Space of modular forms of level 42237, weight 2, and trivial character

• Label: 42237.2.a
• Level: $42237$
• Weight: $2$
• Character orbit: 42237.a
• Rep. character: $\chi_{42237}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1705$
• Newform subspaces: $103$
• Sturm bound: $10640$

Defining parameters

Level:	\( N \)	\(=\)	\( 42237 = 3^{2} \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	42237.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 103 \)
Sturm bound:			\(10640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(42237))\).

	Total	New	Old
Modular forms	5400	1705	3695
Cusp forms	5241	1705	3536
Eisenstein series	159	0	159

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

\(3\)	\(13\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(660\)	\(162\)	\(498\)		\(641\)	\(162\)	\(479\)		\(19\)	\(0\)	\(19\)
\(+\)	\(+\)	\(-\)	\(-\)		\(688\)	\(180\)	\(508\)		\(668\)	\(180\)	\(488\)		\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(+\)	\(-\)		\(680\)	\(178\)	\(502\)		\(660\)	\(178\)	\(482\)		\(20\)	\(0\)	\(20\)
\(+\)	\(-\)	\(-\)	\(+\)		\(672\)	\(162\)	\(510\)		\(652\)	\(162\)	\(490\)		\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(+\)	\(-\)		\(690\)	\(259\)	\(431\)		\(670\)	\(259\)	\(411\)		\(20\)	\(0\)	\(20\)
\(-\)	\(+\)	\(-\)	\(+\)		\(662\)	\(252\)	\(410\)		\(642\)	\(252\)	\(390\)		\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(+\)	\(+\)		\(670\)	\(251\)	\(419\)		\(650\)	\(251\)	\(399\)		\(20\)	\(0\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)		\(678\)	\(261\)	\(417\)		\(658\)	\(261\)	\(397\)		\(20\)	\(0\)	\(20\)
Plus space			\(+\)		\(2664\)	\(827\)	\(1837\)		\(2585\)	\(827\)	\(1758\)		\(79\)	\(0\)	\(79\)
Minus space			\(-\)		\(2736\)	\(878\)	\(1858\)		\(2656\)	\(878\)	\(1778\)		\(80\)	\(0\)	\(80\)

