Space of modular forms of level 5776, weight 2, and trivial character

• Label: 5776.2.a
• Level: $5776$
• Weight: $2$
• Character orbit: 5776.a
• Rep. character: $\chi_{5776}(1,\cdot)$
• Character field: $\Q$
• Dimension: $162$
• Newform subspaces: $57$
• Sturm bound: $1520$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 5776 = 2^{4} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5776.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 57 \)
Sturm bound:			\(1520\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5776))\).

	Total	New	Old
Modular forms	820	179	641
Cusp forms	701	162	539
Eisenstein series	119	17	102

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

\(2\)	\(19\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(200\)	\(40\)	\(160\)		\(171\)	\(40\)	\(131\)		\(29\)	\(0\)	\(29\)
\(+\)	\(-\)	\(-\)		\(210\)	\(45\)	\(165\)		\(180\)	\(45\)	\(135\)		\(30\)	\(0\)	\(30\)
\(-\)	\(+\)	\(-\)		\(210\)	\(49\)	\(161\)		\(180\)	\(41\)	\(139\)		\(30\)	\(8\)	\(22\)
\(-\)	\(-\)	\(+\)		\(200\)	\(45\)	\(155\)		\(170\)	\(36\)	\(134\)		\(30\)	\(9\)	\(21\)
Plus space		\(+\)		\(400\)	\(85\)	\(315\)		\(341\)	\(76\)	\(265\)		\(59\)	\(9\)	\(50\)
Minus space		\(-\)		\(420\)	\(94\)	\(326\)		\(360\)	\(86\)	\(274\)		\(60\)	\(8\)	\(52\)

