Space of modular forms of level 24200, weight 2, and trivial character

• Label: 24200.2.a
• Level: $24200$
• Weight: $2$
• Character orbit: 24200.a
• Rep. character: $\chi_{24200}(1,\cdot)$
• Character field: $\Q$
• Dimension: $518$
• Newform subspaces: $120$
• Sturm bound: $7920$

Defining parameters

Level:	\( N \)	\(=\)	\( 24200 = 2^{3} \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	24200.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 120 \)
Sturm bound:			\(7920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(24200))\).

	Total	New	Old
Modular forms	4104	518	3586
Cusp forms	3817	518	3299
Eisenstein series	287	0	287

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

\(2\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(504\)	\(57\)	\(447\)		\(469\)	\(57\)	\(412\)		\(35\)	\(0\)	\(35\)
\(+\)	\(+\)	\(-\)	\(-\)		\(519\)	\(66\)	\(453\)		\(483\)	\(66\)	\(417\)		\(36\)	\(0\)	\(36\)
\(+\)	\(-\)	\(+\)	\(-\)		\(522\)	\(71\)	\(451\)		\(486\)	\(71\)	\(415\)		\(36\)	\(0\)	\(36\)
\(+\)	\(-\)	\(-\)	\(+\)		\(507\)	\(65\)	\(442\)		\(471\)	\(65\)	\(406\)		\(36\)	\(0\)	\(36\)
\(-\)	\(+\)	\(+\)	\(-\)		\(522\)	\(63\)	\(459\)		\(486\)	\(63\)	\(423\)		\(36\)	\(0\)	\(36\)
\(-\)	\(+\)	\(-\)	\(+\)		\(507\)	\(59\)	\(448\)		\(471\)	\(59\)	\(412\)		\(36\)	\(0\)	\(36\)
\(-\)	\(-\)	\(+\)	\(+\)		\(504\)	\(67\)	\(437\)		\(468\)	\(67\)	\(401\)		\(36\)	\(0\)	\(36\)
\(-\)	\(-\)	\(-\)	\(-\)		\(519\)	\(70\)	\(449\)		\(483\)	\(70\)	\(413\)		\(36\)	\(0\)	\(36\)
Plus space			\(+\)		\(2022\)	\(248\)	\(1774\)		\(1879\)	\(248\)	\(1631\)		\(143\)	\(0\)	\(143\)
Minus space			\(-\)		\(2082\)	\(270\)	\(1812\)		\(1938\)	\(270\)	\(1668\)		\(144\)	\(0\)	\(144\)

