Space of modular forms of level 33282, weight 2, and trivial character

• Label: 33282.2.a
• Level: $33282$
• Weight: $2$
• Character orbit: 33282.a
• Rep. character: $\chi_{33282}(1,\cdot)$
• Character field: $\Q$
• Dimension: $753$
• Newform subspaces: $109$
• Sturm bound: $11352$

Defining parameters

Level:	\( N \)	\(=\)	\( 33282 = 2 \cdot 3^{2} \cdot 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	33282.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 109 \)
Sturm bound:			\(11352\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(33282))\).

	Total	New	Old
Modular forms	5852	753	5099
Cusp forms	5501	753	4748
Eisenstein series	351	0	351

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

\(2\)	\(3\)	\(43\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(715\)	\(81\)	\(634\)		\(672\)	\(81\)	\(591\)		\(43\)	\(0\)	\(43\)
\(+\)	\(+\)	\(-\)	\(-\)		\(747\)	\(70\)	\(677\)		\(703\)	\(70\)	\(633\)		\(44\)	\(0\)	\(44\)
\(+\)	\(-\)	\(+\)	\(-\)		\(737\)	\(115\)	\(622\)		\(693\)	\(115\)	\(578\)		\(44\)	\(0\)	\(44\)
\(+\)	\(-\)	\(-\)	\(+\)		\(726\)	\(110\)	\(616\)		\(682\)	\(110\)	\(572\)		\(44\)	\(0\)	\(44\)
\(-\)	\(+\)	\(+\)	\(-\)		\(737\)	\(81\)	\(656\)		\(693\)	\(81\)	\(612\)		\(44\)	\(0\)	\(44\)
\(-\)	\(+\)	\(-\)	\(+\)		\(727\)	\(70\)	\(657\)		\(683\)	\(70\)	\(613\)		\(44\)	\(0\)	\(44\)
\(-\)	\(-\)	\(+\)	\(+\)		\(737\)	\(105\)	\(632\)		\(693\)	\(105\)	\(588\)		\(44\)	\(0\)	\(44\)
\(-\)	\(-\)	\(-\)	\(-\)		\(726\)	\(121\)	\(605\)		\(682\)	\(121\)	\(561\)		\(44\)	\(0\)	\(44\)
Plus space			\(+\)		\(2905\)	\(366\)	\(2539\)		\(2730\)	\(366\)	\(2364\)		\(175\)	\(0\)	\(175\)
Minus space			\(-\)		\(2947\)	\(387\)	\(2560\)		\(2771\)	\(387\)	\(2384\)		\(176\)	\(0\)	\(176\)

