Space of modular forms of level 5733, weight 2, and trivial character

• Label: 5733.2.a
• Level: $5733$
• Weight: $2$
• Character orbit: 5733.a
• Rep. character: $\chi_{5733}(1,\cdot)$
• Character field: $\Q$
• Dimension: $205$
• Newform subspaces: $54$
• Sturm bound: $1568$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5733.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 54 \)
Sturm bound:			\(1568\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(5\), \(11\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5733))\).

	Total	New	Old
Modular forms	816	205	611
Cusp forms	753	205	548
Eisenstein series	63	0	63

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

\(3\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(96\)	\(18\)	\(78\)		\(89\)	\(18\)	\(71\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)		\(104\)	\(22\)	\(82\)		\(96\)	\(22\)	\(74\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)		\(106\)	\(24\)	\(82\)		\(98\)	\(24\)	\(74\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)		\(102\)	\(18\)	\(84\)		\(94\)	\(18\)	\(76\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)		\(108\)	\(31\)	\(77\)		\(100\)	\(31\)	\(69\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)		\(100\)	\(29\)	\(71\)		\(92\)	\(29\)	\(63\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)		\(98\)	\(30\)	\(68\)		\(90\)	\(30\)	\(60\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)		\(102\)	\(33\)	\(69\)		\(94\)	\(33\)	\(61\)		\(8\)	\(0\)	\(8\)
Plus space			\(+\)		\(396\)	\(95\)	\(301\)		\(365\)	\(95\)	\(270\)		\(31\)	\(0\)	\(31\)
Minus space			\(-\)		\(420\)	\(110\)	\(310\)		\(388\)	\(110\)	\(278\)		\(32\)	\(0\)	\(32\)

