34848.2.a.k	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-2q^{13}+4q^{17}-q^{19}+\cdots\)
34848.2.a.l	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+2q^{13}-4q^{17}-q^{19}+\cdots\)
34848.2.a.m	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$		\(q-2q^{5}-4q^{13}-8q^{17}-q^{25}-4q^{29}+\cdots\)
34848.2.a.n	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{17}-6q^{19}-6q^{23}-q^{25}+\cdots\)
34848.2.a.o	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{17}+6q^{19}+6q^{23}-q^{25}+\cdots\)
34848.2.a.p	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$		\(q-2q^{5}+4q^{13}+8q^{17}-q^{25}+4q^{29}+\cdots\)
34848.2.a.q	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-2q^{13}+4q^{17}+q^{19}+\cdots\)
34848.2.a.r	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+2q^{13}-4q^{17}+q^{19}+\cdots\)
34848.2.a.s	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
34848.2.a.t	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
34848.2.a.u	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+2q^{13}+2q^{17}+4q^{19}+\cdots\)
34848.2.a.v	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+2q^{13}+2q^{19}-9q^{23}+\cdots\)
34848.2.a.w	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-q^{13}+3q^{17}-2q^{19}+\cdots\)
34848.2.a.x	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+q^{13}-3q^{17}-2q^{19}+\cdots\)
34848.2.a.y	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+6q^{13}-4q^{17}-6q^{19}-3q^{23}+\cdots\)
34848.2.a.z	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+6q^{13}-4q^{17}+6q^{19}+3q^{23}+\cdots\)
34848.2.a.ba	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-q^{13}+3q^{17}+2q^{19}+\cdots\)
34848.2.a.bb	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+q^{13}-3q^{17}+2q^{19}+\cdots\)
34848.2.a.bc	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+2q^{13}-2q^{19}+9q^{23}+\cdots\)
34848.2.a.bd	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-2q^{13}-2q^{17}+2q^{19}-6q^{23}+\cdots\)
34848.2.a.be	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+2q^{13}+2q^{17}+2q^{19}+6q^{23}+\cdots\)
34848.2.a.bf	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-4q^{13}-2q^{17}-2q^{23}-5q^{25}+\cdots\)
34848.2.a.bg	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{13}-2q^{17}+6q^{19}+4q^{23}+\cdots\)
34848.2.a.bh	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{13}+2q^{17}+6q^{19}-4q^{23}+\cdots\)
34848.2.a.bi	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-4q^{13}-2q^{17}+2q^{23}-5q^{25}+\cdots\)
34848.2.a.bj	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{13}-2q^{17}-6q^{19}-4q^{23}+\cdots\)
34848.2.a.bk	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{13}+2q^{17}-6q^{19}+4q^{23}+\cdots\)
34848.2.a.bl	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-2q^{13}-2q^{17}-2q^{19}+6q^{23}+\cdots\)
34848.2.a.bm	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+2q^{13}+2q^{17}-2q^{19}-6q^{23}+\cdots\)
34848.2.a.bn	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-q^{13}+5q^{17}-8q^{19}+\cdots\)
34848.2.a.bo	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{13}-5q^{17}-8q^{19}+\cdots\)
34848.2.a.bp	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{13}+5q^{17}+8q^{19}+\cdots\)
34848.2.a.bq	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{13}-5q^{17}+8q^{19}+\cdots\)
34848.2.a.br	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}-4q^{13}+6q^{17}+2q^{19}+\cdots\)
34848.2.a.bs	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{7}-6q^{13}-4q^{17}+5q^{19}+\cdots\)
34848.2.a.bt	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{7}+6q^{13}+4q^{17}+5q^{19}+\cdots\)
34848.2.a.bu	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+2q^{13}-2q^{19}-q^{25}+\cdots\)
34848.2.a.bv	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$		\(q+2q^{5}-6q^{13}+2q^{17}-q^{25}-10q^{29}+\cdots\)
34848.2.a.bw	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{17}-6q^{19}+6q^{23}-q^{25}+\cdots\)
34848.2.a.bx	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{17}+6q^{19}-6q^{23}-q^{25}+\cdots\)
34848.2.a.by	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+6q^{13}+2q^{17}-4q^{19}-4q^{23}+\cdots\)
34848.2.a.bz	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+6q^{13}+2q^{17}+4q^{19}+4q^{23}+\cdots\)
34848.2.a.ca	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}+2q^{13}+2q^{19}-q^{25}+\cdots\)
34848.2.a.cb	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+3q^{7}-6q^{13}-4q^{17}-5q^{19}+\cdots\)
34848.2.a.cc	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+3q^{7}+6q^{13}+4q^{17}-5q^{19}+\cdots\)
34848.2.a.cd	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-4q^{13}+6q^{17}-2q^{19}+\cdots\)
34848.2.a.ce	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-4q^{7}+2q^{13}-8q^{17}+6q^{19}+\cdots\)
34848.2.a.cf	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+4q^{7}+2q^{13}-8q^{17}-6q^{19}+\cdots\)
34848.2.a.cg	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{7}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
34848.2.a.ch	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$		\(q+4q^{5}-4q^{13}-2q^{17}+11q^{25}+\cdots\)
34848.2.a.ci	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$		\(q+4q^{5}+4q^{13}+2q^{17}+11q^{25}+\cdots\)
34848.2.a.cj	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$		\(q+4q^{5}+6q^{13}-8q^{17}+11q^{25}+\cdots\)
34848.2.a.ck	$34848$	$2$	34848.a	1.a	$1$	$1$	$1$	$278.263$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
34848.2.a.cl	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.cm	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$
34848.2.a.cn	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$
34848.2.a.co	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{13}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$
34848.2.a.cp	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{13}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$
34848.2.a.cq	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$
34848.2.a.cr	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$
34848.2.a.cs	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.ct	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.cu	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.cv	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.cw	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.cx	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.cy	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.cz	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$
34848.2.a.da	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.db	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.dc	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.dd	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.de	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$
34848.2.a.df	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.dg	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.dh	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.di	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.dj	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.dk	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-5\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.dl	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.dm	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(5\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.dn	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.do	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.dp	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.dq	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.dr	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.ds	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.dt	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.du	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.dv	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.dw	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.dx	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.dy	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.dz	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$
34848.2.a.ea	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$
34848.2.a.eb	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.ec	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$+$
34848.2.a.ed	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{13}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$+$
34848.2.a.ee	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$
34848.2.a.ef	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$
34848.2.a.eg	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{13}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$
34848.2.a.eh	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$
34848.2.a.ei	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(4\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.ej	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$+$	$+$
34848.2.a.ek	$34848$	$2$	34848.a	1.a	$1$	$2$	$2$	$278.263$	\(\Q(\sqrt{5}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$
