Space of modular forms of level 42320, weight 2, and trivial character

• Label: 42320.2.a
• Level: $42320$
• Weight: $2$
• Character orbit: 42320.a
• Rep. character: $\chi_{42320}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1010$
• Newform subspaces: $154$
• Sturm bound: $13248$

Defining parameters

Level:	\( N \)	\(=\)	\( 42320 = 2^{4} \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	42320.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 154 \)
Sturm bound:			\(13248\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(42320))\).

	Total	New	Old
Modular forms	6768	1010	5758
Cusp forms	6481	1010	5471
Eisenstein series	287	0	287

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

\(2\)	\(5\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(828\)	\(121\)	\(707\)		\(793\)	\(121\)	\(672\)		\(35\)	\(0\)	\(35\)
\(+\)	\(+\)	\(-\)	\(-\)		\(862\)	\(132\)	\(730\)		\(826\)	\(132\)	\(694\)		\(36\)	\(0\)	\(36\)
\(+\)	\(-\)	\(+\)	\(-\)		\(852\)	\(131\)	\(721\)		\(816\)	\(131\)	\(685\)		\(36\)	\(0\)	\(36\)
\(+\)	\(-\)	\(-\)	\(+\)		\(842\)	\(121\)	\(721\)		\(806\)	\(121\)	\(685\)		\(36\)	\(0\)	\(36\)
\(-\)	\(+\)	\(+\)	\(-\)		\(864\)	\(131\)	\(733\)		\(828\)	\(131\)	\(697\)		\(36\)	\(0\)	\(36\)
\(-\)	\(+\)	\(-\)	\(+\)		\(830\)	\(121\)	\(709\)		\(794\)	\(121\)	\(673\)		\(36\)	\(0\)	\(36\)
\(-\)	\(-\)	\(+\)	\(+\)		\(840\)	\(121\)	\(719\)		\(804\)	\(121\)	\(683\)		\(36\)	\(0\)	\(36\)
\(-\)	\(-\)	\(-\)	\(-\)		\(850\)	\(132\)	\(718\)		\(814\)	\(132\)	\(682\)		\(36\)	\(0\)	\(36\)
Plus space			\(+\)		\(3340\)	\(484\)	\(2856\)		\(3197\)	\(484\)	\(2713\)		\(143\)	\(0\)	\(143\)
Minus space			\(-\)		\(3428\)	\(526\)	\(2902\)		\(3284\)	\(526\)	\(2758\)		\(144\)	\(0\)	\(144\)

