Space of modular forms of level 9200, weight 2, and trivial character

• Label: 9200.2.a
• Level: $9200$
• Weight: $2$
• Character orbit: 9200.a
• Rep. character: $\chi_{9200}(1,\cdot)$
• Character field: $\Q$
• Dimension: $209$
• Newform subspaces: $83$
• Sturm bound: $2880$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9200.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 83 \)
Sturm bound:			\(2880\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9200))\).

	Total	New	Old
Modular forms	1476	209	1267
Cusp forms	1405	209	1196
Eisenstein series	71	0	71

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

\(2\)	\(5\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(171\)	\(25\)	\(146\)		\(163\)	\(25\)	\(138\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)		\(198\)	\(25\)	\(173\)		\(189\)	\(25\)	\(164\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)		\(198\)	\(27\)	\(171\)		\(189\)	\(27\)	\(162\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)		\(171\)	\(27\)	\(144\)		\(162\)	\(27\)	\(135\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)		\(180\)	\(29\)	\(151\)		\(171\)	\(29\)	\(142\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)		\(189\)	\(20\)	\(169\)		\(180\)	\(20\)	\(160\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)		\(189\)	\(25\)	\(164\)		\(180\)	\(25\)	\(155\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)		\(180\)	\(31\)	\(149\)		\(171\)	\(31\)	\(140\)		\(9\)	\(0\)	\(9\)
Plus space			\(+\)		\(720\)	\(97\)	\(623\)		\(685\)	\(97\)	\(588\)		\(35\)	\(0\)	\(35\)
Minus space			\(-\)		\(756\)	\(112\)	\(644\)		\(720\)	\(112\)	\(608\)		\(36\)	\(0\)	\(36\)

