Space of modular forms of level 12138, weight 2, and trivial character

• Label: 12138.2.a
• Level: $12138$
• Weight: $2$
• Character orbit: 12138.a
• Rep. character: $\chi_{12138}(1,\cdot)$
• Character field: $\Q$
• Dimension: $270$
• Newform subspaces: $82$
• Sturm bound: $4896$

Defining parameters

Level:	\( N \)	\(=\)	\( 12138 = 2 \cdot 3 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	12138.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 82 \)
Sturm bound:			\(4896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(12138))\).

	Total	New	Old
Modular forms	2520	270	2250
Cusp forms	2377	270	2107
Eisenstein series	143	0	143

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

\(2\)	\(3\)	\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(144\)	\(18\)	\(126\)		\(136\)	\(18\)	\(118\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(170\)	\(16\)	\(154\)		\(161\)	\(16\)	\(145\)		\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(162\)	\(18\)	\(144\)		\(153\)	\(18\)	\(135\)		\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(154\)	\(16\)	\(138\)		\(145\)	\(16\)	\(129\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(162\)	\(18\)	\(144\)		\(153\)	\(18\)	\(135\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(154\)	\(16\)	\(138\)		\(145\)	\(16\)	\(129\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(162\)	\(18\)	\(144\)		\(153\)	\(18\)	\(135\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(152\)	\(16\)	\(136\)		\(143\)	\(16\)	\(127\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(162\)	\(21\)	\(141\)		\(153\)	\(21\)	\(132\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(153\)	\(12\)	\(141\)		\(144\)	\(12\)	\(132\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(153\)	\(14\)	\(139\)		\(144\)	\(14\)	\(130\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(162\)	\(20\)	\(142\)		\(153\)	\(20\)	\(133\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(162\)	\(14\)	\(148\)		\(153\)	\(14\)	\(139\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(153\)	\(20\)	\(133\)		\(144\)	\(20\)	\(124\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(153\)	\(21\)	\(132\)		\(144\)	\(21\)	\(123\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(162\)	\(12\)	\(150\)		\(153\)	\(12\)	\(141\)		\(9\)	\(0\)	\(9\)
Plus space				\(+\)		\(1244\)	\(120\)	\(1124\)		\(1173\)	\(120\)	\(1053\)		\(71\)	\(0\)	\(71\)
Minus space				\(-\)		\(1276\)	\(150\)	\(1126\)		\(1204\)	\(150\)	\(1054\)		\(72\)	\(0\)	\(72\)

