Space of modular forms of level 5929, weight 2, and trivial character

• Label: 5929.2.a
• Level: $5929$
• Weight: $2$
• Character orbit: 5929.a
• Rep. character: $\chi_{5929}(1,\cdot)$
• Character field: $\Q$
• Dimension: $350$
• Newform subspaces: $60$
• Sturm bound: $1232$
• Trace bound: $18$

Defining parameters

Level:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 60 \)
Sturm bound:			\(1232\)
Trace bound:			\(18\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5929))\).

	Total	New	Old
Modular forms	664	395	269
Cusp forms	569	350	219
Eisenstein series	95	45	50

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

\(7\)	\(11\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(160\)	\(88\)	\(72\)		\(137\)	\(80\)	\(57\)		\(23\)	\(8\)	\(15\)
\(+\)	\(-\)	\(-\)		\(172\)	\(102\)	\(70\)		\(148\)	\(92\)	\(56\)		\(24\)	\(10\)	\(14\)
\(-\)	\(+\)	\(-\)		\(172\)	\(105\)	\(67\)		\(148\)	\(93\)	\(55\)		\(24\)	\(12\)	\(12\)
\(-\)	\(-\)	\(+\)		\(160\)	\(100\)	\(60\)		\(136\)	\(85\)	\(51\)		\(24\)	\(15\)	\(9\)
Plus space		\(+\)		\(320\)	\(188\)	\(132\)		\(273\)	\(165\)	\(108\)		\(47\)	\(23\)	\(24\)
Minus space		\(-\)		\(344\)	\(207\)	\(137\)		\(296\)	\(185\)	\(111\)		\(48\)	\(22\)	\(26\)