Trace form

209 * q + 2 * q^3 + 4 * q^7 + 205 * q^9 + 2 * q^13 - 6 * q^17 + 4 * q^19 - 3 * q^23 + 2 * q^27 + 2 * q^29 + 22 * q^31 + 8 * q^33 + 10 * q^37 - 18 * q^39 + 2 * q^41 + 32 * q^43 + 2 * q^47 + 225 * q^49 - 44 * q^51 - 6 * q^53 + 8 * q^57 - 8 * q^59 + 2 * q^61 - 40 * q^63 + 16 * q^67 + 6 * q^71 - 6 * q^73 - 8 * q^77 + 52 * q^79 + 201 * q^81 - 20 * q^83 + 10 * q^87 - 14 * q^89 + 60 * q^91 + 12 * q^93 - 14 * q^97 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9200))\) 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	23
9200.2.a.a	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.d	$1$	$2$	\(0\)	\(-3\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-4q^{7}+6q^{9}-3q^{11}-6q^{13}+\cdots\)
9200.2.a.b	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				92.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-4q^{7}+6q^{9}-2q^{11}+5q^{13}+\cdots\)
9200.2.a.c	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				920.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{7}+6q^{9}-q^{13}+6q^{21}+\cdots\)
9200.2.a.d	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				920.2.e.a	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-3q^{7}+q^{9}+6q^{13}+7q^{17}+\cdots\)
9200.2.a.e	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}-5q^{11}+7q^{13}+\cdots\)
9200.2.a.f	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
9200.2.a.g	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				115.2.b.a	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}+2q^{13}-5q^{17}+\cdots\)
9200.2.a.h	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				2300.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
9200.2.a.i	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				4600.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
9200.2.a.j	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				4600.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+3q^{7}+q^{9}-5q^{11}-5q^{13}+\cdots\)
9200.2.a.k	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				4600.2.a.e	$1$	$2$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
9200.2.a.l	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				184.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}-2q^{9}+2q^{11}-7q^{13}+\cdots\)
9200.2.a.m	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				460.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}-2q^{9}+4q^{11}-q^{13}+\cdots\)
9200.2.a.n	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				920.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{9}-2q^{11}+5q^{13}+4q^{17}+\cdots\)
9200.2.a.o	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				184.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}-2q^{9}+4q^{11}+5q^{13}+\cdots\)
9200.2.a.p	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				46.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9200.2.a.q	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				460.2.a.b	$1$	$2$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}-6q^{11}-6q^{13}-7q^{17}+\cdots\)
9200.2.a.r	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				575.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+q^{11}+q^{13}+5q^{19}+\cdots\)
9200.2.a.s	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+3q^{11}+3q^{13}+8q^{17}+\cdots\)
9200.2.a.t	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				115.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}-2q^{11}+2q^{13}-3q^{17}+\cdots\)
9200.2.a.u	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				575.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+q^{11}-q^{13}+5q^{19}+\cdots\)
9200.2.a.v	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+3q^{11}-3q^{13}-8q^{17}+\cdots\)
9200.2.a.w	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				920.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+6q^{11}+2q^{13}+3q^{17}+\cdots\)
9200.2.a.x	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				184.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-3q^{9}-6q^{11}+2q^{13}-6q^{17}+\cdots\)
9200.2.a.y	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				460.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}-2q^{9}+6q^{11}+q^{13}+\cdots\)
9200.2.a.z	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				920.2.a.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}-2q^{9}-q^{13}+4q^{17}+\cdots\)
9200.2.a.ba	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				92.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}-2q^{9}+q^{13}+6q^{17}+\cdots\)
9200.2.a.bb	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				4600.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
9200.2.a.bc	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				4600.2.a.d	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{7}+q^{9}-5q^{11}+5q^{13}+\cdots\)
9200.2.a.bd	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				4600.2.a.c	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
9200.2.a.be	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.c	$1$	$0$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}-5q^{11}-7q^{13}+\cdots\)
9200.2.a.bf	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
9200.2.a.bg	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				115.2.b.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}-2q^{13}+5q^{17}+\cdots\)
9200.2.a.bh	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				2300.2.a.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots\)
9200.2.a.bi	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				920.2.e.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+3q^{7}+q^{9}-6q^{13}-7q^{17}+\cdots\)
9200.2.a.bj	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				184.2.a.d	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{7}+6q^{9}+5q^{13}+6q^{17}+\cdots\)
9200.2.a.bk	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				460.2.a.d	$1$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{7}+6q^{9}+3q^{13}-4q^{17}+\cdots\)
9200.2.a.bl	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	\(\Q\)	None	✓				1150.2.a.d	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{7}+6q^{9}-3q^{11}+6q^{13}+\cdots\)
9200.2.a.bm	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{5}) \)	None	✓				115.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}-2q^{9}+(1+\beta )q^{11}+\cdots\)
9200.2.a.bn	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{5}) \)	None	✓				4600.2.a.q	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
9200.2.a.bo	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{5}) \)	None	✓				230.2.b.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-3+3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9200.2.a.bp	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{17}) \)	None	✓				1150.2.a.k	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
9200.2.a.bq	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots\)
9200.2.a.br	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{17}) \)	None	✓				184.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{9}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9200.2.a.bs	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{21}) \)	None	✓				230.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{7}+(2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
9200.2.a.bt	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{5}) \)	None	✓				23.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{7}+2q^{9}+(3+\beta )q^{11}+\cdots\)
9200.2.a.bu	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{5}) \)	None	✓				230.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
9200.2.a.bv	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{17}) \)	None	✓				460.2.a.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}-2q^{11}+\cdots\)
9200.2.a.bw	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{17}) \)	None	✓				1150.2.a.k	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
9200.2.a.bx	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.f	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
9200.2.a.by	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{5}) \)	None	✓				230.2.b.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(3-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9200.2.a.bz	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{5}) \)	None	✓				4600.2.a.q	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
9200.2.a.ca	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	\(\Q(\sqrt{13}) \)	None	✓				230.2.a.b	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
9200.2.a.cb	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	\(\Q(\zeta_{14})^+\)	None	✓				4600.2.a.w	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
9200.2.a.cc	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	3.3.321.1	None	✓				2300.2.a.j	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-2\beta _{1}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cd	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	3.3.621.1	None	✓				920.2.a.g	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9200.2.a.ce	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	3.3.2597.1	None	✓				920.2.a.h	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
9200.2.a.cf	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	3.3.1101.1	None	✓				230.2.a.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cg	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	3.3.321.1	None	✓				2300.2.a.j	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+2\beta _{1}q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
9200.2.a.ch	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	\(\Q(\zeta_{14})^+\)	None	✓				4600.2.a.w	$1$	$1$	\(0\)	\(2\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(2-2\beta _{1})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.ci	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	3.3.229.1	None	✓				920.2.a.i	$1$	$1$	\(0\)	\(2\)	\(0\)	\(7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(2-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cj	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.13448.1	None	✓				230.2.b.b	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(-1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.ck	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.5744.1	None	✓				115.2.b.b	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-2-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
9200.2.a.cl	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.15317.1	None	✓				115.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-1-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.cm	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.53121.1	None	✓		✓		2300.2.a.l	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cn	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.15529.1	None	✓				4600.2.a.ba	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.co	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.53121.1	None	✓				2300.2.a.l	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cp	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.15529.1	None	✓				4600.2.a.ba	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cq	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.5744.1	None	✓				115.2.b.b	$1$	$1$	\(0\)	\(2\)	\(0\)	\(6\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(2+\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cr	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.13448.1	None	✓				230.2.b.b	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(1+\beta _{3})q^{7}+(2+2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cs	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.791953.1	None	✓				4600.2.a.bc	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
9200.2.a.ct	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.521397.1	None	✓		✓		4600.2.a.bd	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cu	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.13955077.1	None	✓				920.2.a.j	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{3}-\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cv	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.521397.1	None	✓				4600.2.a.bd	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cw	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.791953.1	None	✓				4600.2.a.bc	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
9200.2.a.cx	$9200$	$2$	9200.a	1.a	$1$	$6$	$6$	$73.462$	6.6.143376304.1	None	✓		✓		460.2.c.a	$1$	$1$	\(0\)	\(-4\)	\(0\)	\(-9\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.cy	$9200$	$2$	9200.a	1.a	$1$	$6$	$6$	$73.462$	6.6.143376304.1	None	✓				460.2.c.a	$1$	$0$	\(0\)	\(4\)	\(0\)	\(9\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(2-\beta _{3})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cz	$9200$	$2$	9200.a	1.a	$1$	$7$	$7$	$73.462$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				920.2.e.b	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.da	$9200$	$2$	9200.a	1.a	$1$	$7$	$7$	$73.462$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		575.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+\beta _{2}q^{7}+(1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.db	$9200$	$2$	9200.a	1.a	$1$	$7$	$7$	$73.462$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		575.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-\beta _{2}q^{7}+(1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.dc	$9200$	$2$	9200.a	1.a	$1$	$7$	$7$	$73.462$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				920.2.e.b	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\beta _{6})q^{9}+\cdots\)
9200.2.a.dd	$9200$	$2$	9200.a	1.a	$1$	$8$	$8$	$73.462$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		920.2.e.c	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-7\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.de	$9200$	$2$	9200.a	1.a	$1$	$8$	$8$	$73.462$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		920.2.e.c	$1$	$0$	\(0\)	\(3\)	\(0\)	\(7\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9200)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4600))\)\(^{\oplus 2}\)