Trace form

518 * q + 2 * q^3 + 518 * q^9 + 4 * q^13 + 6 * q^19 + 12 * q^23 + 20 * q^27 - 16 * q^29 + 4 * q^31 - 6 * q^37 + 8 * q^39 - 10 * q^41 + 8 * q^43 - 8 * q^47 + 546 * q^49 + 34 * q^51 + 2 * q^53 - 32 * q^57 - 2 * q^59 - 12 * q^61 - 12 * q^63 + 6 * q^67 - 16 * q^69 + 28 * q^71 + 12 * q^73 + 8 * q^79 + 502 * q^81 - 8 * q^83 - 18 * q^89 + 24 * q^93 - 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(24200))\) 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	5	11
24200.2.a.a	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{7}+6q^{9}-4q^{13}-5q^{17}+\cdots\)
24200.2.a.b	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{7}+6q^{9}-6q^{13}+3q^{17}+\cdots\)
24200.2.a.c	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{7}+q^{9}+4q^{17}-4q^{19}+\cdots\)
24200.2.a.d	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{7}+q^{9}+4q^{13}+4q^{19}+\cdots\)
24200.2.a.e	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
24200.2.a.f	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-5q^{7}-2q^{9}-6q^{13}+4q^{17}+\cdots\)
24200.2.a.g	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}-2q^{9}-4q^{13}-4q^{17}+\cdots\)
24200.2.a.h	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}-2q^{9}+4q^{13}-3q^{17}+\cdots\)
24200.2.a.i	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}-q^{17}-q^{19}+q^{21}+\cdots\)
24200.2.a.j	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}-2q^{9}-4q^{13}+3q^{17}+\cdots\)
24200.2.a.k	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}-2q^{9}+4q^{13}+4q^{17}+\cdots\)
24200.2.a.l	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+5q^{7}-2q^{9}+6q^{13}-4q^{17}+\cdots\)
24200.2.a.m	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}-3q^{13}-3q^{17}+4q^{19}+\cdots\)
24200.2.a.n	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
24200.2.a.o	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}-4q^{13}-4q^{17}+6q^{29}+\cdots\)
24200.2.a.p	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}+8q^{19}+8q^{23}-10q^{29}+\cdots\)
24200.2.a.q	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}-2q^{13}-2q^{17}-6q^{19}+\cdots\)
24200.2.a.r	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}-2q^{13}-2q^{17}+6q^{19}+\cdots\)
24200.2.a.s	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+2q^{13}+2q^{17}-6q^{19}+\cdots\)
24200.2.a.t	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+2q^{13}+2q^{17}+6q^{19}+\cdots\)
24200.2.a.u	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-3q^{9}+3q^{13}+3q^{17}-4q^{19}+\cdots\)
24200.2.a.v	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-3q^{9}+6q^{13}-6q^{17}-4q^{19}+\cdots\)
24200.2.a.w	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-5q^{7}-2q^{9}-6q^{13}+4q^{17}+\cdots\)
24200.2.a.x	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}-2q^{9}+q^{17}-q^{19}+q^{21}+\cdots\)
24200.2.a.y	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+5q^{7}-2q^{9}+6q^{13}-4q^{17}+\cdots\)
24200.2.a.z	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
24200.2.a.ba	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{7}+q^{9}-4q^{13}+4q^{19}+\cdots\)
24200.2.a.bb	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}-2q^{13}+6q^{17}+2q^{23}+\cdots\)
24200.2.a.bc	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}+2q^{13}-6q^{17}+2q^{23}+\cdots\)
24200.2.a.bd	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{7}+q^{9}-4q^{17}-4q^{19}+\cdots\)
24200.2.a.be	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{7}+6q^{9}-6q^{17}-4q^{19}+\cdots\)
24200.2.a.bf	$24200$	$2$	24200.a	1.a	$1$	$1$	$1$	$193.238$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{7}+6q^{9}+4q^{13}+5q^{17}+\cdots\)
24200.2.a.bg	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.bh	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.bi	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.bj	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.bk	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.bl	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.bm	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.bn	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.bo	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.bp	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.bq	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.br	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.bs	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.bt	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.bu	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{3}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.bv	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.bw	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.bx	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{17}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.by	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.bz	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.ca	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.cb	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.cc	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cd	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.ce	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.cf	$24200$	$2$	24200.a	1.a	$1$	$2$	$2$	$193.238$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.cg	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.837.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.ch	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.788.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.ci	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.404.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cj	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.404.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.ck	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.788.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.cl	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.1229.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cm	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.1229.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cn	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.568.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.co	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.568.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.cp	$24200$	$2$	24200.a	1.a	$1$	$3$	$3$	$193.238$	3.3.837.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.cq	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.53401.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.cr	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.53401.1	None	✓	?				$-1$		\(0\)	\(-3\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cs	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.5225.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.ct	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.5225.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cu	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.54764.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.cv	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.54764.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cw	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.725.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.cx	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.4752.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.cy	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.4752.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(6\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.cz	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.725.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(7\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.da	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.53401.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.db	$24200$	$2$	24200.a	1.a	$1$	$4$	$4$	$193.238$	4.4.53401.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.dc	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.8653488.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.dd	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.8653488.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.de	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.19850940.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.df	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.19850940.1	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.dg	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.19850940.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.dh	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.19850940.1	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.di	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.8653488.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.dj	$24200$	$2$	24200.a	1.a	$1$	$5$	$5$	$193.238$	5.5.8653488.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.dk	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.45753625.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.dl	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.299273216.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.dm	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.299273216.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.dn	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.45753625.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(0\)	\(6\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.do	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.22733568.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.dp	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.299273216.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.dq	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.299273216.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.dr	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.22733568.1	None	✓	?				$-1$		\(0\)	\(2\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.ds	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.25903625.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-7\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.dt	$24200$	$2$	24200.a	1.a	$1$	$6$	$6$	$193.238$	6.6.25903625.1	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(7\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.du	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-6\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.dv	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.dw	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.dx	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-1\)	\(0\)	\(6\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.dy	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	8.8.\(\cdots\).1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$
24200.2.a.dz	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	8.8.\(\cdots\).1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$
24200.2.a.ea	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.eb	$24200$	$2$	24200.a	1.a	$1$	$8$	$8$	$193.238$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.ec	$24200$	$2$	24200.a	1.a	$1$	$10$	$10$	$193.238$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.ed	$24200$	$2$	24200.a	1.a	$1$	$10$	$10$	$193.238$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-4\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.ee	$24200$	$2$	24200.a	1.a	$1$	$10$	$10$	$193.238$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(4\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.ef	$24200$	$2$	24200.a	1.a	$1$	$10$	$10$	$193.238$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(4\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.eg	$24200$	$2$	24200.a	1.a	$1$	$12$	$12$	$193.238$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-3\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.eh	$24200$	$2$	24200.a	1.a	$1$	$12$	$12$	$193.238$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-3\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.ei	$24200$	$2$	24200.a	1.a	$1$	$12$	$12$	$193.238$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
24200.2.a.ej	$24200$	$2$	24200.a	1.a	$1$	$12$	$12$	$193.238$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(3\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.ek	$24200$	$2$	24200.a	1.a	$1$	$16$	$16$	$193.238$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-10\)		$-$	$-$	$+$	$+$
24200.2.a.el	$24200$	$2$	24200.a	1.a	$1$	$16$	$16$	$193.238$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(10\)		$+$	$-$	$+$	$-$
24200.2.a.em	$24200$	$2$	24200.a	1.a	$1$	$18$	$18$	$193.238$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-4\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
24200.2.a.en	$24200$	$2$	24200.a	1.a	$1$	$18$	$18$	$193.238$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(-4\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
24200.2.a.eo	$24200$	$2$	24200.a	1.a	$1$	$18$	$18$	$193.238$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(4\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
24200.2.a.ep	$24200$	$2$	24200.a	1.a	$1$	$18$	$18$	$193.238$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?	✓			$-1$		\(0\)	\(4\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(24200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(24200)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3025))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(6050))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(12100))\)\(^{\oplus 2}\)