Trace form

270 * q - 2 * q^2 + 270 * q^4 - 4 * q^5 - 2 * q^8 + 270 * q^9 - 4 * q^10 - 8 * q^11 - 20 * q^13 - 8 * q^15 + 270 * q^16 - 2 * q^18 - 16 * q^19 - 4 * q^20 - 2 * q^21 + 258 * q^25 - 4 * q^26 - 12 * q^29 - 8 * q^30 - 16 * q^31 - 2 * q^32 - 16 * q^33 + 8 * q^35 + 270 * q^36 - 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^40 - 4 * q^41 - 2 * q^42 - 8 * q^43 - 8 * q^44 - 4 * q^45 + 16 * q^47 + 270 * q^49 + 2 * q^50 - 20 * q^52 + 36 * q^53 - 16 * q^57 + 12 * q^58 + 32 * q^59 - 8 * q^60 - 4 * q^61 + 32 * q^62 + 270 * q^64 + 24 * q^65 - 40 * q^67 - 8 * q^70 + 16 * q^71 - 2 * q^72 + 12 * q^73 - 12 * q^74 - 32 * q^75 - 16 * q^76 - 16 * q^77 - 4 * q^80 + 270 * q^81 + 28 * q^82 - 2 * q^84 - 8 * q^86 - 36 * q^89 - 4 * q^90 - 16 * q^93 - 16 * q^94 + 32 * q^95 + 12 * q^97 - 2 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(12138))\) 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	7	17
12138.2.a.a	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.b	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.c	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
12138.2.a.d	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.e	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
12138.2.a.f	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(3\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.g	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.h	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
12138.2.a.i	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.j	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.k	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
12138.2.a.l	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.m	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
12138.2.a.n	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
12138.2.a.o	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.p	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.q	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
12138.2.a.r	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
12138.2.a.s	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.t	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
12138.2.a.u	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-1\)	\(3\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
12138.2.a.v	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.w	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.x	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
12138.2.a.y	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.z	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
12138.2.a.ba	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
12138.2.a.bb	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
12138.2.a.bc	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
12138.2.a.bd	$12138$	$2$	12138.a	1.a	$1$	$1$	$1$	$96.922$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
12138.2.a.be	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{41}) \)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(-1\)	\(2\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bf	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.bg	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bh	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.bi	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(2\)	\(2\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bj	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{33}) \)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(3\)	\(-2\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.bk	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(2\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.bl	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(-2\)	\(2\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bm	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(2\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bn	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(-2\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.bo	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{6}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bp	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.bq	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.br	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.bs	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.bt	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{21}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bu	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{21}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.bv	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.bw	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.bx	$12138$	$2$	12138.a	1.a	$1$	$2$	$2$	$96.922$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.by	$12138$	$2$	12138.a	1.a	$1$	$4$	$4$	$96.922$	4.4.7232.1	None	✓	?				$-1$		\(-4\)	\(-4\)	\(-4\)	\(4\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.bz	$12138$	$2$	12138.a	1.a	$1$	$4$	$4$	$96.922$	4.4.7232.1	None	✓	?				$-1$		\(-4\)	\(4\)	\(4\)	\(-4\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.ca	$12138$	$2$	12138.a	1.a	$1$	$4$	$4$	$96.922$	4.4.40293.1	None	✓	?				$-1$		\(4\)	\(-4\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.cb	$12138$	$2$	12138.a	1.a	$1$	$4$	$4$	$96.922$	\(\Q(\zeta_{16})^+\)	None	✓	?				$-1$		\(4\)	\(-4\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.cc	$12138$	$2$	12138.a	1.a	$1$	$4$	$4$	$96.922$	\(\Q(\zeta_{16})^+\)	None	✓	?				$-1$		\(4\)	\(4\)	\(-4\)	\(4\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.cd	$12138$	$2$	12138.a	1.a	$1$	$4$	$4$	$96.922$	4.4.40293.1	None	✓	?				$-1$		\(4\)	\(4\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.ce	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.428564992.1	None	✓	?				$-1$		\(-6\)	\(-6\)	\(2\)	\(-6\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.cf	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.3916917.1	None	✓	?				$-1$		\(-6\)	\(-6\)	\(3\)	\(-6\)		$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.cg	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.7328637.1	None	✓	?				$-1$		\(-6\)	\(-6\)	\(3\)	\(-6\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.ch	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.5911461.1	None	✓	?				$-1$		\(-6\)	\(-6\)	\(3\)	\(6\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.ci	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.1292517.1	None	✓	?	✓			$-1$		\(-6\)	\(-6\)	\(3\)	\(6\)		$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.cj	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.5911461.1	None	✓	?	✓			$-1$		\(-6\)	\(6\)	\(-3\)	\(-6\)		$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.ck	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.1292517.1	None	✓	?				$-1$		\(-6\)	\(6\)	\(-3\)	\(-6\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.cl	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.7328637.1	None	✓	?				$-1$		\(-6\)	\(6\)	\(-3\)	\(6\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.cm	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.3916917.1	None	✓	?				$-1$		\(-6\)	\(6\)	\(-3\)	\(6\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.cn	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.428564992.1	None	✓	?				$-1$		\(-6\)	\(6\)	\(-2\)	\(6\)		$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.co	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.134742528.1	None	✓	?				$-1$		\(6\)	\(-6\)	\(-6\)	\(-6\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.cp	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.24334749.1	None	✓	?	✓			$-1$		\(6\)	\(-6\)	\(-3\)	\(-6\)		$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.cq	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.18298629.1	None	✓	?	✓			$-1$		\(6\)	\(-6\)	\(-3\)	\(6\)		$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.cr	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.1397493.1	None	✓	?				$-1$		\(6\)	\(-6\)	\(9\)	\(-6\)		$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.cs	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.7328637.1	None	✓	?				$-1$		\(6\)	\(-6\)	\(9\)	\(6\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.ct	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.7328637.1	None	✓	?	✓			$-1$		\(6\)	\(6\)	\(-9\)	\(-6\)		$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
12138.2.a.cu	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.1397493.1	None	✓	?	✓			$-1$		\(6\)	\(6\)	\(-9\)	\(6\)		$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.cv	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.18298629.1	None	✓	?				$-1$		\(6\)	\(6\)	\(3\)	\(-6\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.cw	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.24334749.1	None	✓	?				$-1$		\(6\)	\(6\)	\(3\)	\(6\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.cx	$12138$	$2$	12138.a	1.a	$1$	$6$	$6$	$96.922$	6.6.134742528.1	None	✓	?				$-1$		\(6\)	\(6\)	\(6\)	\(6\)		$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
12138.2.a.cy	$12138$	$2$	12138.a	1.a	$1$	$8$	$8$	$96.922$	8.8.\(\cdots\).1	None	✓	?	✓			$-1$		\(-8\)	\(-8\)	\(-12\)	\(-8\)		$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.cz	$12138$	$2$	12138.a	1.a	$1$	$8$	$8$	$96.922$	8.8.\(\cdots\).1	None	✓	?	✓			$-1$		\(-8\)	\(-8\)	\(-4\)	\(8\)		$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.da	$12138$	$2$	12138.a	1.a	$1$	$8$	$8$	$96.922$	8.8.\(\cdots\).1	None	✓	?	✓			$-1$		\(-8\)	\(8\)	\(4\)	\(-8\)		$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
12138.2.a.db	$12138$	$2$	12138.a	1.a	$1$	$8$	$8$	$96.922$	8.8.\(\cdots\).1	None	✓	?	✓			$-1$		\(-8\)	\(8\)	\(12\)	\(8\)		$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.dc	$12138$	$2$	12138.a	1.a	$1$	$12$	$12$	$96.922$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(12\)	\(-12\)	\(-4\)	\(12\)		$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
12138.2.a.dd	$12138$	$2$	12138.a	1.a	$1$	$12$	$12$	$96.922$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(12\)	\(12\)	\(4\)	\(-12\)		$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(12138))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(12138)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4046))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6069))\)\(^{\oplus 2}\)