Space of modular forms of level 7623, weight 2, and trivial character

• Label: 7623.2.a
• Level: $7623$
• Weight: $2$
• Character orbit: 7623.a
• Rep. character: $\chi_{7623}(1,\cdot)$
• Character field: $\Q$
• Dimension: $273$
• Newform subspaces: $81$
• Sturm bound: $2112$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7623.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 81 \)
Sturm bound:			\(2112\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7623))\).

	Total	New	Old
Modular forms	1104	273	831
Cusp forms	1009	273	736
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.

\(3\)	\(7\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(132\)	\(26\)	\(106\)		\(121\)	\(26\)	\(95\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(142\)	\(30\)	\(112\)		\(130\)	\(30\)	\(100\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(144\)	\(34\)	\(110\)		\(132\)	\(34\)	\(98\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(134\)	\(20\)	\(114\)		\(122\)	\(20\)	\(102\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(144\)	\(41\)	\(103\)		\(132\)	\(41\)	\(91\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(134\)	\(40\)	\(94\)		\(122\)	\(40\)	\(82\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(132\)	\(37\)	\(95\)		\(120\)	\(37\)	\(83\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(142\)	\(45\)	\(97\)		\(130\)	\(45\)	\(85\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(532\)	\(123\)	\(409\)		\(485\)	\(123\)	\(362\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(572\)	\(150\)	\(422\)		\(524\)	\(150\)	\(374\)		\(48\)	\(0\)	\(48\)