Trace form

1705 * q + 3 * q^2 + 1711 * q^4 - 6 * q^5 - 4 * q^7 + 3 * q^8 - 10 * q^10 - q^13 - 20 * q^14 + 1719 * q^16 + 6 * q^17 - 14 * q^20 - 4 * q^22 - 16 * q^23 + 1703 * q^25 - 3 * q^26 - 36 * q^28 - 6 * q^29 + 4 * q^31 - 21 * q^32 - 22 * q^34 - 28 * q^35 + 22 * q^37 - 66 * q^40 + 14 * q^41 - 24 * q^43 + 20 * q^44 + 24 * q^46 - 36 * q^47 + 1713 * q^49 - 19 * q^50 - 7 * q^52 - 10 * q^53 - 12 * q^55 - 64 * q^56 - 14 * q^58 + 36 * q^59 + 30 * q^61 - 44 * q^62 + 1751 * q^64 + 2 * q^65 - 6 * q^68 + 36 * q^70 + 4 * q^71 - 42 * q^73 + 30 * q^74 + 12 * q^77 - 8 * q^79 - 86 * q^80 - 46 * q^82 - 52 * q^83 + 28 * q^85 - 8 * q^86 + 12 * q^88 - 14 * q^89 - 8 * q^91 - 96 * q^92 + 40 * q^94 - 50 * q^97 + 99 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(42237))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	13	19
42237.2.a.a	$42237$	$2$	42237.a	1.a	$1$	$1$	$1$	$337.264$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}-3q^{7}+3q^{11}-q^{13}+\cdots\)
42237.2.a.b	$42237$	$2$	42237.a	1.a	$1$	$1$	$1$	$337.264$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{5}+5q^{7}-3q^{8}-3q^{10}+\cdots\)
42237.2.a.c	$42237$	$2$	42237.a	1.a	$1$	$1$	$1$	$337.264$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-4q^{7}-3q^{8}-2q^{10}+\cdots\)
42237.2.a.d	$42237$	$2$	42237.a	1.a	$1$	$1$	$1$	$337.264$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+3q^{7}-3q^{8}-q^{10}+\cdots\)
42237.2.a.e	$42237$	$2$	42237.a	1.a	$1$	$1$	$1$	$337.264$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+3q^{5}+q^{7}-3q^{8}+3q^{10}+\cdots\)
42237.2.a.f	$42237$	$2$	42237.a	1.a	$1$	$1$	$1$	$337.264$	\(\Q\)	None	✓	?				$-1$		\(2\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
42237.2.a.g	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.h	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.i	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.j	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.k	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.l	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$
42237.2.a.m	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.n	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$
42237.2.a.o	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{3}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$
42237.2.a.p	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.q	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.r	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.s	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.t	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.u	$42237$	$2$	42237.a	1.a	$1$	$2$	$2$	$337.264$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.v	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(-3\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.w	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	3.3.148.1	None	✓	?				$-1$		\(-2\)	\(0\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.x	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	3.3.469.1	None	✓	?				$-1$		\(-1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.y	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	3.3.993.1	None	✓	?				$-1$		\(-1\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.z	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.ba	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bb	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	3.3.621.1	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bc	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	3.3.469.1	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.bd	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	3.3.993.1	None	✓	?				$-1$		\(1\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.be	$42237$	$2$	42237.a	1.a	$1$	$3$	$3$	$337.264$	3.3.148.1	None	✓	?				$-1$		\(2\)	\(0\)	\(-1\)	\(-5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.bf	$42237$	$2$	42237.a	1.a	$1$	$4$	$4$	$337.264$	4.4.6809.1	None	✓	?				$-1$		\(-3\)	\(0\)	\(8\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bg	$42237$	$2$	42237.a	1.a	$1$	$4$	$4$	$337.264$	4.4.11324.1	None	✓	?				$-1$		\(-1\)	\(0\)	\(4\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.bh	$42237$	$2$	42237.a	1.a	$1$	$5$	$5$	$337.264$	5.5.504568.1	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bi	$42237$	$2$	42237.a	1.a	$1$	$5$	$5$	$337.264$	5.5.2655049.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.bj	$42237$	$2$	42237.a	1.a	$1$	$5$	$5$	$337.264$	5.5.2762272.1	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bk	$42237$	$2$	42237.a	1.a	$1$	$5$	$5$	$337.264$	5.5.288565.1	None	✓	?				$-1$		\(4\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bl	$42237$	$2$	42237.a	1.a	$1$	$6$	$6$	$337.264$	6.6.26092352.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.bm	$42237$	$2$	42237.a	1.a	$1$	$6$	$6$	$337.264$	6.6.26092352.1	None	✓	?				$-1$		\(4\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.bn	$42237$	$2$	42237.a	1.a	$1$	$8$	$8$	$337.264$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.bo	$42237$	$2$	42237.a	1.a	$1$	$8$	$8$	$337.264$	8.8.\(\cdots\).1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-10\)		$+$	$-$	$-$	$+$
