Space of modular forms of level 18032, weight 2, and trivial character

• Label: 18032.2.a
• Level: $18032$
• Weight: $2$
• Character orbit: 18032.a
• Rep. character: $\chi_{18032}(1,\cdot)$
• Character field: $\Q$
• Dimension: $451$
• Newform subspaces: $105$
• Sturm bound: $5376$

Defining parameters

Level:	\( N \)	\(=\)	\( 18032 = 2^{4} \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	18032.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 105 \)
Sturm bound:			\(5376\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(18032))\).

	Total	New	Old
Modular forms	2736	451	2285
Cusp forms	2641	451	2190
Eisenstein series	95	0	95

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

\(2\)	\(7\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(324\)	\(56\)	\(268\)		\(313\)	\(56\)	\(257\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(360\)	\(56\)	\(304\)		\(348\)	\(56\)	\(292\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(360\)	\(57\)	\(303\)		\(348\)	\(57\)	\(291\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(324\)	\(57\)	\(267\)		\(312\)	\(57\)	\(255\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(336\)	\(60\)	\(276\)		\(324\)	\(60\)	\(264\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(348\)	\(48\)	\(300\)		\(336\)	\(48\)	\(288\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(348\)	\(54\)	\(294\)		\(336\)	\(54\)	\(282\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(336\)	\(63\)	\(273\)		\(324\)	\(63\)	\(261\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(1344\)	\(215\)	\(1129\)		\(1297\)	\(215\)	\(1082\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(1392\)	\(236\)	\(1156\)		\(1344\)	\(236\)	\(1108\)		\(48\)	\(0\)	\(48\)