Trace form

1010 * q + 2 * q^3 + 6 * q^7 + 1006 * q^9 + 4 * q^11 + 2 * q^15 - 4 * q^17 + 8 * q^19 + 4 * q^21 + 1010 * q^25 + 20 * q^27 - 4 * q^29 + 20 * q^31 + 6 * q^35 - 8 * q^37 + 28 * q^39 + 8 * q^41 + 14 * q^43 + 4 * q^45 - 22 * q^47 + 1022 * q^49 - 4 * q^51 - 16 * q^53 - 4 * q^55 + 8 * q^57 - 8 * q^59 - 16 * q^61 + 6 * q^63 + 4 * q^65 + 18 * q^67 - 4 * q^71 - 4 * q^73 + 2 * q^75 + 16 * q^79 + 998 * q^81 - 50 * q^83 - 8 * q^85 - 36 * q^87 + 4 * q^89 - 12 * q^91 - 8 * q^93 - 8 * q^95 + 4 * q^97 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(42320))\) 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	5	23
42320.2.a.a	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}+2q^{7}+6q^{9}-3q^{13}+\cdots\)
42320.2.a.b	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
42320.2.a.c	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}-5q^{11}+\cdots\)
42320.2.a.d	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+3q^{7}+q^{9}-2q^{11}+\cdots\)
42320.2.a.e	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-3q^{7}+q^{9}+2q^{11}+\cdots\)
42320.2.a.f	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-2q^{7}+q^{9}+5q^{11}+\cdots\)
42320.2.a.g	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+2q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
42320.2.a.h	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}-2q^{9}-4q^{13}+\cdots\)
42320.2.a.i	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
42320.2.a.j	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}-2q^{9}-4q^{13}+\cdots\)
42320.2.a.k	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}-2q^{9}+q^{13}-q^{15}+\cdots\)
42320.2.a.l	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
42320.2.a.m	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}-3q^{11}-6q^{13}+\cdots\)
42320.2.a.n	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots\)
42320.2.a.o	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}-3q^{11}-2q^{13}+\cdots\)
42320.2.a.p	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}+3q^{11}-2q^{13}+\cdots\)
42320.2.a.q	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots\)
42320.2.a.r	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
42320.2.a.s	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}+3q^{11}-6q^{13}+\cdots\)
42320.2.a.t	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
42320.2.a.u	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
42320.2.a.v	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+2q^{11}-5q^{13}+\cdots\)
42320.2.a.w	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+4q^{11}+q^{13}+\cdots\)
42320.2.a.x	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-4q^{11}+q^{13}+\cdots\)
42320.2.a.y	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
42320.2.a.z	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-3q^{7}+q^{9}-6q^{11}+\cdots\)
42320.2.a.ba	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
42320.2.a.bb	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+3q^{7}+q^{9}+6q^{11}+\cdots\)
42320.2.a.bc	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-2q^{7}+6q^{9}-2q^{11}+\cdots\)
42320.2.a.bd	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-2q^{7}+6q^{9}+q^{13}+\cdots\)
42320.2.a.be	$42320$	$2$	42320.a	1.a	$1$	$1$	$1$	$337.927$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+2q^{7}+6q^{9}+2q^{11}+\cdots\)
42320.2.a.bf	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(-3\)	\(-2\)	\(3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.bg	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(-8\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.bh	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.bi	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.bj	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.bk	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.bl	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.bm	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.bn	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(8\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.bo	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.bp	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.bq	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.br	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.bs	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.bt	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.bu	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.bv	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.bw	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.bx	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.by	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.bz	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ca	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.cb	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cc	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{21}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.cd	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ce	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.cf	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.cg	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.ch	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.ci	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.cj	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ck	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.cl	$42320$	$2$	42320.a	1.a	$1$	$2$	$2$	$337.927$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cm	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.229.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(-3\)	\(7\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.cn	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.2597.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.co	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.761.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(-3\)	\(3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.cp	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.961.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(-3\)	\(5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.cq	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.961.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(3\)	\(-5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cr	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.761.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(3\)	\(-3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cs	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.1101.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ct	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.229.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.cu	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.229.1	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cv	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.621.1	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cw	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cx	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.1509.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cy	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.1257.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.cz	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.785.1	None	✓	?				$-1$		\(0\)	\(1\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.da	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.1509.1	None	✓	?				$-1$		\(0\)	\(1\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.db	$42320$	$2$	42320.a	1.a	$1$	$3$	$3$	$337.927$	3.3.1257.1	None	✓	?				$-1$		\(0\)	\(1\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.dc	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.dd	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(4\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.de	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.59457.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(-4\)	\(-1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.df	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.4752.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(-4\)	\(6\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dg	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.4752.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(4\)	\(-6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.dh	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.59457.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(4\)	\(1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.di	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.2777.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dj	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.2777.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(4\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.dk	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.dl	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.dm	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.65057.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-4\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dn	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.65057.1	None	✓	?				$-1$		\(0\)	\(1\)	\(4\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.do	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.15317.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dp	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.13888.