Trace form

162 * q + 2 * q^5 + 2 * q^7 + 144 * q^9 - 2 * q^11 + 2 * q^13 - 12 * q^15 - 2 * q^17 + 8 * q^21 + 10 * q^23 + 132 * q^25 + 2 * q^29 + 8 * q^33 - 12 * q^35 + 2 * q^37 + 14 * q^39 - 2 * q^41 + 14 * q^43 + 18 * q^45 - 14 * q^47 + 116 * q^49 - 4 * q^51 - 6 * q^53 + 24 * q^55 + 16 * q^59 + 10 * q^61 + 30 * q^63 - 12 * q^65 + 20 * q^67 + 24 * q^69 - 4 * q^71 - 2 * q^73 + 4 * q^75 - 10 * q^77 + 8 * q^79 + 82 * q^81 + 2 * q^83 + 12 * q^85 - 12 * q^87 - 18 * q^89 + 40 * q^91 - 8 * q^93 - 10 * q^97 - 58 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5776))\) 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	19
5776.2.a.a	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				722.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+3q^{7}+6q^{9}+2q^{11}+\cdots\)
5776.2.a.b	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				152.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
5776.2.a.c	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				19.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
5776.2.a.d	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				38.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
5776.2.a.e	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				152.2.i.b	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
5776.2.a.f	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				76.2.e.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+4q^{11}+q^{13}+\cdots\)
5776.2.a.g	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				38.2.c.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
5776.2.a.h	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				152.2.i.a	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{9}+4q^{11}-5q^{13}+\cdots\)
5776.2.a.i	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	\(\Q(\sqrt{-19}) \)	✓				361.2.a.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-q^{5}-3q^{7}-3q^{9}+5q^{11}-7q^{17}+\cdots\)
5776.2.a.j	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				152.2.i.b	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
5776.2.a.k	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				76.2.e.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+4q^{11}-q^{13}+\cdots\)
5776.2.a.l	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				152.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots\)
5776.2.a.m	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				38.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}-2q^{9}+6q^{11}-5q^{13}+\cdots\)
5776.2.a.n	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				38.2.c.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
5776.2.a.o	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				152.2.i.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-2q^{9}+4q^{11}+5q^{13}+\cdots\)
5776.2.a.p	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				76.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
5776.2.a.q	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	\(\Q\)	None	✓				722.2.a.a	$1$	$0$	\(0\)	\(3\)	\(2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{5}+3q^{7}+6q^{9}+2q^{11}+\cdots\)
5776.2.a.r	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.d	$1$	$1$	\(0\)	\(-4\)	\(1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
5776.2.a.s	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.c	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-2\beta )q^{5}-3q^{7}+\cdots\)
5776.2.a.t	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				722.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(-5\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2\beta q^{3}+(-3+\beta )q^{5}+(2-2\beta )q^{7}+\cdots\)
5776.2.a.u	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				2888.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(5\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2\beta q^{3}+(2+\beta )q^{5}+2q^{7}+(1+4\beta )q^{9}+\cdots\)
5776.2.a.v	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{17}) \)	None	✓				2888.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
5776.2.a.w	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				1444.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2\beta q^{5}+(-1-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
5776.2.a.x	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				2888.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2\beta q^{5}+(-3+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
5776.2.a.y	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	✓				1444.2.a.e	$2$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+\beta q^{5}+(2-\beta )q^{7}-3q^{9}+(-2-\beta )q^{11}+\cdots\)
5776.2.a.z	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{7}) \)	None	✓				38.2.c.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-\beta )q^{5}+(-1-\beta )q^{7}+4q^{9}+\cdots\)
5776.2.a.ba	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{7}) \)	None	✓				38.2.c.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+4q^{9}+\cdots\)
5776.2.a.bb	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{17}) \)	None	✓				2888.2.a.h	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
5776.2.a.bc	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				1444.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}+(-1-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
5776.2.a.bd	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				2888.2.a.i	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2\beta q^{5}+(-3+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
5776.2.a.be	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				722.2.a.h	$1$	$1$	\(0\)	\(2\)	\(-5\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+(-3+\beta )q^{5}+(2-2\beta )q^{7}+\cdots\)
5776.2.a.bf	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				2888.2.a.g	$1$	$0$	\(0\)	\(2\)	\(5\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+(2+\beta )q^{5}+2q^{7}+(1+4\beta )q^{9}+\cdots\)
5776.2.a.bg	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.c	$1$	$1$	\(0\)	\(3\)	\(2\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2-2\beta )q^{5}-3q^{7}+(-1+\cdots)q^{9}+\cdots\)
5776.2.a.bh	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	\(\Q(\sqrt{5}) \)	None	✓				361.2.a.d	$1$	$1$	\(0\)	\(4\)	\(1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+(1-\beta )q^{5}+2\beta q^{7}+q^{9}+(-4+\cdots)q^{11}+\cdots\)
5776.2.a.bi	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				19.2.e.a	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-1+\beta _{1})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5776.2.a.bj	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				152.2.q.b	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
5776.2.a.bk	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	3.3.316.1	None	✓				152.2.i.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
5776.2.a.bl	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				152.2.q.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1+2\beta _{1})q^{7}+\cdots\)
5776.2.a.bm	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				152.2.q.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1+2\beta _{1})q^{7}+\cdots\)
5776.2.a.bn	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				38.2.e.a	$1$	$0$	\(0\)	\(0\)	\(6\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+2q^{5}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
5776.2.a.bo	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				38.2.e.a	$1$	$1$	\(0\)	\(0\)	\(6\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+2q^{5}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
5776.2.a.bp	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	3.3.961.1	None	✓				152.2.a.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
5776.2.a.bq	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	3.3.316.1	None	✓				152.2.i.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
5776.2.a.br	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				19.2.e.a	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-1+\beta _{1})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5776.2.a.bs	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	\(\Q(\zeta_{18})^+\)	None	✓				152.2.q.b	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+2\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots\)
5776.2.a.bt	$5776$	$2$	5776.a	1.a	$1$	$4$	$4$	$46.122$	\(\Q(\zeta_{20})^+\)	None	✓				722.2.a.m	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2}-\beta _{3})q^{3}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
5776.2.a.bu	$5776$	$2$	5776.a	1.a	$1$	$4$	$4$	$46.122$	\(\Q(\zeta_{20})^+\)	None	✓				361.2.a.i	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-2-2\beta _{2})q^{5}+(1-2\beta _{2}+\cdots)q^{7}+\cdots\)
5776.2.a.bv	$5776$	$2$	5776.a	1.a	$1$	$4$	$4$	$46.122$	\(\Q(\zeta_{20})^+\)	None	✓				722.2.a.m	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2}+\beta _{3})q^{3}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
5776.2.a.bw	$5776$	$2$	5776.a	1.a	$1$	$6$	$6$	$46.122$	6.6.20319417.1	None	✓				76.2.i.a	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}-\beta _{4}q^{5}+(1+\cdots)q^{7}+\cdots\)
5776.2.a.bx	$5776$	$2$	5776.a	1.a	$1$	$6$	$6$	$46.122$	6.6.3022625.1	None	✓				2888.2.a.t	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(2\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
5776.2.a.by	$5776$	$2$	5776.a	1.a	$1$	$6$	$6$	$46.122$	6.6.20319417.1	None	✓		✓		76.2.i.a	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}-\beta _{4}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
5776.2.a.bz	$5776$	$2$	5776.a	1.a	$1$	$6$	$6$	$46.122$	6.6.3022625.1	None	✓				2888.2.a.t	$1$	$0$	\(0\)	\(3\)	\(2\)	\(2\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
5776.2.a.ca	$5776$	$2$	5776.a	1.a	$1$	$8$	$8$	$46.122$	8.8.\(\cdots\).1	None	✓				2888.2.a.v	$1$	$1$	\(0\)	\(-6\)	\(-2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
5776.2.a.cb	$5776$	$2$	5776.a	1.a	$1$	$8$	$8$	$46.122$	8.8.\(\cdots\).1	None	✓		✓		1444.2.a.i	$2$	$0$	\(0\)	\(0\)	\(14\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{3}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots\)
5776.2.a.cc	$5776$	$2$	5776.a	1.a	$1$	$8$	$8$	$46.122$	8.8.\(\cdots\).1	None	✓				2888.2.a.v	$1$	$1$	\(0\)	\(6\)	\(-2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
5776.2.a.cd	$5776$	$2$	5776.a	1.a	$1$	$9$	$9$	$46.122$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		152.2.q.c	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-9\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
5776.2.a.ce	$5776$	$2$	5776.a	1.a	$1$	$9$	$9$	$46.122$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		152.2.q.c	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5776))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5776)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\)\(^{\oplus 2}\)