Space of modular forms of level 20181, weight 2, and trivial character

• Label: 20181.2.a
• Level: $20181$
• Weight: $2$
• Character orbit: 20181.a
• Rep. character: $\chi_{20181}(1,\cdot)$
• Character field: $\Q$
• Dimension: $928$
• Newform subspaces: $80$
• Sturm bound: $5290$

Defining parameters

Level:	\( N \)	\(=\)	\( 20181 = 3 \cdot 7 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	20181.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 80 \)
Sturm bound:			\(5290\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(20181))\).

	Total	New	Old
Modular forms	2708	928	1780
Cusp forms	2581	928	1653
Eisenstein series	127	0	127

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

\(3\)	\(7\)	\(31\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(325\)	\(113\)	\(212\)		\(310\)	\(113\)	\(197\)		\(15\)	\(0\)	\(15\)
\(+\)	\(+\)	\(-\)	\(-\)		\(350\)	\(120\)	\(230\)		\(334\)	\(120\)	\(214\)		\(16\)	\(0\)	\(16\)
\(+\)	\(-\)	\(+\)	\(-\)		\(341\)	\(111\)	\(230\)		\(325\)	\(111\)	\(214\)		\(16\)	\(0\)	\(16\)
\(+\)	\(-\)	\(-\)	\(+\)		\(336\)	\(120\)	\(216\)		\(320\)	\(120\)	\(200\)		\(16\)	\(0\)	\(16\)
\(-\)	\(+\)	\(+\)	\(-\)		\(352\)	\(127\)	\(225\)		\(336\)	\(127\)	\(209\)		\(16\)	\(0\)	\(16\)
\(-\)	\(+\)	\(-\)	\(+\)		\(327\)	\(105\)	\(222\)		\(311\)	\(105\)	\(206\)		\(16\)	\(0\)	\(16\)
\(-\)	\(-\)	\(+\)	\(+\)		\(336\)	\(97\)	\(239\)		\(320\)	\(97\)	\(223\)		\(16\)	\(0\)	\(16\)
\(-\)	\(-\)	\(-\)	\(-\)		\(341\)	\(135\)	\(206\)		\(325\)	\(135\)	\(190\)		\(16\)	\(0\)	\(16\)
Plus space			\(+\)		\(1324\)	\(435\)	\(889\)		\(1261\)	\(435\)	\(826\)		\(63\)	\(0\)	\(63\)
Minus space			\(-\)		\(1384\)	\(493\)	\(891\)		\(1320\)	\(493\)	\(827\)		\(64\)	\(0\)	\(64\)