Trace form

753 * q + q^2 + 753 * q^4 - 2 * q^5 - 4 * q^7 + q^8 - 6 * q^11 + 4 * q^13 + 4 * q^14 + 753 * q^16 - 6 * q^17 + 8 * q^19 - 2 * q^20 - 8 * q^22 - 20 * q^23 + 757 * q^25 + 2 * q^26 - 4 * q^28 - 6 * q^29 + 8 * q^31 + q^32 + 6 * q^34 + 22 * q^37 - 2 * q^38 + 2 * q^41 - 6 * q^44 - 4 * q^46 - 4 * q^47 + 753 * q^49 - 9 * q^50 + 4 * q^52 - 12 * q^53 - 4 * q^55 + 4 * q^56 + 12 * q^58 + 10 * q^59 - 30 * q^61 - 4 * q^62 + 753 * q^64 + 2 * q^67 - 6 * q^68 - 20 * q^70 - 24 * q^71 - 2 * q^73 + 8 * q^76 + 12 * q^79 - 2 * q^80 - 18 * q^82 - 34 * q^83 + 8 * q^85 - 8 * q^88 + 18 * q^89 + 16 * q^91 - 20 * q^92 + 4 * q^94 - 8 * q^95 + 2 * q^97 + 9 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(33282))\) 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	43
33282.2.a.a	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}+3q^{7}-q^{8}+3q^{10}+\cdots\)
33282.2.a.b	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-4q^{7}-q^{8}+2q^{10}+\cdots\)
33282.2.a.c	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots\)
33282.2.a.d	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots\)
33282.2.a.e	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots\)
33282.2.a.f	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots\)
33282.2.a.g	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots\)
33282.2.a.h	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}-5q^{11}-2q^{13}+\cdots\)
33282.2.a.i	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
33282.2.a.j	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(1\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+5q^{7}-q^{8}-q^{10}+\cdots\)
33282.2.a.k	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots\)
33282.2.a.l	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-3q^{7}-q^{8}-3q^{10}+\cdots\)
33282.2.a.m	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
33282.2.a.n	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
33282.2.a.o	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(3\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+3q^{7}-q^{8}-3q^{10}+\cdots\)
33282.2.a.p	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}+4q^{7}-q^{8}-4q^{10}+\cdots\)
33282.2.a.q	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}-4q^{7}+q^{8}-4q^{10}+\cdots\)
33282.2.a.r	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-3q^{7}+q^{8}-3q^{10}+\cdots\)
33282.2.a.s	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
33282.2.a.t	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
33282.2.a.u	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+3q^{7}+q^{8}-3q^{10}+\cdots\)
33282.2.a.v	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-2q^{10}+\cdots\)
33282.2.a.w	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots\)
33282.2.a.x	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
33282.2.a.y	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
33282.2.a.z	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}-5q^{11}-2q^{13}+\cdots\)
33282.2.a.ba	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-4q^{7}+q^{8}+2q^{10}+\cdots\)
33282.2.a.bb	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots\)
33282.2.a.bc	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots\)
33282.2.a.bd	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots\)
33282.2.a.be	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots\)
33282.2.a.bf	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots\)
33282.2.a.bg	$33282$	$2$	33282.a	1.a	$1$	$1$	$1$	$265.758$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
33282.2.a.bh	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-5\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.bi	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.bj	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.bk	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.bl	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{21}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.bm	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.bn	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.bo	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.bp	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.bq	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.br	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.bs	$33282$	$2$	33282.a	1.a	$1$	$2$	$2$	$265.758$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(5\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.bt	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(-3\)	\(0\)	\(-2\)	\(11\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.bu	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(-3\)	\(0\)	\(-1\)	\(-9\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.bv	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(-3\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.bw	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(-3\)	\(0\)	\(5\)	\(-5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.bx	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(3\)	\(0\)	\(-5\)	\(5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.by	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(3\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.bz	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(3\)	\(0\)	\(1\)	\(9\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.ca	$33282$	$2$	33282.a	1.a	$1$	$3$	$3$	$265.758$	\(\Q(\zeta_{14})^+\)	None	✓	?				$-1$		\(3\)	\(0\)	\(2\)	\(-11\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.cb	$33282$	$2$	33282.a	1.a	$1$	$4$	$4$	$265.758$	4.4.8112.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.cc	$33282$	$2$	33282.a	1.a	$1$	$4$	$4$	$265.758$	4.4.8112.1	None	✓	?				$-1$		\(-4\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.cd	$33282$	$2$	33282.a	1.a	$1$	$4$	$4$	$265.758$	4.4.8112.1	None	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.ce	$33282$	$2$	33282.a	1.a	$1$	$4$	$4$	$265.758$	4.4.8112.1	None	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.cf	$33282$	$2$	33282.a	1.a	$1$	$5$	$5$	$265.758$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(-5\)	\(0\)	\(-4\)	\(-7\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.cg	$33282$	$2$	33282.a	1.a	$1$	$5$	$5$	$265.758$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(-5\)	\(0\)	\(1\)	\(-7\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.ch	$33282$	$2$	33282.a	1.a	$1$	$5$	$5$	$265.758$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(5\)	\(0\)	\(-1\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.ci	$33282$	$2$	33282.a	1.a	$1$	$5$	$5$	$265.758$	\(\Q(\zeta_{22})^+\)	None	✓	?				$-1$		\(5\)	\(0\)	\(4\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.cj	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	\(\Q(\zeta_{21})^+\)	None	✓	?				$-1$		\(-6\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.ck	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	6.6.72070817.1	None	✓	?				$-1$		\(-6\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.cl	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	6.6.6369853.1	None	✓	?				$-1$		\(-6\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.cm	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	\(\Q(\zeta_{21})^+\)	None	✓	?				$-1$		\(-6\)	\(0\)	\(4\)	\(-1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.cn	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	\(\Q(\zeta_{21})^+\)	None	✓	?				