Space of modular forms of level 4761, weight 2, and trivial character

• Label: 4761.2.a
• Level: $4761$
• Weight: $2$
• Character orbit: 4761.a
• Rep. character: $\chi_{4761}(1,\cdot)$
• Character field: $\Q$
• Dimension: $200$
• Newform subspaces: $50$
• Sturm bound: $1104$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4761 = 3^{2} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4761.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 50 \)
Sturm bound:			\(1104\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4761))\).

	Total	New	Old
Modular forms	600	221	379
Cusp forms	505	200	305
Eisenstein series	95	21	74

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

\(3\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(144\)	\(36\)	\(108\)		\(121\)	\(36\)	\(85\)		\(23\)	\(0\)	\(23\)
\(+\)	\(-\)	\(-\)		\(156\)	\(48\)	\(108\)		\(132\)	\(48\)	\(84\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)		\(156\)	\(71\)	\(85\)		\(132\)	\(61\)	\(71\)		\(24\)	\(10\)	\(14\)
\(-\)	\(-\)	\(+\)		\(144\)	\(66\)	\(78\)		\(120\)	\(55\)	\(65\)		\(24\)	\(11\)	\(13\)
Plus space		\(+\)		\(288\)	\(102\)	\(186\)		\(241\)	\(91\)	\(150\)		\(47\)	\(11\)	\(36\)
Minus space		\(-\)		\(312\)	\(119\)	\(193\)		\(264\)	\(109\)	\(155\)		\(48\)	\(10\)	\(38\)