42237.2.a.bp	$42237$	$2$	42237.a	1.a	$1$	$8$	$8$	$337.264$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bq	$42237$	$2$	42237.a	1.a	$1$	$9$	$9$	$337.264$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(-3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.br	$42237$	$2$	42237.a	1.a	$1$	$9$	$9$	$337.264$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.bs	$42237$	$2$	42237.a	1.a	$1$	$9$	$9$	$337.264$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.bt	$42237$	$2$	42237.a	1.a	$1$	$9$	$9$	$337.264$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.bu	$42237$	$2$	42237.a	1.a	$1$	$9$	$9$	$337.264$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-7\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.bv	$42237$	$2$	42237.a	1.a	$1$	$9$	$9$	$337.264$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.bw	$42237$	$2$	42237.a	1.a	$1$	$9$	$9$	$337.264$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bx	$42237$	$2$	42237.a	1.a	$1$	$10$	$10$	$337.264$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$
42237.2.a.by	$42237$	$2$	42237.a	1.a	$1$	$11$	$11$	$337.264$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(0\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.bz	$42237$	$2$	42237.a	1.a	$1$	$11$	$11$	$337.264$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-5\)	\(3\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.ca	$42237$	$2$	42237.a	1.a	$1$	$11$	$11$	$337.264$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-4\)	\(5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.cb	$42237$	$2$	42237.a	1.a	$1$	$11$	$11$	$337.264$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-5\)	\(3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.cc	$42237$	$2$	42237.a	1.a	$1$	$11$	$11$	$337.264$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-4\)	\(5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.cd	$42237$	$2$	42237.a	1.a	$1$	$11$	$11$	$337.264$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.ce	$42237$	$2$	42237.a	1.a	$1$	$12$	$12$	$337.264$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(0\)	\(9\)	\(-1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.cf	$42237$	$2$	42237.a	1.a	$1$	$12$	$12$	$337.264$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(0\)	\(9\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.cg	$42237$	$2$	42237.a	1.a	$1$	$14$	$14$	$337.264$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(-3\)	\(0\)	\(5\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.ch	$42237$	$2$	42237.a	1.a	$1$	$14$	$14$	$337.264$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(6\)		$+$	$+$	$-$	$-$
42237.2.a.ci	$42237$	$2$	42237.a	1.a	$1$	$14$	$14$	$337.264$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(3\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.cj	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(-7\)	\(0\)	\(5\)	\(-6\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.ck	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(-5\)	\(0\)	\(5\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.cl	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$
42237.2.a.cm	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-6\)		$+$	$-$	$-$	$+$
42237.2.a.cn	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(6\)		$+$	$+$	$+$	$+$
42237.2.a.co	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(6\)		$+$	$-$	$+$	$-$
42237.2.a.cp	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(5\)	\(0\)	\(5\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.cq	$42237$	$2$	42237.a	1.a	$1$	$18$	$18$	$337.264$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(7\)	\(0\)	\(5\)	\(-6\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.cr	$42237$	$2$	42237.a	1.a	$1$	$20$	$20$	$337.264$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(-4\)	\(0\)	\(-13\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.cs	$42237$	$2$	42237.a	1.a	$1$	$20$	$20$	$337.264$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(4\)	\(0\)	\(-13\)	\(7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.ct	$42237$	$2$	42237.a	1.a	$1$	$22$	$22$	$337.264$		None	✓	?				$-1$		\(-1\)	\(0\)	\(-9\)	\(8\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.cu	$42237$	$2$	42237.a	1.a	$1$	$22$	$22$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(10\)		$+$	$-$	$+$	$-$