Trace form

928 * q - 4 * q^2 + 928 * q^4 - 8 * q^5 + 4 * q^6 - 2 * q^7 - 12 * q^8 + 928 * q^9 - 8 * q^10 - 8 * q^12 - 8 * q^13 - 2 * q^14 + 920 * q^16 - 16 * q^17 - 4 * q^18 + 2 * q^21 + 16 * q^22 + 8 * q^23 + 12 * q^24 + 912 * q^25 + 16 * q^26 - 6 * q^28 - 24 * q^29 + 12 * q^32 + 24 * q^34 + 4 * q^35 + 928 * q^36 - 8 * q^37 + 64 * q^38 + 24 * q^40 - 16 * q^41 + 2 * q^42 - 8 * q^43 + 40 * q^44 - 8 * q^45 + 8 * q^46 + 32 * q^47 - 32 * q^48 + 928 * q^49 + 36 * q^50 + 8 * q^51 - 24 * q^52 - 16 * q^53 + 4 * q^54 - 32 * q^55 - 18 * q^56 + 16 * q^58 - 16 * q^60 - 8 * q^61 - 2 * q^63 + 912 * q^64 - 56 * q^65 - 8 * q^66 - 16 * q^67 + 16 * q^68 + 8 * q^69 - 12 * q^70 - 8 * q^71 - 12 * q^72 - 24 * q^73 - 16 * q^74 - 16 * q^75 - 16 * q^76 + 8 * q^78 + 32 * q^79 - 48 * q^80 + 928 * q^81 + 8 * q^82 + 32 * q^83 + 6 * q^84 + 40 * q^85 - 64 * q^86 - 24 * q^87 + 40 * q^88 - 8 * q^90 + 12 * q^91 + 32 * q^92 + 48 * q^94 + 64 * q^95 + 68 * q^96 - 8 * q^97 - 4 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(20181))\) 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	7	31
20181.2.a.a	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(-1\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
20181.2.a.b	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(-1\)	\(4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
20181.2.a.c	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots\)
20181.2.a.d	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(1\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots\)
20181.2.a.e	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
20181.2.a.f	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(-2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
20181.2.a.g	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
20181.2.a.h	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
20181.2.a.i	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+2q^{12}+\cdots\)
20181.2.a.j	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-2q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
20181.2.a.k	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(4\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+4q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
20181.2.a.l	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-2q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
20181.2.a.m	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
20181.2.a.n	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
20181.2.a.o	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
20181.2.a.p	$20181$	$2$	20181.a	1.a	$1$	$1$	$1$	$161.146$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
20181.2.a.q	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-3\)	\(-2\)	\(-4\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.r	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-3\)	\(2\)	\(-4\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.s	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.t	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.u	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.v	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(4\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.w	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{6}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.x	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.y	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.z	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.ba	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(-2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bb	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(-2\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.bc	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.bd	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(2\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.be	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(1\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bf	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(1\)	\(2\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bg	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bh	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bi	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bj	$20181$	$2$	20181.a	1.a	$1$	$2$	$2$	$161.146$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bk	$20181$	$2$	20181.a	1.a	$1$	$3$	$3$	$161.146$	3.3.469.1	None	✓	?				$-1$		\(-2\)	\(-3\)	\(-4\)	\(-3\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.bl	$20181$	$2$	20181.a	1.a	$1$	$3$	$3$	$161.146$	3.3.469.1	None	✓	?				$-1$		\(-2\)	\(3\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bm	$20181$	$2$	20181.a	1.a	$1$	$3$	$3$	$161.146$	3.3.148.1	None	✓	?				$-1$		\(-1\)	\(3\)	\(-4\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bn	$20181$	$2$	20181.a	1.a	$1$	$3$	$3$	$161.146$	3.3.148.1	None	✓	?				$-1$		\(1\)	\(3\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bo	$20181$	$2$	20181.a	1.a	$1$	$5$	$5$	$161.146$	5.5.1881008.1	None	✓	?				$-1$		\(3\)	\(-5\)	\(-3\)	\(5\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.bp	$20181$	$2$	20181.a	1.a	$1$	$5$	$5$	$161.146$	5.5.1881008.1	None	✓	?				$-1$		\(3\)	\(5\)	\(-3\)	\(5\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bq	$20181$	$2$	20181.a	1.a	$1$	$6$	$6$	$161.146$	6.6.159652448.1	None	✓	?				$-1$		\(0\)	\(-6\)	\(8\)	\(-6\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.br	$20181$	$2$	20181.a	1.a	$1$	$6$	$6$	$161.146$	6.6.6782000.1	None	✓	?				$-1$		\(1\)	\(-6\)	\(-7\)	\(6\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bs	$20181$	$2$	20181.a	1.a	$1$	$6$	$6$	$161.146$	6.6.216318320.1	None	✓	?				$-1$		\(1\)	\(-6\)	\(5\)	\(6\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bt	$20181$	$2$	20181.a	1.a	$1$	$6$	$6$	$161.146$	6.6.6782000.1	None	✓	?				