Trace form

200 * q + 190 * q^4 - 4 * q^5 + 6 * q^7 - 6 * q^8 + 4 * q^10 + 6 * q^11 - 8 * q^14 + 170 * q^16 - 10 * q^20 + 14 * q^22 + 162 * q^25 + 8 * q^26 + 22 * q^28 - 2 * q^29 + 2 * q^31 + 8 * q^32 - 18 * q^34 + 18 * q^35 + 4 * q^37 - 6 * q^38 + 4 * q^40 + 2 * q^41 + 12 * q^43 + 28 * q^44 + 18 * q^47 + 156 * q^49 + 52 * q^50 + 6 * q^52 - 26 * q^53 - 14 * q^56 - 24 * q^58 - 4 * q^59 - 6 * q^61 + 40 * q^62 + 184 * q^64 - 26 * q^65 - 26 * q^67 - 32 * q^68 - 18 * q^70 + 18 * q^71 - 20 * q^73 - 24 * q^74 + 26 * q^76 - 24 * q^77 - 4 * q^79 + 20 * q^80 - 2 * q^82 - 2 * q^83 - 50 * q^85 + 40 * q^86 + 18 * q^88 - 26 * q^89 + 2 * q^91 - 2 * q^94 + 20 * q^97 + 2 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4761))\) 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	23
4761.2.a.a	$4761$	$2$	4761.a	1.a	$1$	$1$	$1$	$38.017$	\(\Q\)	None	✓				1587.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{5}+4q^{7}+3q^{8}+4q^{10}+\cdots\)
4761.2.a.b	$4761$	$2$	4761.a	1.a	$1$	$1$	$1$	$38.017$	\(\Q\)	None	✓				69.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{7}+3q^{8}+4q^{11}+\cdots\)
4761.2.a.c	$4761$	$2$	4761.a	1.a	$1$	$1$	$1$	$38.017$	\(\Q\)	None	✓				1587.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{5}-4q^{7}+3q^{8}-4q^{10}+\cdots\)
4761.2.a.d	$4761$	$2$	4761.a	1.a	$1$	$1$	$1$	$38.017$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			4761.2.a.d	$2$	$2$	\(0\)	\(0\)	\(0\)	\(-5\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-5q^{7}-7q^{13}+4q^{16}-8q^{19}+\cdots\)
4761.2.a.e	$4761$	$2$	4761.a	1.a	$1$	$1$	$1$	$38.017$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			4761.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(5\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+5q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots\)
4761.2.a.f	$4761$	$2$	4761.a	1.a	$1$	$1$	$1$	$38.017$	\(\Q\)	None	✓				1587.2.a.a	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{7}+4q^{11}-3q^{13}+\cdots\)
4761.2.a.g	$4761$	$2$	4761.a	1.a	$1$	$1$	$1$	$38.017$	\(\Q\)	None	✓				1587.2.a.a	$1$	$1$	\(2\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{7}-4q^{11}-3q^{13}+\cdots\)
4761.2.a.h	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓	✓			4761.2.a.h	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-\beta q^{5}+3q^{8}+\beta q^{10}+\cdots\)
4761.2.a.i	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓				529.2.a.d	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
4761.2.a.j	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓				529.2.a.d	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
4761.2.a.k	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓				207.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
4761.2.a.l	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	None	✓				1587.2.a.k	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
4761.2.a.m	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	None	✓				1587.2.a.k	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
4761.2.a.n	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	None	✓				1587.2.a.j	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2\beta q^{5}-\beta q^{7}+2\beta q^{11}-5q^{13}+\cdots\)
4761.2.a.o	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	✓			4761.2.a.o	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+\beta q^{7}+7q^{13}+4q^{16}+2\beta q^{19}+\cdots\)
4761.2.a.p	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓				1587.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-2-\beta )q^{5}+(1-2\beta )q^{7}+\cdots\)
4761.2.a.q	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓				1587.2.a.g	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{5}+(-1+2\beta )q^{7}+\cdots\)
4761.2.a.r	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	None	✓	✓			4761.2.a.r	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-3q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
4761.2.a.s	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	None	✓				529.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
4761.2.a.t	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	None	✓				529.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{5}+(3+\beta )q^{7}-\beta q^{8}+\cdots\)
4761.2.a.u	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{3}) \)	None	✓	✓			4761.2.a.r	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
4761.2.a.v	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{5}) \)	None	✓				69.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}+(-1-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
4761.2.a.w	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{5}) \)	None	✓				23.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-2\beta q^{5}+(-2+\cdots)q^{7}+\cdots\)
4761.2.a.x	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓				1587.2.a.f	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2\beta q^{5}-3\beta q^{7}-3q^{8}+\cdots\)
4761.2.a.y	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓	✓			4761.2.a.h	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+\beta q^{10}+\cdots\)
4761.2.a.z	$4761$	$2$	4761.a	1.a	$1$	$2$	$2$	$38.017$	\(\Q(\sqrt{2}) \)	None	✓				207.2.a.b	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