Trace form

350 * q - 2 * q^2 + 2 * q^3 + 324 * q^4 - 2 * q^5 - 6 * q^6 + 308 * q^9 - 4 * q^10 + 20 * q^12 + 2 * q^13 + 10 * q^15 + 268 * q^16 - 4 * q^17 - 4 * q^18 - 12 * q^20 + 6 * q^23 - 16 * q^24 + 250 * q^25 + 24 * q^26 + 14 * q^27 + 8 * q^29 + 46 * q^30 + 18 * q^31 + 28 * q^32 + 236 * q^36 - 28 * q^37 + 12 * q^38 - 16 * q^39 + 6 * q^40 - 18 * q^41 + 18 * q^43 - 4 * q^45 + 18 * q^46 + 20 * q^47 + 12 * q^48 + 22 * q^51 + 26 * q^52 - 26 * q^53 - 34 * q^54 + 8 * q^57 - 22 * q^58 - 6 * q^59 + 76 * q^60 - 10 * q^61 + 6 * q^62 + 112 * q^64 - 28 * q^65 + 2 * q^67 - 6 * q^68 - 2 * q^69 - 18 * q^71 + 40 * q^72 + 2 * q^73 - 30 * q^74 + 48 * q^75 + 20 * q^76 - 30 * q^79 + 72 * q^80 + 198 * q^81 + 8 * q^82 + 22 * q^83 - 66 * q^85 + 72 * q^86 - 60 * q^87 + 14 * q^89 + 42 * q^90 + 100 * q^92 + 22 * q^93 - 36 * q^94 + 40 * q^95 + 32 * q^96 + 26 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5929))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	11
5929.2.a.a	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	None	✓				121.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}+3q^{8}+\cdots\)
5929.2.a.b	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	None	✓				77.2.a.c	$1$	$1$	\(-1\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}+2q^{5}+2q^{6}+3q^{8}+\cdots\)
5929.2.a.c	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓				49.2.a.a	$2$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-q^{2}-q^{4}+3q^{8}-3q^{9}-q^{16}+3q^{18}+\cdots\)
5929.2.a.d	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	None	✓				77.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-3q^{5}-2q^{9}+2q^{12}+\cdots\)
5929.2.a.e	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓				121.2.a.b	$2$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+q^{3}-2q^{4}+3q^{5}-2q^{9}-2q^{12}+\cdots\)
5929.2.a.f	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	None	✓				77.2.a.a	$1$	$1$	\(0\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{4}+q^{5}+6q^{9}-6q^{12}+\cdots\)
5929.2.a.g	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	None	✓				121.2.a.a	$1$	$1$	\(1\)	\(-2\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-3q^{8}+\cdots\)
5929.2.a.h	$5929$	$2$	5929.a	1.a	$1$	$1$	$1$	$47.343$	\(\Q\)	None	✓				11.2.a.a	$1$	$1$	\(2\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{9}+\cdots\)
5929.2.a.i	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{5}) \)	None	✓				847.2.a.d	$1$	$1$	\(-3\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(1-\beta )q^{3}+3\beta q^{4}+\cdots\)
5929.2.a.j	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{5}) \)	None	✓				77.2.m.a	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
5929.2.a.k	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{13}) \)	None	✓				847.2.a.e	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+\beta q^{3}+(1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
5929.2.a.l	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{5}) \)	None	✓				77.2.m.a	$1$	$0$	\(-1\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
5929.2.a.m	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{5}) \)	None	✓				77.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{3}+3q^{4}+2q^{5}+\cdots\)
5929.2.a.n	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{11}) \)	\(\Q(\sqrt{-11}) \)	✓	✓			5929.2.a.n	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+\beta q^{3}-2q^{4}+\beta q^{5}+8q^{9}-2\beta q^{12}+\cdots\)
5929.2.a.o	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{5}) \)	None	✓				77.2.m.a	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
5929.2.a.p	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{13}) \)	None	✓				847.2.a.e	$1$	$1$	\(1\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+\beta q^{3}+(1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
5929.2.a.q	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{5}) \)	None	✓				77.2.m.a	$1$	$1$	\(1\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
5929.2.a.r	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{2}) \)	None	✓				539.2.a.e	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}-q^{4}+\beta q^{5}-\beta q^{6}-3q^{8}+\cdots\)
5929.2.a.s	$5929$	$2$	5929.a	1.a	$1$	$2$	$2$	$47.343$	\(\Q(\sqrt{5}) \)	None	✓				847.2.a.d	$1$	$1$	\(3\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1-\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots\)
5929.2.a.t	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.568.1	None	✓				847.2.a.i	$1$	$0$	\(-2\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots\)
5929.2.a.u	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	\(\Q(\zeta_{18})^+\)	None	✓				77.2.e.a	$1$	$1$	\(0\)	\(-3\)	\(-6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
5929.2.a.v	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.257.1	None	✓				77.2.e.b	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
5929.2.a.w	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.257.1	None	✓				77.2.e.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
5929.2.a.x	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	\(\Q(\zeta_{18})^+\)	None	✓				77.2.e.a	$1$	$0$	\(0\)	\(3\)	\(6\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
5929.2.a.y	$5929$	$2$	5929.a	1.a	$1$	$3$	$3$	$47.343$	3.3.568.1	None	✓				847.2.a.i	$1$	$0$	\(2\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}+(3+\beta _{2})q^{4}+\cdots\)
5929.2.a.z	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{14 +2 \sqrt{5}})\)	None	✓	✓			5929.2.a.z	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
5929.2.a.ba	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{10 +2 \sqrt{17}})\)	None	✓				539.2.a.k	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(2-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5929.2.a.bb	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{11 +2 \sqrt{5}})\)	None	✓				77.2.f.a	$1$	$1$	\(-2\)	\(2\)	\(6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5929.2.a.bc	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{70 -14 \sqrt{5}})\)	\(\Q(\sqrt{-7}) \)	✓				539.2.f.c	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(\beta _{2}+\beta _{3})q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{8}+\cdots\)