$-1$		\(1\)	\(6\)	\(-7\)	\(6\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.bu	$20181$	$2$	20181.a	1.a	$1$	$7$	$7$	$161.146$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(-7\)	\(-4\)	\(-7\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bv	$20181$	$2$	20181.a	1.a	$1$	$7$	$7$	$161.146$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(7\)	\(-4\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bw	$20181$	$2$	20181.a	1.a	$1$	$8$	$8$	$161.146$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(-8\)	\(-2\)	\(-8\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.bx	$20181$	$2$	20181.a	1.a	$1$	$8$	$8$	$161.146$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(8\)	\(-2\)	\(-8\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.by	$20181$	$2$	20181.a	1.a	$1$	$9$	$9$	$161.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(-9\)	\(-4\)	\(9\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.bz	$20181$	$2$	20181.a	1.a	$1$	$9$	$9$	$161.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(9\)	\(-4\)	\(9\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.ca	$20181$	$2$	20181.a	1.a	$1$	$9$	$9$	$161.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(-9\)	\(2\)	\(-9\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.cb	$20181$	$2$	20181.a	1.a	$1$	$9$	$9$	$161.146$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(9\)	\(2\)	\(-9\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.cc	$20181$	$2$	20181.a	1.a	$1$	$12$	$12$	$161.146$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(-12\)	\(-9\)	\(12\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.cd	$20181$	$2$	20181.a	1.a	$1$	$12$	$12$	$161.146$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(12\)	\(-9\)	\(12\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.ce	$20181$	$2$	20181.a	1.a	$1$	$14$	$14$	$161.146$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(-3\)	\(-14\)	\(-1\)	\(-14\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.cf	$20181$	$2$	20181.a	1.a	$1$	$14$	$14$	$161.146$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	?				$-1$		\(-3\)	\(14\)	\(-1\)	\(-14\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.cg	$20181$	$2$	20181.a	1.a	$1$	$16$	$16$	$161.146$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-16\)	\(0\)	\(16\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.ch	$20181$	$2$	20181.a	1.a	$1$	$16$	$16$	$161.146$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(16\)	\(0\)	\(16\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.ci	$20181$	$2$	20181.a	1.a	$1$	$16$	$16$	$161.146$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(4\)	\(-16\)	\(13\)	\(16\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.cj	$20181$	$2$	20181.a	1.a	$1$	$16$	$16$	$161.146$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	?				$-1$		\(4\)	\(16\)	\(13\)	\(16\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.ck	$20181$	$2$	20181.a	1.a	$1$	$18$	$18$	$161.146$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(3\)	\(-18\)	\(-1\)	\(-18\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.cl	$20181$	$2$	20181.a	1.a	$1$	$18$	$18$	$161.146$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(3\)	\(18\)	\(-1\)	\(-18\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.cm	$20181$	$2$	20181.a	1.a	$1$	$28$	$28$	$161.146$		None	✓	?				$-1$		\(-5\)	\(-28\)	\(-14\)	\(28\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.cn	$20181$	$2$	20181.a	1.a	$1$	$28$	$28$	$161.146$		None	✓	?				$-1$		\(-5\)	\(28\)	\(-14\)	\(28\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.co	$20181$	$2$	20181.a	1.a	$1$	$28$	$28$	$161.146$		None	✓	?				$-1$		\(-4\)	\(-28\)	\(0\)	\(-28\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.cp	$20181$	$2$	20181.a	1.a	$1$	$28$	$28$	$161.146$		None	✓	?				$-1$		\(-4\)	\(28\)	\(0\)	\(-28\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.cq	$20181$	$2$	20181.a	1.a	$1$	$28$	$28$	$161.146$		None	✓	?				$-1$		\(-3\)	\(-28\)	\(-2\)	\(-28\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.cr	$20181$	$2$	20181.a	1.a	$1$	$28$	$28$	$161.146$		None	✓	?				$-1$		\(-3\)	\(28\)	\(-2\)	\(-28\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.cs	$20181$	$2$	20181.a	1.a	$1$	$36$	$36$	$161.146$		None	✓	?	✓			$-1$		\(-4\)	\(-36\)	\(0\)	\(36\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
20181.2.a.ct	$20181$	$2$	20181.a	1.a	$1$	$36$	$36$	$161.146$		None	✓	?				$-1$		\(-4\)	\(36\)	\(0\)	\(36\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.cu	$20181$	$2$	20181.a	1.a	$1$	$36$	$36$	$161.146$		None	✓	?	✓			$-1$		\(3\)	\(-36\)	\(-2\)	\(-36\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.cv	$20181$	$2$	20181.a	1.a	$1$	$36$	$36$	$161.146$		None	✓	?				$-1$		\(3\)	\(36\)	\(-2\)	\(-36\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.cw	$20181$	$2$	20181.a	1.a	$1$	$36$	$36$	$161.146$		None	✓	?				$-1$		\(5\)	\(-36\)	\(18\)	\(36\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.cx	$20181$	$2$	20181.a	1.a	$1$	$36$	$36$	$161.146$		None	✓	?				$-1$		\(5\)	\(36\)	\(18\)	\(36\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
20181.2.a.cy	$20181$	$2$	20181.a	1.a	$1$	$48$	$48$	$161.146$		None	✓	?	✓			$-1$		\(0\)	\(-48\)	\(0\)	\(48\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
20181.2.a.cz	$20181$	$2$	20181.a	1.a	$1$	$48$	$48$	$161.146$		None	✓	?	✓			$-1$		\(0\)	\(48\)	\(0\)	\(48\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.da	$20181$	$2$	20181.a	1.a	$1$	$64$	$64$	$161.146$		None	✓	?	✓			$-1$		\(0\)	\(-64\)	\(0\)	\(-64\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
20181.2.a.db	$20181$	$2$	20181.a	1.a	$1$	$64$	$64$	$161.146$		None	✓	?	✓			$-1$		\(0\)	\(64\)	\(0\)	\(-64\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(20181))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(20181)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(217))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(651))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(961))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2883))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6727))\)\(^{\oplus 2}\)