42237.2.a.cv	$42237$	$2$	42237.a	1.a	$1$	$22$	$22$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(10\)		$+$	$+$	$-$	$-$
42237.2.a.cw	$42237$	$2$	42237.a	1.a	$1$	$22$	$22$	$337.264$		None	✓	?				$-1$		\(1\)	\(0\)	\(-9\)	\(8\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.cx	$42237$	$2$	42237.a	1.a	$1$	$27$	$27$	$337.264$		None	✓	?				$-1$		\(-3\)	\(0\)	\(-3\)	\(-9\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.cy	$42237$	$2$	42237.a	1.a	$1$	$27$	$27$	$337.264$		None	✓	?				$-1$		\(-3\)	\(0\)	\(9\)	\(-21\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.cz	$42237$	$2$	42237.a	1.a	$1$	$27$	$27$	$337.264$		None	✓	?				$-1$		\(-3\)	\(0\)	\(9\)	\(-9\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.da	$42237$	$2$	42237.a	1.a	$1$	$27$	$27$	$337.264$		None	✓	?				$-1$		\(3\)	\(0\)	\(-3\)	\(-9\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.db	$42237$	$2$	42237.a	1.a	$1$	$27$	$27$	$337.264$		None	✓	?				$-1$		\(3\)	\(0\)	\(9\)	\(-21\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.dc	$42237$	$2$	42237.a	1.a	$1$	$27$	$27$	$337.264$		None	✓	?				$-1$		\(3\)	\(0\)	\(9\)	\(-9\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.dd	$42237$	$2$	42237.a	1.a	$1$	$28$	$28$	$337.264$		None	✓	?				$-1$		\(-4\)	\(0\)	\(12\)	\(-14\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.de	$42237$	$2$	42237.a	1.a	$1$	$28$	$28$	$337.264$		None	✓	?				$-1$		\(4\)	\(0\)	\(12\)	\(-14\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.df	$42237$	$2$	42237.a	1.a	$1$	$30$	$30$	$337.264$		None	✓	?				$-1$		\(-3\)	\(0\)	\(-3\)	\(18\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.dg	$42237$	$2$	42237.a	1.a	$1$	$30$	$30$	$337.264$		None	✓	?				$-1$		\(3\)	\(0\)	\(-3\)	\(18\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.dh	$42237$	$2$	42237.a	1.a	$1$	$33$	$33$	$337.264$		None	✓	?				$-1$		\(-3\)	\(0\)	\(-15\)	\(15\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.di	$42237$	$2$	42237.a	1.a	$1$	$33$	$33$	$337.264$		None	✓	?				$-1$		\(-3\)	\(0\)	\(9\)	\(3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.dj	$42237$	$2$	42237.a	1.a	$1$	$33$	$33$	$337.264$		None	✓	?	✓			$-1$		\(3\)	\(0\)	\(-15\)	\(15\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
42237.2.a.dk	$42237$	$2$	42237.a	1.a	$1$	$33$	$33$	$337.264$		None	✓	?	✓			$-1$		\(3\)	\(0\)	\(9\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
42237.2.a.dl	$42237$	$2$	42237.a	1.a	$1$	$36$	$36$	$337.264$		None	✓	?				$-1$		\(-12\)	\(0\)	\(-2\)	\(8\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.dm	$42237$	$2$	42237.a	1.a	$1$	$36$	$36$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-16\)		$+$	$-$	$-$	$+$
42237.2.a.dn	$42237$	$2$	42237.a	1.a	$1$	$36$	$36$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-16\)		$+$	$+$	$-$	$-$
42237.2.a.do	$42237$	$2$	42237.a	1.a	$1$	$36$	$36$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-12\)		$+$	$-$	$-$	$+$
42237.2.a.dp	$42237$	$2$	42237.a	1.a	$1$	$36$	$36$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-12\)		$+$	$+$	$-$	$-$
42237.2.a.dq	$42237$	$2$	42237.a	1.a	$1$	$36$	$36$	$337.264$		None	✓	?				$-1$		\(12\)	\(0\)	\(-2\)	\(8\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.dr	$42237$	$2$	42237.a	1.a	$1$	$44$	$44$	$337.264$		None	✓	?	✓			$-1$		\(-4\)	\(0\)	\(-20\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
42237.2.a.ds	$42237$	$2$	42237.a	1.a	$1$	$44$	$44$	$337.264$		None	✓	?	✓			$-1$		\(4\)	\(0\)	\(-20\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
42237.2.a.dt	$42237$	$2$	42237.a	1.a	$1$	$54$	$54$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-18\)		$+$	$+$	$+$	$+$
42237.2.a.du	$42237$	$2$	42237.a	1.a	$1$	$54$	$54$	$337.264$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(-18\)		$+$	$-$	$-$	$+$
42237.2.a.dv	$42237$	$2$	42237.a	1.a	$1$	$66$	$66$	$337.264$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(30\)		$+$	$+$	$-$	$-$
42237.2.a.dw	$42237$	$2$	42237.a	1.a	$1$	$66$	$66$	$337.264$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(30\)		$+$	$-$	$+$	$-$
42237.2.a.dx	$42237$	$2$	42237.a	1.a	$1$	$72$	$72$	$337.264$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$
42237.2.a.dy	$42237$	$2$	42237.a	1.a	$1$	$72$	$72$	$337.264$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(42237))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(42237)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(247))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(741))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2223))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3249))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4693))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14079))\)\(^{\oplus 2}\)