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.dq	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	4.4.13888.1	None	✓	?				$-1$		\(0\)	\(2\)	\(4\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.dr	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(4\)	\(-4\)	\(8\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ds	$42320$	$2$	42320.a	1.a	$1$	$4$	$4$	$337.927$	\(\Q(\zeta_{24})^+\)	None	✓	?				$-1$		\(0\)	\(4\)	\(4\)	\(-8\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.dt	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	5.5.5680693.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(-5\)	\(2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.du	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	5.5.5680693.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(5\)	\(-2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dv	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	5.5.4180641.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(-5\)	\(3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.dw	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	5.5.4180641.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(5\)	\(-3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dx	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	5.5.13955077.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dy	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(0\)	\(4\)	\(-5\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.dz	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(0\)	\(4\)	\(5\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.ea	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(0\)	\(5\)	\(-5\)	\(3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.eb	$42320$	$2$	42320.a	1.a	$1$	$5$	$5$	$337.927$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(0\)	\(5\)	\(5\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ec	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.4829696.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(-6\)	\(6\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ed	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.4829696.1	None	✓	?				$-1$		\(0\)	\(-4\)	\(6\)	\(-6\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.ee	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-6\)	\(7\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ef	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(6\)	\(-7\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.eg	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.35140096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-6\)	\(-6\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.eh	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.35140096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(6\)	\(6\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ei	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.252973568.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-6\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ej	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.252973568.1	None	✓	?				$-1$		\(0\)	\(2\)	\(6\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.ek	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.27387072.1	None	✓	?				$-1$		\(0\)	\(6\)	\(-6\)	\(-6\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.el	$42320$	$2$	42320.a	1.a	$1$	$6$	$6$	$337.927$	6.6.27387072.1	None	✓	?				$-1$		\(0\)	\(6\)	\(6\)	\(6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.em	$42320$	$2$	42320.a	1.a	$1$	$8$	$8$	$337.927$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(-8\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.en	$42320$	$2$	42320.a	1.a	$1$	$8$	$8$	$337.927$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(8\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.eo	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(-10\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.ep	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(10\)	\(7\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.eq	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-10\)	\(4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.er	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(10\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.es	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(-10\)	\(-8\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.et	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(10\)	\(8\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.eu	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(5\)	\(-10\)	\(-9\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ev	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(5\)	\(-10\)	\(-5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ew	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(5\)	\(10\)	\(5\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ex	$42320$	$2$	42320.a	1.a	$1$	$10$	$10$	$337.927$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(5\)	\(10\)	\(9\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ey	$42320$	$2$	42320.a	1.a	$1$	$12$	$12$	$337.927$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-12\)	\(8\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.ez	$42320$	$2$	42320.a	1.a	$1$	$12$	$12$	$337.927$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(12\)	\(-8\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.fa	$42320$	$2$	42320.a	1.a	$1$	$15$	$15$	$337.927$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-5\)	\(-15\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.fb	$42320$	$2$	42320.a	1.a	$1$	$15$	$15$	$337.927$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-5\)	\(15\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.fc	$42320$	$2$	42320.a	1.a	$1$	$15$	$15$	$337.927$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-15\)	\(6\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.fd	$42320$	$2$	42320.a	1.a	$1$	$15$	$15$	$337.927$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(15\)	\(-6\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.fe	$42320$	$2$	42320.a	1.a	$1$	$16$	$16$	$337.927$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(-16\)	\(12\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.ff	$42320$	$2$	42320.a	1.a	$1$	$16$	$16$	$337.927$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(16\)	\(-12\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.fg	$42320$	$2$	42320.a	1.a	$1$	$16$	$16$	$337.927$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(-16\)	\(-12\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.fh	$42320$	$2$	42320.a	1.a	$1$	$16$	$16$	$337.927$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(16\)	\(12\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.fi	$42320$	$2$	42320.a	1.a	$1$	$20$	$20$	$337.927$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(-20\)	\(-16\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.fj	$42320$	$2$	42320.a	1.a	$1$	$20$	$20$	$337.927$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(20\)	\(16\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.fk	$42320$	$2$	42320.a	1.a	$1$	$24$	$24$	$337.927$		None	✓	?				$-1$		\(0\)	\(4\)	\(-24\)	\(-8\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.fl	$42320$	$2$	42320.a	1.a	$1$	$24$	$24$	$337.927$		None	✓	?				$-1$		\(0\)	\(4\)	\(24\)	\(8\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.fm	$42320$	$2$	42320.a	1.a	$1$	$25$	$25$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(-10\)	\(-25\)	\(14\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.fn	$42320$	$2$	42320.a	1.a	$1$	$25$	$25$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(-10\)	\(25\)	\(-14\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.fo	$42320$	$2$	42320.a	1.a	$1$	$25$	$25$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(0\)	\(-25\)	\(6\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.fp	$42320$	$2$	42320.a	1.a	$1$	$25$	$25$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(0\)	\(25\)	\(-6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.fq	$42320$	$2$	42320.a	1.a	$1$	$25$	$25$	$337.927$		None	✓	?				$-1$		\(0\)	\(5\)	\(-25\)	\(1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.fr	$42320$	$2$	42320.a	1.a	$1$	$25$	$25$	$337.927$		None	✓	?				$-1$		\(0\)	\(5\)	\(25\)	\(-1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.fs	$42320$	$2$	42320.a	1.a	$1$	$30$	$30$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(-5\)	\(-30\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
42320.2.a.ft	$42320$	$2$	42320.a	1.a	$1$	$30$	$30$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(-5\)	\(30\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
42320.2.a.fu	$42320$	$2$	42320.a	1.a	$1$	$30$	$30$	$337.927$		None	✓	?				$-1$		\(0\)	\(6\)	\(-30\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.fv	$42320$	$2$	42320.a	1.a	$1$	$30$	$30$	$337.927$		None	✓	?				$-1$		\(0\)	\(6\)	\(30\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
42320.2.a.fw	$42320$	$2$	42320.a	1.a	$1$	$35$	$35$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(-6\)	\(-35\)	\(1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
42320.2.a.fx	$42320$	$2$	42320.a	1.a	$1$	$35$	$35$	$337.927$		None	✓	?	✓			$-1$		\(0\)	\(-6\)	\(35\)	\(-1\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(42320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(42320)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(8464))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(10580))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21160))\)\(^{\oplus 2}\)