Trace form

205 * q - 3 * q^2 + 199 * q^4 - 2 * q^5 - 15 * q^8 - 10 * q^10 - 12 * q^11 - q^13 + 183 * q^16 - 2 * q^17 - 4 * q^19 - 30 * q^20 + 8 * q^22 - 8 * q^23 + 227 * q^25 + 3 * q^26 - 2 * q^29 - 12 * q^31 - 3 * q^32 + 30 * q^34 + 14 * q^37 - 4 * q^38 + 18 * q^40 + 6 * q^41 - 20 * q^43 - 12 * q^44 - 8 * q^46 - 4 * q^47 + 23 * q^50 - 7 * q^52 - 26 * q^53 - 12 * q^55 + 6 * q^58 - 4 * q^59 - 50 * q^61 + 4 * q^62 + 179 * q^64 - 6 * q^65 - 12 * q^67 - 2 * q^68 - 8 * q^71 + 6 * q^73 - 38 * q^74 + 8 * q^76 - 48 * q^79 - 90 * q^80 + 42 * q^82 + 20 * q^83 - 16 * q^85 + 64 * q^86 + 108 * q^88 + 22 * q^89 + 52 * q^92 + 28 * q^94 + 16 * q^95 + 38 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5733))\) 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	13
5733.2.a.a	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				273.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-2q^{10}+2q^{11}+\cdots\)
5733.2.a.b	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				819.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+q^{13}-q^{16}-2q^{17}+\cdots\)
5733.2.a.c	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				91.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+3q^{11}-q^{13}+\cdots\)
5733.2.a.d	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				91.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+3q^{8}+3q^{11}+q^{13}+\cdots\)
5733.2.a.e	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				39.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
5733.2.a.f	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				91.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-3q^{5}-q^{13}+4q^{16}-6q^{17}+\cdots\)
5733.2.a.g	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				1911.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}+2q^{11}-q^{13}+4q^{16}+\cdots\)
5733.2.a.h	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				1911.2.a.d	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+2q^{11}+q^{13}+4q^{16}+\cdots\)
5733.2.a.i	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				273.2.i.a	$1$	$0$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
5733.2.a.j	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				819.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}+q^{13}-q^{16}+2q^{17}+\cdots\)
5733.2.a.k	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				273.2.i.a	$1$	$0$	\(1\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
5733.2.a.l	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				91.2.a.a	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}+6q^{11}+\cdots\)
5733.2.a.m	$5733$	$2$	5733.a	1.a	$1$	$1$	$1$	$45.778$	\(\Q\)	None	✓				273.2.a.a	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+2q^{11}+\cdots\)
5733.2.a.n	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{2}) \)	None	✓				273.2.a.c	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-3+\beta )q^{8}+\cdots\)
5733.2.a.o	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{7}) \)	None	✓	✓			5733.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-\beta q^{5}+2\beta q^{11}-q^{13}+4q^{16}+\cdots\)
5733.2.a.p	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{7}) \)	None	✓	✓			5733.2.a.o	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-\beta q^{5}-2\beta q^{11}+q^{13}+4q^{16}+\cdots\)
5733.2.a.q	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{2}) \)	None	✓				1911.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+2q^{11}+\cdots\)
5733.2.a.r	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{2}) \)	None	✓				1911.2.a.i	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+2q^{11}+\cdots\)
5733.2.a.s	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{2}) \)	None	✓				91.2.a.c	$1$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(3-\beta )q^{5}-2\beta q^{8}+(-2+3\beta )q^{10}+\cdots\)
5733.2.a.t	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{3}) \)	None	✓				117.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{8}-2\beta q^{11}-q^{13}+\cdots\)
5733.2.a.u	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{2}) \)	None	✓				39.2.a.b	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
5733.2.a.v	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{5}) \)	None	✓				91.2.e.b	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+(1+\cdots)q^{8}+\cdots\)
5733.2.a.w	$5733$	$2$	5733.a	1.a	$1$	$2$	$2$	$45.778$	\(\Q(\sqrt{5}) \)	None	✓				91.2.e.b	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
5733.2.a.x	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	3.3.316.1	None	✓				91.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
5733.2.a.y	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	\(\Q(\zeta_{18})^+\)	None	✓				273.2.i.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{8}+\cdots\)
5733.2.a.z	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	\(\Q(\zeta_{18})^+\)	None	✓				273.2.i.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{8}+\cdots\)
5733.2.a.ba	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	\(\Q(\zeta_{14})^+\)	None	✓				273.2.i.c	$1$	$1$	\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5733.2.a.bb	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	\(\Q(\zeta_{14})^+\)	None	✓				273.2.i.c	$1$	$1$	\(2\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
5733.2.a.bc	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	3.3.316.1	None	✓				273.2.a.d	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5733.2.a.bd	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	3.3.404.1	None	✓				637.2.a.h	$1$	$1$	\(2\)	\(0\)	\(-5\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
5733.2.a.be	$5733$	$2$	5733.a	1.a	$1$	$3$	$3$	$45.778$	3.3.404.1	None	✓				637.2.a.h	$1$	$0$	\(2\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
5733.2.a.bf	$5733$	$2$	5733.a	1.a	$1$	$4$	$4$	$45.778$	4.4.17428.1	None	✓				273.2.a.e	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
5733.2.a.bg	$5733$	$2$	5733.a	1.a	$1$	$4$	$4$	$45.778$	4.4.7168.1	None	✓	✓			5733.2.a.bg	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
5733.2.a.bh	$5733$	$2$	5733.a	1.a	$1$	$4$	$4$	$45.778$	4.4.7168.1	None	✓	✓			5733.2.a.bg	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5733.2.a.bi	$5733$	$2$	5733.a	1.a	$1$	$4$	$4$	$45.778$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓				819.2.a.l	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
5733.2.a.bj	$5733$	$2$	5733.a	1.a	$1$	$4$	$4$	$45.778$	4.4.69777.1	None	✓				273.2.i.d	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
5733.2.a.bk	$5733$	$2$	5733.a	1.a	$1$	$4$	$4$	$45.778$	4.4.69777.1	None	✓				273.2.i.d	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
5733.2.a.bl	$5733$	$2$	5733.a	1.a	$1$	$5$	$5$	$45.778$	5.5.746052.1	None	✓				91.2.e.c	$1$	$1$	\(-4\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
5733.2.a.bm	$5733$	$2$	5733.a	1.a	$1$	$5$	$5$	$45.778$	5.5.746052.1	None	✓				91.2.e.c	$1$	$1$	\(-4\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{3}-\beta _{4})q^{4}+\cdots\)
5733.2.a.bn	$5733$	$2$	5733.a	1.a	$1$	$5$	$5$	$45.778$	5.5.2196544.1	None	✓				1911.2.a.v	$1$	$0$	\(-2\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
5733.2.a.bo	$5733$	$2$	5733.a	1.a	$1$	$5$	$5$	$45.778$	5.5.2196544.1	None	✓				1911.2.a.v	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
5733.2.a.bp	$5733$	$2$	5733.a	1.a	$1$	$5$	$5$	$45.778$	5.5.375116.1	None	✓				273.2.i.e	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5733.2.a.bq	$5733$	$2$	5733.a	1.a	$1$	$5$	$5$	$45.778$	5.5.375116.1	None	✓				273.2.i.e	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1-\beta _{4})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
5733.2.a.br	$5733$	$2$	5733.a	1.a	$1$	$6$	$6$	$45.778$	6.6.4507648.1	None	✓				637.2.a.m	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5733.2.a.bs	$5733$	$2$	5733.a	1.a	$1$	$6$	$6$	$45.778$	6.6.46162368.1	None	✓				819.2.j.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots\)
5733.2.a.bt	$5733$	$2$	5733.a	1.a	$1$	$6$	$6$	$45.778$	6.6.46162368.1	None	✓		✓		819.2.j.i	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots\)
5733.2.a.bu	$5733$	$2$	5733.a	1.a	$1$	$6$	$6$	$45.778$	6.6.4507648.1	None	✓				637.2.a.m	$1$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
5733.2.a.bv	$5733$	$2$	5733.a	1.a	$1$	$6$	$6$	$45.778$	6.6.199374400.1	None	✓				819.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(2\beta _{4}+\cdots)q^{8}+\cdots\)
5733.2.a.bw	$5733$	$2$	5733.a	1.a	$1$	$10$	$10$	$45.778$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		1911.2.a.x	$1$	$1$	\(-4\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots\)
5733.2.a.bx	$5733$	$2$	5733.a	1.a	$1$	$10$	$10$	$45.778$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		1911.2.a.x	$1$	$0$	\(-4\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
5733.2.a.by	$5733$	$2$	5733.a	1.a	$1$	$10$	$10$	$45.778$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				819.2.j.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
5733.2.a.bz	$5733$	$2$	5733.a	1.a	$1$	$10$	$10$	$45.778$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		819.2.j.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
5733.2.a.ca	$5733$	$2$	5733.a	1.a	$1$	$12$	$12$	$45.778$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		5733.2.a.ca	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
5733.2.a.cb	$5733$	$2$	5733.a	1.a	$1$	$12$	$12$	$45.778$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		5733.2.a.ca	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5733))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5733)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(819))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\)\(^{\oplus 2}\)