Space of modular forms of level 31734, weight 2, and trivial character

• Label: 31734.2.a
• Level: $31734$
• Weight: $2$
• Character orbit: 31734.a
• Rep. character: $\chi_{31734}(1,\cdot)$
• Character field: $\Q$
• Dimension: $700$
• Newform subspaces: $53$
• Sturm bound: $11088$

Defining parameters

Level:	\( N \)	\(=\)	\( 31734 = 2 \cdot 3^{2} \cdot 41 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31734.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 53 \)
Sturm bound:			\(11088\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(31734))\).

	Total	New	Old
Modular forms	5560	700	4860
Cusp forms	5529	700	4829
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(41\)	\(43\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(327\)	\(29\)	\(298\)		\(326\)	\(29\)	\(297\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(365\)	\(41\)	\(324\)		\(363\)	\(41\)	\(322\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(359\)	\(41\)	\(318\)		\(357\)	\(41\)	\(316\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(337\)	\(29\)	\(308\)		\(335\)	\(29\)	\(306\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(356\)	\(55\)	\(301\)		\(354\)	\(55\)	\(299\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(341\)	\(52\)	\(289\)		\(339\)	\(52\)	\(287\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(342\)	\(50\)	\(292\)		\(340\)	\(50\)	\(290\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(351\)	\(53\)	\(298\)		\(349\)	\(53\)	\(296\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(347\)	\(41\)	\(306\)		\(345\)	\(41\)	\(304\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(351\)	\(29\)	\(322\)		\(349\)	\(29\)	\(320\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(351\)	\(29\)	\(322\)		\(349\)	\(29\)	\(320\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(343\)	\(41\)	\(302\)		\(341\)	\(41\)	\(300\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(342\)	\(49\)	\(293\)		\(340\)	\(49\)	\(291\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(351\)	\(58\)	\(293\)		\(349\)	\(58\)	\(291\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(356\)	\(56\)	\(300\)		\(354\)	\(56\)	\(298\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(341\)	\(47\)	\(294\)		\(339\)	\(47\)	\(292\)		\(2\)	\(0\)	\(2\)
Plus space				\(+\)		\(2732\)	\(314\)	\(2418\)		\(2717\)	\(314\)	\(2403\)		\(15\)	\(0\)	\(15\)
Minus space				\(-\)		\(2828\)	\(386\)	\(2442\)		\(2812\)	\(386\)	\(2426\)		\(16\)	\(0\)	\(16\)