Trace form

273 * q + q^2 + 269 * q^4 + 6 * q^5 - q^7 - 3 * q^8 + 6 * q^10 + 6 * q^13 - 3 * q^14 + 269 * q^16 + 14 * q^17 - 8 * q^19 - 6 * q^20 - 12 * q^23 + 287 * q^25 + 2 * q^26 - 3 * q^28 + 22 * q^29 - 8 * q^31 - 35 * q^32 + 2 * q^34 + 6 * q^35 + 6 * q^37 - 24 * q^38 + 6 * q^40 + 22 * q^41 + 12 * q^43 + 20 * q^46 - 12 * q^47 + 273 * q^49 - 65 * q^50 + 50 * q^52 + 10 * q^53 - 15 * q^56 + 34 * q^58 - 8 * q^59 + 18 * q^61 + 4 * q^62 + 309 * q^64 + 20 * q^65 + 4 * q^67 + 30 * q^68 + 18 * q^70 - 2 * q^73 + 22 * q^74 + 36 * q^76 - 36 * q^79 + 22 * q^80 + 38 * q^82 + 12 * q^83 + 16 * q^85 + 12 * q^86 + 26 * q^89 - 6 * q^91 - 20 * q^92 - 36 * q^94 - 20 * q^95 - 14 * q^97 + q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\) 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	11
7623.2.a.a	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.b	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓	✓			7623.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.c	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓	✓			7623.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.d	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+3q^{5}-q^{7}-6q^{10}+\cdots\)
7623.2.a.e	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
7623.2.a.f	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				231.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.g	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				21.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.h	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{5}+q^{7}+3q^{8}-3q^{10}+\cdots\)
7623.2.a.i	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				77.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.j	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				77.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.k	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.e	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.l	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.e	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}+q^{7}-4q^{13}+4q^{16}+\cdots\)
7623.2.a.m	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
7623.2.a.n	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				77.2.a.c	$1$	$0$	\(1\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots\)
7623.2.a.o	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.c	$1$	$1$	\(1\)	\(0\)	\(3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+3q^{5}-q^{7}-3q^{8}+3q^{10}+\cdots\)
7623.2.a.p	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓	✓			7623.2.a.b	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.q	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.b	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.r	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓	✓			7623.2.a.b	$1$	$1$	\(2\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.s	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	\(\Q\)	None	✓				2541.2.a.a	$1$	$0$	\(2\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots\)
7623.2.a.t	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				847.2.a.d	$1$	$1$	\(-3\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+\cdots\)
7623.2.a.u	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.a	$1$	$1$	\(-3\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}-\beta q^{5}+q^{7}+\cdots\)
7623.2.a.v	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				693.2.a.e	$1$	$0$	\(-3\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}-q^{7}+\cdots\)
7623.2.a.w	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.c	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+(-2+3\beta )q^{5}-q^{7}+3q^{8}+\cdots\)
7623.2.a.x	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{3}) \)	None	✓				2541.2.a.o	$1$	$1$	\(-2\)	\(0\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
7623.2.a.y	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				2541.2.a.q	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.z	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.b	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.ba	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.d	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bb	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				2541.2.a.r	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.bc	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{13}) \)	None	✓				847.2.a.e	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bd	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{13}) \)	None	✓				693.2.a.g	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.be	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{17}) \)	None	✓				2541.2.a.u	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+q^{7}+(-4+\cdots)q^{8}+\cdots\)
7623.2.a.bf	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{21}) \)	None	✓				231.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(-6\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(3+\beta )q^{4}-3q^{5}-q^{7}+(-5+\cdots)q^{8}+\cdots\)
7623.2.a.bg	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{13}) \)	None	✓	✓			7623.2.a.bg	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{4}-\beta q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
7623.2.a.bh	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{13}) \)	None	✓	✓			7623.2.a.bg	$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{4}-\beta q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
7623.2.a.bi	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{3}) \)	None	✓				63.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+2\beta q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bj	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{2}+3q^{4}-\beta q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bk	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{2}+3q^{4}+(-1+\beta )q^{5}+\cdots\)
7623.2.a.bl	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				77.2.a.d	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}+2q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bm	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.a.c	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bn	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				2541.2.a.q	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.bo	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.b	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bp	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.d	$1$	$1$	\(1\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bq	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				2541.2.a.r	$1$	$1$	\(1\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.br	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{13}) \)	None	✓				693.2.a.g	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}+3q^{8}+\cdots\)
7623.2.a.bs	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{13}) \)	None	✓				847.2.a.e	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bt	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{17}) \)	None	✓				2541.2.a.u	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}-q^{5}-q^{7}+(4+\beta )q^{8}+\cdots\)
7623.2.a.bu	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.c	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+(-2+3\beta )q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.bv	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{3}) \)	None	✓				2541.2.a.o	$1$	$0$	\(2\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
7623.2.a.bw	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				693.2.a.e	$1$	$0$	\(3\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bx	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				847.2.a.d	$1$	$0$	\(3\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.by	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	\(\Q(\sqrt{5}) \)	None	✓				231.2.j.a	$1$	$1$	\(3\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}-\beta q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bz	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.568.1	None	✓				847.2.a.i	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
7623.2.a.ca	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.316.1	None	✓				2541.2.a.bh	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cb	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.837.1	None	✓				231.2.a.d	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cc	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.316.1	None	✓				2541.2.a.bh	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cd	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.229.1	None	✓				231.2.a.e	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.ce	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.568.1	None	✓				847.2.a.i	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
7623.2.a.cf	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.7488.1	None	✓				2541.2.a.bk	$1$	$1$	\(-2\)	\(0\)	\(-6\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7623.2.a.cg	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.7488.1	None	✓				2541.2.a.bl	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7623.2.a.ch	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.2525.1	None	✓				77.2.f.a	$1$	$0$	\(-2\)	\(0\)	\(6\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.ci	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.725.1	None	✓				231.2.j.f	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
7623.2.a.cj	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	\(\Q(\sqrt{2}, \sqrt{7})\)	None	✓	✓			7623.2.a.cj	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{5}-q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{10}+\cdots\)
7623.2.a.ck	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	\(\Q(\sqrt{2}, \sqrt{7})\)	None	✓	✓			7623.2.a.cj	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{5}+q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{10}+\cdots\)
7623.2.a.cl	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.725.1	None	✓				231.2.j.f	$1$	$0$	\(1\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+2\beta _{2}q^{5}+\cdots\)
7623.2.a.cm	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.7488.1	None	✓				2541.2.a.bk	$1$	$0$	\(2\)	\(0\)	\(-6\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7623.2.a.cn	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.7488.1	None	✓				2541.2.a.bl	$1$	$1$	\(2\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7623.2.a.co	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.2525.1	None	✓				77.2.f.a	$1$	$0$	\(2\)	\(0\)	\(6\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.cp	$7623$	$2$	7623.a	1.a	$1$	$6$	$6$	$60.870$	6.6.7674048.1	None	✓				847.2.a.m	$1$	$1$	\(-4\)	\(0\)	\(4\)	\(6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
7623.2.a.cq	$7623$	$2$	7623.a	1.a	$1$	$6$	$6$	$60.870$	6.6.3829849.1	None	✓	✓			7623.2.a.cq	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
7623.2.a.cr	$7623$	$2$	7623.a	1.a	$1$	$6$	$6$	$60.870$	6.6.3829849.1	None	✓	✓			7623.2.a.cq	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
7623.2.a.cs	$7623$	$2$	7623.a	1.a	$1$	$6$	$6$	$60.870$	6.6.7674048.1	None	✓				847.2.a.m	$1$	$0$	\(4\)	\(0\)	\(4\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
7623.2.a.ct	$7623$	$2$	7623.a	1.a	$1$	$8$	$8$	$60.870$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		77.2.f.b	$1$	$1$	\(-1\)	\(0\)	\(-10\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{5}+\beta _{6})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
7623.2.a.cu	$7623$	$2$	7623.a	1.a	$1$	$8$	$8$	$60.870$	8.8.6988960000.1	None	✓				693.2.m.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{7})q^{5}-q^{7}+\cdots\)
7623.2.a.cv	$7623$	$2$	7623.a	1.a	$1$	$8$	$8$	$60.870$	8.8.6988960000.1	None	✓		✓		693.2.m.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)
7623.2.a.cw	$7623$	$2$	7623.a	1.a	$1$	$8$	$8$	$60.870$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		77.2.f.b	$1$	$1$	\(1\)	\(0\)	\(-10\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{5}+\beta _{6})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
7623.2.a.cx	$7623$	$2$	7623.a	1.a	$1$	$10$	$10$	$60.870$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		231.2.j.g	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-10\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}-q^{7}+\cdots\)
7623.2.a.cy	$7623$	$2$	7623.a	1.a	$1$	$10$	$10$	$60.870$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		231.2.j.g	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(10\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+q^{7}+\cdots\)
7623.2.a.cz	$7623$	$2$	7623.a	1.a	$1$	$12$	$12$	$60.870$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		7623.2.a.cz	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-12\)		$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}-q^{7}+\cdots\)
7623.2.a.da	$7623$	$2$	7623.a	1.a	$1$	$12$	$12$	$60.870$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7623.2.a.cz	$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+q^{7}+\cdots\)
7623.2.a.db	$7623$	$2$	7623.a	1.a	$1$	$16$	$16$	$60.870$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		693.2.m.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots\)
7623.2.a.dc	$7623$	$2$	7623.a	1.a	$1$	$16$	$16$	$60.870$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		693.2.m.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7623))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7623)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\)\(^{\oplus 2}\)