34848.2.a.el	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.229.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.em	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.1304.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.en	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.1304.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.eo	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.ep	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.eq	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.er	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.es	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.1304.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.et	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.1304.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.eu	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.229.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.ev	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.404.1	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.ew	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.404.1	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.ex	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.404.1	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.ey	$34848$	$2$	34848.a	1.a	$1$	$3$	$3$	$278.263$	3.3.404.1	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.ez	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{20})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$
34848.2.a.fa	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{20})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$-$	$+$
34848.2.a.fb	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-8\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.fc	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(8\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.fd	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.22000.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$
34848.2.a.fe	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{5}, \sqrt{11})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$
34848.2.a.ff	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{5}, \sqrt{11})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$
34848.2.a.fg	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.22000.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$
34848.2.a.fh	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.7488.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$
34848.2.a.fi	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.fj	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.fk	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{3}, \sqrt{23})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
34848.2.a.fl	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{3}, \sqrt{11})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
34848.2.a.fm	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{24})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
34848.2.a.fn	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{3}, \sqrt{11})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
34848.2.a.fo	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{24})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
34848.2.a.fp	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{3}, \sqrt{23})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
34848.2.a.fq	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.7488.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$
34848.2.a.fr	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.13968.1	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.fs	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.13968.1	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.ft	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{5}, \sqrt{11})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$
34848.2.a.fu	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\sqrt{5}, \sqrt{11})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$
34848.2.a.fv	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.13968.1	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.fw	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.13968.1	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.fx	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.4400.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(-6\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.fy	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.4400.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(-6\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.fz	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.4400.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(6\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.ga	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.4400.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.gb	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{20})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$+$	$-$
34848.2.a.gc	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.4400.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$-$	$+$
34848.2.a.gd	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	4.4.4400.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$+$	$+$
34848.2.a.ge	$34848$	$2$	34848.a	1.a	$1$	$4$	$4$	$278.263$	\(\Q(\zeta_{20})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(0\)		$+$	$+$	$-$	$-$
34848.2.a.gf	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.510590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(-5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.gg	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.66590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(-5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.gh	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.66590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(-5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.gi	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.510590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(-5\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.gj	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.510590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(5\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.gk	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.66590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.gl	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.66590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.gm	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.510590000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-5\)	\(5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.gn	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.19898000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.go	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.19898000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.gp	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.360848016.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.gq	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.360848016.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.gr	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.71057088.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.gs	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.71057088.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.gt	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.71057088.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.gu	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.71057088.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.gv	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.360848016.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.gw	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.360848016.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.gx	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.19898000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.gy	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.19898000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.gz	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.6662000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.ha	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.6662000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.hb	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.6662000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.hc	$34848$	$2$	34848.a	1.a	$1$	$6$	$6$	$278.263$	6.6.6662000.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.hd	$34848$	$2$	34848.a	1.a	$1$	$8$	$8$	$278.263$	8.8.\(\cdots\).1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.he	$34848$	$2$	34848.a	1.a	$1$	$8$	$8$	$278.263$	8.8.\(\cdots\).1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
34848.2.a.hf	$34848$	$2$	34848.a	1.a	$1$	$12$	$12$	$278.263$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
34848.2.a.hg	$34848$	$2$	34848.a	1.a	$1$	$12$	$12$	$278.263$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
34848.2.a.hh	$34848$	$2$	34848.a	1.a	$1$	$12$	$12$	$278.263$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
34848.2.a.hi	$34848$	$2$	34848.a	1.a	$1$	$12$	$12$	$278.263$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(34848))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(34848)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1056))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2178))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2904))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3872))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4356))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5808))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(8712))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17424))\)\(^{\oplus 2}\)