5929.2.a.bd	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{2}, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)	✓	✓			5929.2.a.bd	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-\beta _{1}q^{3}-2q^{4}+(\beta _{1}+\beta _{2})q^{5}+(3+\beta _{3})q^{9}+\cdots\)
5929.2.a.be	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\zeta_{24})^+\)	None	✓	✓			5929.2.a.be	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+q^{4}-2\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots\)
5929.2.a.bf	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	✓			5929.2.a.bf	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+3q^{4}+\beta _{1}q^{5}-\beta _{3}q^{8}-3q^{9}+\cdots\)
5929.2.a.bg	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{70 -14 \sqrt{5}})\)	\(\Q(\sqrt{-7}) \)	✓				539.2.f.c	$2$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{2}+(2-\beta _{2}+\beta _{3})q^{4}+(2\beta _{1}+2\beta _{2}+\cdots)q^{8}+\cdots\)
5929.2.a.bh	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{14 +2 \sqrt{5}})\)	None	✓	✓			5929.2.a.z	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
5929.2.a.bi	$5929$	$2$	5929.a	1.a	$1$	$4$	$4$	$47.343$	\(\Q(\sqrt{11 +2 \sqrt{5}})\)	None	✓				77.2.f.a	$1$	$0$	\(2\)	\(2\)	\(6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5929.2.a.bj	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.7674048.1	None	✓				847.2.a.m	$1$	$0$	\(-4\)	\(2\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5929.2.a.bk	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.58383808.1	None	✓				847.2.e.e	$2$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
5929.2.a.bl	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.58383808.1	None	✓				847.2.e.e	$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2}+\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
5929.2.a.bm	$5929$	$2$	5929.a	1.a	$1$	$6$	$6$	$47.343$	6.6.7674048.1	None	✓				847.2.a.m	$1$	$0$	\(4\)	\(2\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5929.2.a.bn	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				847.2.e.f	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5929.2.a.bo	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				847.2.e.f	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5929.2.a.bp	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				847.2.e.f	$1$	$0$	\(0\)	\(3\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)
5929.2.a.bq	$5929$	$2$	5929.a	1.a	$1$	$7$	$7$	$47.343$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				847.2.e.f	$1$	$0$	\(0\)	\(3\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)
5929.2.a.br	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	8.8.\(\cdots\).1	None	✓				539.2.f.f	$2$	$1$	\(-4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-1-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5929.2.a.bs	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				77.2.f.b	$1$	$1$	\(-1\)	\(-4\)	\(-10\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
5929.2.a.bt	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				77.2.f.b	$1$	$0$	\(1\)	\(-4\)	\(-10\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{7})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
5929.2.a.bu	$5929$	$2$	5929.a	1.a	$1$	$8$	$8$	$47.343$	8.8.\(\cdots\).1	None	✓				539.2.f.f	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-1-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5929.2.a.bv	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				539.2.a.l	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(2+\beta _{9})q^{4}-\beta _{7}q^{5}+\cdots\)
5929.2.a.bw	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				77.2.m.b	$1$	$1$	\(-1\)	\(-3\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
5929.2.a.bx	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				77.2.m.b	$1$	$0$	\(-1\)	\(3\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
5929.2.a.by	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				77.2.m.b	$1$	$0$	\(1\)	\(-3\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
5929.2.a.bz	$5929$	$2$	5929.a	1.a	$1$	$10$	$10$	$47.343$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		77.2.m.b	$1$	$1$	\(1\)	\(3\)	\(2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{3}+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
5929.2.a.ca	$5929$	$2$	5929.a	1.a	$1$	$12$	$12$	$47.343$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			5929.2.a.ca	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
5929.2.a.cb	$5929$	$2$	5929.a	1.a	$1$	$12$	$12$	$47.343$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			5929.2.a.ca	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{2}+\beta _{1}q^{3}+(1+\beta _{9})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
5929.2.a.cc	$5929$	$2$	5929.a	1.a	$1$	$12$	$12$	$47.343$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			5929.2.a.cc	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}-\beta _{8}q^{3}+(2-\beta _{10})q^{4}+(\beta _{7}+\cdots)q^{5}+\cdots\)
5929.2.a.cd	$5929$	$2$	5929.a	1.a	$1$	$14$	$14$	$47.343$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				847.2.e.j	$2$	$1$	\(0\)	\(-6\)	\(-8\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5929.2.a.ce	$5929$	$2$	5929.a	1.a	$1$	$14$	$14$	$47.343$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		847.2.e.j	$2$	$0$	\(0\)	\(6\)	\(8\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
5929.2.a.cf	$5929$	$2$	5929.a	1.a	$1$	$16$	$16$	$47.343$	16.16.\(\cdots\).1	None	✓	✓			5929.2.a.cf	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{12}q^{2}-\beta _{5}q^{3}+(1+\beta _{13})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
5929.2.a.cg	$5929$	$2$	5929.a	1.a	$1$	$24$	$24$	$47.343$		None	✓		✓		539.2.f.i	$2$	$1$	\(-10\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
5929.2.a.ch	$5929$	$2$	5929.a	1.a	$1$	$24$	$24$	$47.343$		None	✓		✓		539.2.f.i	$2$	$0$	\(10\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5929))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5929)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 2}\)