4761.2.a.ba	$4761$	$2$	4761.a	1.a	$1$	$3$	$3$	$38.017$	3.3.621.1	\(\Q(\sqrt{-23}) \)	✓				529.2.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-3-2\beta _{1}+\cdots)q^{8}+\cdots\)
4761.2.a.bb	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	None	✓	✓			4761.2.a.bb	$2$	$1$	\(-8\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-2\beta _{1}q^{5}+(-2\beta _{1}-\beta _{3})q^{7}+\cdots\)
4761.2.a.bc	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	\(\Q(\sqrt{-3}) \)	✓	✓			4761.2.a.bc	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(3\beta _{1}+2\beta _{3})q^{7}+\beta _{2}q^{13}+\cdots\)
4761.2.a.bd	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	None	✓				1587.2.a.n	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
4761.2.a.be	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	None	✓	✓			4761.2.a.be	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{8}+\cdots\)
4761.2.a.bf	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	4.4.268960.2	None	✓	✓			4761.2.a.bf	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-\beta _{1}q^{5}+\beta _{2}q^{7}+\cdots\)
4761.2.a.bg	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	4.4.268960.2	None	✓	✓			4761.2.a.bf	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
4761.2.a.bh	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	None	✓	✓			4761.2.a.bh	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+4q^{4}-\beta _{3}q^{5}-\beta _{2}q^{7}+2\beta _{1}q^{8}+\cdots\)
4761.2.a.bi	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\sqrt{2}, \sqrt{13})\)	None	✓				529.2.a.h	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1+\beta _{3})q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
4761.2.a.bj	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	None	✓				529.2.a.g	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
4761.2.a.bk	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	None	✓				1587.2.a.m	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2+2\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
4761.2.a.bl	$4761$	$2$	4761.a	1.a	$1$	$4$	$4$	$38.017$	\(\Q(\zeta_{24})^+\)	None	✓	✓			4761.2.a.bb	$2$	$1$	\(8\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2\beta _{1}q^{5}+(2\beta _{1}+\beta _{3})q^{7}+\cdots\)
4761.2.a.bm	$4761$	$2$	4761.a	1.a	$1$	$5$	$5$	$38.017$	\(\Q(\zeta_{22})^+\)	None	✓				69.2.e.b	$1$	$1$	\(-2\)	\(0\)	\(-7\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{4})q^{2}+(2\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4761.2.a.bn	$4761$	$2$	4761.a	1.a	$1$	$5$	$5$	$38.017$	\(\Q(\zeta_{22})^+\)	None	✓				23.2.c.a	$1$	$1$	\(-2\)	\(0\)	\(-7\)	\(8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{4})q^{2}+(2\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4761.2.a.bo	$4761$	$2$	4761.a	1.a	$1$	$5$	$5$	$38.017$	\(\Q(\zeta_{22})^+\)	None	✓				23.2.c.a	$1$	$0$	\(-2\)	\(0\)	\(7\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{4})q^{2}+(2\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4761.2.a.bp	$4761$	$2$	4761.a	1.a	$1$	$5$	$5$	$38.017$	\(\Q(\zeta_{22})^+\)	None	✓				69.2.e.b	$1$	$0$	\(-2\)	\(0\)	\(7\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{4})q^{2}+(2\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4761.2.a.bq	$4761$	$2$	4761.a	1.a	$1$	$5$	$5$	$38.017$	\(\Q(\zeta_{22})^+\)	None	✓				69.2.e.a	$1$	$1$	\(2\)	\(0\)	\(-3\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{3}-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{4}+\cdots\)
4761.2.a.br	$4761$	$2$	4761.a	1.a	$1$	$5$	$5$	$38.017$	\(\Q(\zeta_{22})^+\)	None	✓				69.2.e.a	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{3}-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{4}+\cdots\)
4761.2.a.bs	$4761$	$2$	4761.a	1.a	$1$	$6$	$6$	$38.017$	6.6.2803712.1	None	✓				1587.2.a.s	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots\)
4761.2.a.bt	$4761$	$2$	4761.a	1.a	$1$	$10$	$10$	$38.017$	10.10.\(\cdots\).1	None	✓				69.2.e.c	$1$	$0$	\(2\)	\(0\)	\(-8\)	\(19\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4761.2.a.bu	$4761$	$2$	4761.a	1.a	$1$	$10$	$10$	$38.017$	10.10.\(\cdots\).1	None	✓		✓		69.2.e.c	$1$	$1$	\(2\)	\(0\)	\(8\)	\(-19\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)
4761.2.a.bv	$4761$	$2$	4761.a	1.a	$1$	$12$	$12$	$38.017$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		1587.2.a.v	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(2-\beta _{7}+\beta _{9})q^{4}-\beta _{6}q^{5}+\cdots\)
4761.2.a.bw	$4761$	$2$	4761.a	1.a	$1$	$20$	$20$	$38.017$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		207.2.i.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-18\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2}-\beta _{3})q^{4}+\beta _{19}q^{5}+\cdots\)
4761.2.a.bx	$4761$	$2$	4761.a	1.a	$1$	$20$	$20$	$38.017$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓		✓		207.2.i.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(18\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2}-\beta _{3})q^{4}-\beta _{19}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4761))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4761)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 2}\)