Trace form

700 * q + 700 * q^4 - 8 * q^5 - 8 * q^7 - 8 * q^10 - 20 * q^11 + 4 * q^13 + 700 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^20 - 16 * q^23 + 716 * q^25 - 16 * q^26 - 8 * q^28 + 16 * q^31 - 8 * q^35 + 32 * q^37 - 4 * q^38 - 8 * q^40 - 8 * q^41 - 20 * q^44 - 24 * q^47 + 700 * q^49 - 32 * q^50 + 4 * q^52 - 28 * q^53 + 20 * q^58 + 8 * q^59 - 24 * q^61 - 8 * q^62 + 700 * q^64 + 36 * q^67 + 8 * q^68 + 8 * q^70 - 16 * q^71 - 16 * q^74 + 8 * q^76 - 48 * q^77 + 64 * q^79 - 8 * q^80 + 16 * q^83 - 24 * q^89 + 32 * q^91 - 16 * q^92 + 16 * q^94 - 16 * q^95 - 56 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(31734))\) 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	41	43
31734.2.a.a	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-2q^{11}+\cdots\)
31734.2.a.b	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+5q^{11}+\cdots\)
31734.2.a.c	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-3\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
31734.2.a.d	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-3q^{7}-q^{8}+2q^{10}+\cdots\)
31734.2.a.e	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots\)
31734.2.a.f	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{13}+q^{14}+\cdots\)
31734.2.a.g	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots\)
31734.2.a.h	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+4q^{11}+\cdots\)
31734.2.a.i	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+2q^{7}-q^{8}-3q^{10}+\cdots\)
31734.2.a.j	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-5q^{7}+q^{8}-3q^{10}+\cdots\)
31734.2.a.k	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+4q^{7}+q^{8}-2q^{10}+\cdots\)
31734.2.a.l	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{11}+\cdots\)
31734.2.a.m	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(-3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots\)
31734.2.a.n	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-2q^{11}+\cdots\)
31734.2.a.o	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+2q^{11}+\cdots\)
31734.2.a.p	$31734$	$2$	31734.a	1.a	$1$	$1$	$1$	$253.397$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
31734.2.a.q	$31734$	$2$	31734.a	1.a	$1$	$2$	$2$	$253.397$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-4\)	\(4\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.r	$31734$	$2$	31734.a	1.a	$1$	$2$	$2$	$253.397$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.s	$31734$	$2$	31734.a	1.a	$1$	$2$	$2$	$253.397$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.t	$31734$	$2$	31734.a	1.a	$1$	$3$	$3$	$253.397$	3.3.404.1	None	✓	?				$-1$		\(-3\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.u	$31734$	$2$	31734.a	1.a	$1$	$4$	$4$	$253.397$	4.4.42656.1	None	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.v	$31734$	$2$	31734.a	1.a	$1$	$9$	$9$	$253.397$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-9\)	\(0\)	\(3\)	\(-9\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.w	$31734$	$2$	31734.a	1.a	$1$	$11$	$11$	$253.397$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(-11\)	\(0\)	\(7\)	\(-8\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.x	$31734$	$2$	31734.a	1.a	$1$	$12$	$12$	$253.397$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(0\)	\(4\)	\(-10\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.y	$31734$	$2$	31734.a	1.a	$1$	$12$	$12$	$253.397$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(0\)	\(6\)	\(-6\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.z	$31734$	$2$	31734.a	1.a	$1$	$12$	$12$	$253.397$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.ba	$31734$	$2$	31734.a	1.a	$1$	$12$	$12$	$253.397$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(0\)	\(6\)	\(11\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.bb	$31734$	$2$	31734.a	1.a	$1$	$13$	$13$	$253.397$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?				$-1$		\(13\)	\(0\)	\(3\)	\(-9\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.bc	$31734$	$2$	31734.a	1.a	$1$	$13$	$13$	$253.397$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?				$-1$		\(13\)	\(0\)	\(5\)	\(-10\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.bd	$31734$	$2$	31734.a	1.a	$1$	$14$	$14$	$253.397$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(14\)	\(0\)	\(-4\)	\(7\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.be	$31734$	$2$	31734.a	1.a	$1$	$16$	$16$	$253.397$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(-16\)	\(0\)	\(-7\)	\(3\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.bf	$31734$	$2$	31734.a	1.a	$1$	$16$	$16$	$253.397$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(-16\)	\(0\)	\(13\)	\(-4\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.bg	$31734$	$2$	31734.a	1.a	$1$	$17$	$17$	$253.397$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?	✓			$-1$		\(-17\)	\(0\)	\(-3\)	\(-1\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.bh	$31734$	$2$	31734.a	1.a	$1$	$17$	$17$	$253.397$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(-17\)	\(0\)	\(11\)	\(-3\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.bi	$31734$	$2$	31734.a	1.a	$1$	$17$	$17$	$253.397$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(17\)	\(0\)	\(3\)	\(-9\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.bj	$31734$	$2$	31734.a	1.a	$1$	$17$	$17$	$253.397$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	?				$-1$		\(17\)	\(0\)	\(9\)	\(3\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.bk	$31734$	$2$	31734.a	1.a	$1$	$18$	$18$	$253.397$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(18\)	\(0\)	\(-9\)	\(-9\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.bl	$31734$	$2$	31734.a	1.a	$1$	$18$	$18$	$253.397$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(18\)	\(0\)	\(5\)	\(5\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.bm	$31734$	$2$	31734.a	1.a	$1$	$20$	$20$	$253.397$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(-20\)	\(0\)	\(-11\)	\(0\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.bn	$31734$	$2$	31734.a	1.a	$1$	$20$	$20$	$253.397$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?	✓			$-1$		\(20\)	\(0\)	\(-5\)	\(-9\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.bo	$31734$	$2$	31734.a	1.a	$1$	$20$	$20$	$253.397$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?	✓			$-1$		\(20\)	\(0\)	\(-4\)	\(13\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.bp	$31734$	$2$	31734.a	1.a	$1$	$21$	$21$	$253.397$		None	✓	?	✓			$-1$		\(-21\)	\(0\)	\(-7\)	\(11\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.bq	$31734$	$2$	31734.a	1.a	$1$	$22$	$22$	$253.397$		None	✓	?	✓			$-1$		\(-22\)	\(0\)	\(-5\)	\(15\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.br	$31734$	$2$	31734.a	1.a	$1$	$22$	$22$	$253.397$		None	✓	?	✓			$-1$		\(22\)	\(0\)	\(-3\)	\(9\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.bs	$31734$	$2$	31734.a	1.a	$1$	$24$	$24$	$253.397$		None	✓	?	✓			$-1$		\(-24\)	\(0\)	\(-10\)	\(4\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.bt	$31734$	$2$	31734.a	1.a	$1$	$29$	$29$	$253.397$		None	✓	?	✓	✓		$-1$		\(-29\)	\(0\)	\(1\)	\(-9\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.bu	$31734$	$2$	31734.a	1.a	$1$	$29$	$29$	$253.397$		None	✓	?	✓	✓		$-1$		\(-29\)	\(0\)	\(1\)	\(-5\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.bv	$31734$	$2$	31734.a	1.a	$1$	$29$	$29$	$253.397$		None	✓	?	✓	✓		$-1$		\(29\)	\(0\)	\(-1\)	\(-9\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
31734.2.a.bw	$31734$	$2$	31734.a	1.a	$1$	$29$	$29$	$253.397$		None	✓	?	✓	✓		$-1$		\(29\)	\(0\)	\(-1\)	\(-5\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
31734.2.a.bx	$31734$	$2$	31734.a	1.a	$1$	$40$	$40$	$253.397$		None	✓	?	✓			$-1$		\(-40\)	\(0\)	\(4\)	\(10\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.by	$31734$	$2$	31734.a	1.a	$1$	$40$	$40$	$253.397$		None	✓	?	✓			$-1$		\(40\)	\(0\)	\(-4\)	\(10\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
31734.2.a.bz	$31734$	$2$	31734.a	1.a	$1$	$41$	$41$	$253.397$		None	✓	?	✓	✓		$-1$		\(-41\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
31734.2.a.ca	$31734$	$2$	31734.a	1.a	$1$	$41$	$41$	$253.397$		None	✓	?	✓	✓		$-1$		\(41\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(31734))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(31734)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(258))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(387))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(738))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(774))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1763))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3526))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(10578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15867))\)\(^{\oplus 2}\)