$-1$		\(-6\)	\(0\)	\(9\)	\(-5\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.co	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	\(\Q(\zeta_{21})^+\)	None	✓	?				$-1$		\(6\)	\(0\)	\(-9\)	\(5\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.cp	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	\(\Q(\zeta_{21})^+\)	None	✓	?				$-1$		\(6\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.cq	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	6.6.6369853.1	None	✓	?				$-1$		\(6\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.cr	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	6.6.72070817.1	None	✓	?				$-1$		\(6\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.cs	$33282$	$2$	33282.a	1.a	$1$	$6$	$6$	$265.758$	\(\Q(\zeta_{21})^+\)	None	✓	?				$-1$		\(6\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.ct	$33282$	$2$	33282.a	1.a	$1$	$9$	$9$	$265.758$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-9\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.cu	$33282$	$2$	33282.a	1.a	$1$	$9$	$9$	$265.758$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-9\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.cv	$33282$	$2$	33282.a	1.a	$1$	$9$	$9$	$265.758$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(-9\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.cw	$33282$	$2$	33282.a	1.a	$1$	$9$	$9$	$265.758$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(9\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.cx	$33282$	$2$	33282.a	1.a	$1$	$9$	$9$	$265.758$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(9\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.cy	$33282$	$2$	33282.a	1.a	$1$	$9$	$9$	$265.758$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(9\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.cz	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(-10\)	\(0\)	\(-5\)	\(-7\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.da	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(-10\)	\(0\)	\(-5\)	\(4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.db	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(-10\)	\(0\)	\(4\)	\(-9\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.dc	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\Q(\zeta_{44})^+\)	None	✓	?				$-1$		\(-10\)	\(0\)	\(10\)	\(-10\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.dd	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\Q(\zeta_{44})^+\)	None	✓	?				$-1$		\(10\)	\(0\)	\(-10\)	\(10\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.de	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(10\)	\(0\)	\(-4\)	\(9\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.df	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(10\)	\(0\)	\(5\)	\(-4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.dg	$33282$	$2$	33282.a	1.a	$1$	$10$	$10$	$265.758$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(10\)	\(0\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.dh	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(0\)	\(-9\)	\(7\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.di	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(0\)	\(-4\)	\(-3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.dj	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(0\)	\(-3\)	\(7\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.dk	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(0\)	\(7\)	\(-5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.dl	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(0\)	\(-7\)	\(5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.dm	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(0\)	\(3\)	\(-7\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.dn	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(0\)	\(4\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.do	$33282$	$2$	33282.a	1.a	$1$	$12$	$12$	$265.758$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(0\)	\(9\)	\(-7\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.dp	$33282$	$2$	33282.a	1.a	$1$	$15$	$15$	$265.758$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?	✓			$-1$		\(-15\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.dq	$33282$	$2$	33282.a	1.a	$1$	$15$	$15$	$265.758$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(-15\)	\(0\)	\(11\)	\(-1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.dr	$33282$	$2$	33282.a	1.a	$1$	$15$	$15$	$265.758$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(-15\)	\(0\)	\(11\)	\(1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.ds	$33282$	$2$	33282.a	1.a	$1$	$15$	$15$	$265.758$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(15\)	\(0\)	\(-11\)	\(-1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.dt	$33282$	$2$	33282.a	1.a	$1$	$15$	$15$	$265.758$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(15\)	\(0\)	\(-11\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.du	$33282$	$2$	33282.a	1.a	$1$	$15$	$15$	$265.758$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?	✓			$-1$		\(15\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.dv	$33282$	$2$	33282.a	1.a	$1$	$20$	$20$	$265.758$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(-20\)	\(0\)	\(-6\)	\(20\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.dw	$33282$	$2$	33282.a	1.a	$1$	$20$	$20$	$265.758$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(-20\)	\(0\)	\(8\)	\(10\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.dx	$33282$	$2$	33282.a	1.a	$1$	$20$	$20$	$265.758$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(20\)	\(0\)	\(-8\)	\(-10\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.dy	$33282$	$2$	33282.a	1.a	$1$	$20$	$20$	$265.758$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	?				$-1$		\(20\)	\(0\)	\(6\)	\(-20\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.dz	$33282$	$2$	33282.a	1.a	$1$	$24$	$24$	$265.758$		None	✓	?	✓			$-1$		\(-24\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
33282.2.a.ea	$33282$	$2$	33282.a	1.a	$1$	$24$	$24$	$265.758$		None	✓	?				$-1$		\(-24\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.eb	$33282$	$2$	33282.a	1.a	$1$	$24$	$24$	$265.758$		None	✓	?	✓			$-1$		\(24\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
33282.2.a.ec	$33282$	$2$	33282.a	1.a	$1$	$24$	$24$	$265.758$		None	✓	?				$-1$		\(24\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
33282.2.a.ed	$33282$	$2$	33282.a	1.a	$1$	$40$	$40$	$265.758$		None	✓	?	✓			$-1$		\(-40\)	\(0\)	\(-24\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
33282.2.a.ee	$33282$	$2$	33282.a	1.a	$1$	$40$	$40$	$265.758$		None	✓	?	✓			$-1$		\(40\)	\(0\)	\(24\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(33282))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(33282)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(258))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(387))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(774))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1849))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3698))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5547))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11094))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(16641))\)\(^{\oplus 2}\)