Trace form

451 * q - 2 * q^3 - 2 * q^5 + 447 * q^9 - 2 * q^13 - 2 * q^17 - 4 * q^19 - 3 * q^23 + 461 * q^25 - 14 * q^27 - 2 * q^29 - 10 * q^31 + 8 * q^33 - 10 * q^37 - 42 * q^39 + 6 * q^41 - 32 * q^43 - 10 * q^45 + 22 * q^47 - 4 * q^51 + 6 * q^53 - 8 * q^55 - 8 * q^57 - 8 * q^59 - 2 * q^61 + 12 * q^65 + 8 * q^67 - 22 * q^71 - 2 * q^73 - 94 * q^75 - 28 * q^79 + 443 * q^81 + 20 * q^83 - 12 * q^85 - 22 * q^87 + 6 * q^89 + 12 * q^93 - 40 * q^95 - 26 * q^97 - 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(18032))\) 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	7	23
18032.2.a.a	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+6q^{9}+6q^{11}-q^{13}-q^{23}+\cdots\)
18032.2.a.b	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+6q^{9}-2q^{11}+5q^{13}+\cdots\)
18032.2.a.c	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+4q^{5}+6q^{9}-2q^{11}-5q^{13}+\cdots\)
18032.2.a.d	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}+q^{9}+4q^{15}+2q^{17}+\cdots\)
18032.2.a.e	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}+q^{9}+4q^{11}+4q^{15}+\cdots\)
18032.2.a.f	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}+6q^{17}+6q^{19}-q^{23}+\cdots\)
18032.2.a.g	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
18032.2.a.h	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{9}+2q^{11}+3q^{13}+q^{23}+\cdots\)
18032.2.a.i	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{9}+2q^{11}-7q^{13}+\cdots\)
18032.2.a.j	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{9}+4q^{11}+5q^{13}+\cdots\)
18032.2.a.k	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-3q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
18032.2.a.l	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3q^{9}-4q^{11}-6q^{13}+2q^{17}+\cdots\)
18032.2.a.m	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3q^{9}+4q^{13}+4q^{17}-2q^{19}+\cdots\)
18032.2.a.n	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}-6q^{11}+2q^{13}-6q^{17}-6q^{19}+\cdots\)
18032.2.a.o	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{9}+4q^{11}-4q^{13}+8q^{17}+\cdots\)
18032.2.a.p	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{9}+q^{13}+6q^{17}+2q^{19}+\cdots\)
18032.2.a.q	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{9}+6q^{11}+3q^{13}-q^{23}+\cdots\)
18032.2.a.r	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{9}+2q^{11}+q^{13}+\cdots\)
18032.2.a.s	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
18032.2.a.t	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
18032.2.a.u	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}-4q^{11}-6q^{13}-q^{23}+\cdots\)
18032.2.a.v	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}-4q^{11}-6q^{17}-6q^{19}+\cdots\)
18032.2.a.w	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{9}-6q^{11}+4q^{13}+\cdots\)
18032.2.a.x	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{9}+4q^{15}-2q^{17}+\cdots\)
18032.2.a.y	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+q^{9}+4q^{11}+4q^{15}+\cdots\)
18032.2.a.z	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{5}+6q^{9}-2q^{11}+q^{13}+\cdots\)
18032.2.a.ba	$18032$	$2$	18032.a	1.a	$1$	$1$	$1$	$143.986$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+6q^{9}+5q^{13}+6q^{17}+6q^{19}+\cdots\)
18032.2.a.bb	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.bc	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.bd	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.be	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.bf	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.bg	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.bh	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.bi	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.bj	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$
18032.2.a.bk	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$
18032.2.a.bl	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
18032.2.a.bm	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$
18032.2.a.bn	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
18032.2.a.bo	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$
18032.2.a.bp	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$
18032.2.a.bq	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.br	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$
18032.2.a.bs	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
18032.2.a.bt	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.bu	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.bv	$18032$	$2$	18032.a	1.a	$1$	$2$	$2$	$143.986$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.bw	$18032$	$2$	18032.a	1.a	$1$	$3$	$3$	$143.986$	3.3.148.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.bx	$18032$	$2$	18032.a	1.a	$1$	$3$	$3$	$143.986$	3.3.568.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.by	$18032$	$2$	18032.a	1.a	$1$	$3$	$3$	$143.986$	3.3.316.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.bz	$18032$	$2$	18032.a	1.a	$1$	$3$	$3$	$143.986$	3.3.148.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.ca	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.14013.1	None	✓	?				$-1$		\(0\)	\(-5\)	\(5\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.cb	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.8468.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.cc	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.1957.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(7\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.cd	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{30 +2 \sqrt{13}})\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(-5\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.ce	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.14013.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.cf	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\zeta_{24})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
18032.2.a.cg	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\zeta_{24})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.ch	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{10 +2 \sqrt{17}})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$
18032.2.a.ci	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{2}, \sqrt{5})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$
18032.2.a.cj	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.34196.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.ck	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{18 +2 \sqrt{73}})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$
18032.2.a.cl	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{10 +2 \sqrt{17}})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$
18032.2.a.cm	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{7}, \sqrt{15})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$
18032.2.a.cn	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\zeta_{24})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.co	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{2}, \sqrt{13})\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.cp	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.14013.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.cq	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	\(\Q(\sqrt{30 +2 \sqrt{13}})\)	None	✓	?				$-1$		\(0\)	\(1\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.cr	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.1957.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-7\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.cs	$18032$	$2$	18032.a	1.a	$1$	$4$	$4$	$143.986$	4.4.14013.1	None	✓	?				$-1$		\(0\)	\(5\)	\(-5\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.ct	$18032$	$2$	18032.a	1.a	$1$	$5$	$5$	$143.986$	5.5.3385684.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.cu	$18032$	$2$	18032.a	1.a	$1$	$5$	$5$	$143.986$	5.5.2147108.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.cv	$18032$	$2$	18032.a	1.a	$1$	$5$	$5$	$143.986$	5.5.8580816.1	None	✓	?				$-1$		\(0\)	\(1\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.cw	$18032$	$2$	18032.a	1.a	$1$	$5$	$5$	$143.986$	5.5.6963152.1	None	✓	?				$-1$		\(0\)	\(3\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.cx	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.2803712.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$
18032.2.a.cy	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.1229312.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$
18032.2.a.cz	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.79480832.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$
18032.2.a.da	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.524361728.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$
18032.2.a.db	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.217653248.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$
18032.2.a.dc	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.89672832.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$
18032.2.a.dd	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.73156608.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.de	$18032$	$2$	18032.a	1.a	$1$	$6$	$6$	$143.986$	6.6.2803712.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$
18032.2.a.df	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-5\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.dg	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-5\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.dh	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.di	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.dj	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.dk	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(3\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.dl	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(5\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.dm	$18032$	$2$	18032.a	1.a	$1$	$7$	$7$	$143.986$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(5\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.dn	$18032$	$2$	18032.a	1.a	$1$	$8$	$8$	$143.986$	8.8.\(\cdots\).1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$
18032.2.a.do	$18032$	$2$	18032.a	1.a	$1$	$10$	$10$	$143.986$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$
18032.2.a.dp	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(1\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.dq	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.dr	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-9\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
18032.2.a.ds	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(7\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.dt	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(2\)	\(-7\)	\(0\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
18032.2.a.du	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(2\)	\(9\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.dv	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
18032.2.a.dw	$18032$	$2$	18032.a	1.a	$1$	$11$	$11$	$143.986$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
18032.2.a.dx	$18032$	$2$	18032.a	1.a	$1$	$14$	$14$	$143.986$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$
18032.2.a.dy	$18032$	$2$	18032.a	1.a	$1$	$14$	$14$	$143.986$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$
18032.2.a.dz	$18032$	$2$	18032.a	1.a	$1$	$18$	$18$	$143.986$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$
18032.2.a.ea	$18032$	$2$	18032.a	1.a	$1$	$18$	$18$	$143.986$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(18032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(18032)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2254))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4508))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(9016))\)\(^{\oplus 2}\)