Space of modular forms of level 5808, weight 2, and trivial character

• Label: 5808.2.a
• Level: $5808$
• Weight: $2$
• Character orbit: 5808.a
• Rep. character: $\chi_{5808}(1,\cdot)$
• Character field: $\Q$
• Dimension: $109$
• Newform subspaces: $67$
• Sturm bound: $2112$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5808 = 2^{4} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5808.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 67 \)
Sturm bound:			\(2112\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5808))\).

	Total	New	Old
Modular forms	1128	109	1019
Cusp forms	985	109	876
Eisenstein series	143	0	143

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

\(2\)	\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(138\)	\(12\)	\(126\)		\(121\)	\(12\)	\(109\)		\(17\)	\(0\)	\(17\)
\(+\)	\(+\)	\(-\)	\(-\)		\(144\)	\(15\)	\(129\)		\(126\)	\(15\)	\(111\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)		\(144\)	\(18\)	\(126\)		\(126\)	\(18\)	\(108\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(-\)	\(+\)		\(138\)	\(10\)	\(128\)		\(120\)	\(10\)	\(110\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)		\(144\)	\(12\)	\(132\)		\(126\)	\(12\)	\(114\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)	\(+\)		\(138\)	\(15\)	\(123\)		\(120\)	\(15\)	\(105\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)	\(+\)		\(138\)	\(12\)	\(126\)		\(120\)	\(12\)	\(108\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)		\(144\)	\(15\)	\(129\)		\(126\)	\(15\)	\(111\)		\(18\)	\(0\)	\(18\)
Plus space			\(+\)		\(552\)	\(49\)	\(503\)		\(481\)	\(49\)	\(432\)		\(71\)	\(0\)	\(71\)
Minus space			\(-\)		\(576\)	\(60\)	\(516\)		\(504\)	\(60\)	\(444\)		\(72\)	\(0\)	\(72\)

Trace form

109 * q + q^3 - 2 * q^5 + 4 * q^7 + 109 * q^9 - 2 * q^13 - 2 * q^15 + 2 * q^17 - 8 * q^19 - 8 * q^23 + 115 * q^25 + q^27 - 10 * q^29 - 8 * q^31 - 24 * q^35 - 10 * q^37 + 6 * q^39 + 10 * q^41 + 8 * q^43 - 2 * q^45 - 24 * q^47 + 125 * q^49 - 10 * q^51 - 2 * q^53 + 4 * q^57 + 4 * q^59 + 14 * q^61 + 4 * q^63 + 20 * q^65 - 12 * q^67 + 8 * q^69 + 32 * q^71 + 18 * q^73 + 15 * q^75 + 12 * q^79 + 109 * q^81 + 20 * q^83 + 12 * q^85 - 6 * q^87 + 26 * q^89 + 56 * q^91 + 8 * q^93 + 32 * q^95 + 10 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5808))\) 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	3	11
5808.2.a.a	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				1452.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-5q^{7}+q^{9}+2q^{13}+\cdots\)
5808.2.a.b	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				66.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-2q^{7}+q^{9}-4q^{13}+\cdots\)
5808.2.a.c	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				1452.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+5q^{7}+q^{9}-2q^{13}+\cdots\)
5808.2.a.d	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{13}+\cdots\)
5808.2.a.e	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{13}+\cdots\)
5808.2.a.f	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				264.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+4q^{7}+q^{9}-6q^{13}+\cdots\)
5808.2.a.g	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				726.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}-5q^{13}+q^{15}+\cdots\)
5808.2.a.h	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				726.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}+5q^{13}+q^{15}+\cdots\)
5808.2.a.i	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.m	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-6q^{13}-4q^{17}+\cdots\)
5808.2.a.j	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.m	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+6q^{13}+4q^{17}+\cdots\)
5808.2.a.k	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				264.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+2q^{17}+8q^{19}+\cdots\)
5808.2.a.l	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				66.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
5808.2.a.m	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				132.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
5808.2.a.n	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				1452.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{7}+q^{9}+5q^{13}+\cdots\)
5808.2.a.o	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				1452.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+2q^{7}+q^{9}-5q^{13}+\cdots\)
5808.2.a.p	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				264.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{7}+q^{9}-4q^{15}+\cdots\)
5808.2.a.q	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.a	$1$	$2$	\(0\)	\(1\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-4q^{7}+q^{9}-6q^{13}+\cdots\)
5808.2.a.r	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+4q^{7}+q^{9}+6q^{13}+\cdots\)
5808.2.a.s	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				24.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
5808.2.a.t	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				33.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots\)
5808.2.a.u	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				726.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}+q^{9}-3q^{13}-q^{15}+\cdots\)
5808.2.a.v	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				1452.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}-3q^{13}-q^{15}+\cdots\)
5808.2.a.w	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}+3q^{17}+\cdots\)
5808.2.a.x	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+q^{13}-q^{15}-3q^{17}+\cdots\)
5808.2.a.y	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				1452.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+3q^{13}-q^{15}+\cdots\)
5808.2.a.z	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				726.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}+q^{9}+3q^{13}-q^{15}+\cdots\)
5808.2.a.ba	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				726.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-6q^{13}+6q^{17}+6q^{19}+\cdots\)
5808.2.a.bb	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				726.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+6q^{13}-6q^{17}-6q^{19}+\cdots\)
5808.2.a.bc	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				66.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}+6q^{13}+\cdots\)
5808.2.a.bd	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.f	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{15}+\cdots\)
5808.2.a.be	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				264.2.a.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
5808.2.a.bf	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				132.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
5808.2.a.bg	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				2904.2.a.f	$1$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{15}+\cdots\)
5808.2.a.bh	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				363.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-q^{7}+q^{9}-2q^{13}+4q^{15}+\cdots\)
5808.2.a.bi	$5808$	$2$	5808.a	1.a	$1$	$1$	$1$	$46.377$	\(\Q\)	None	✓				363.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{7}+q^{9}+2q^{13}+4q^{15}+\cdots\)
5808.2.a.bj	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.c	$1$	$1$	\(0\)	\(-2\)	\(-5\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta )q^{5}+(-3+2\beta )q^{7}+\cdots\)
5808.2.a.bk	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.c	$1$	$0$	\(0\)	\(-2\)	\(-5\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.bl	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.a	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}-3q^{7}+q^{9}+(5+\cdots)q^{13}+\cdots\)
5808.2.a.bm	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.a	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+3q^{7}+q^{9}+(-5+\cdots)q^{13}+\cdots\)
5808.2.a.bn	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				132.2.i.a	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(-3+2\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.bo	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{33}) \)	None	✓				2904.2.a.t	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(-1+\beta )q^{7}+q^{9}+(2+\cdots)q^{13}+\cdots\)
5808.2.a.bp	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{33}) \)	None	✓				2904.2.a.t	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(1-\beta )q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
5808.2.a.bq	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				132.2.i.a	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(3-2\beta )q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots\)
5808.2.a.br	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.a	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+3\beta )q^{5}-3\beta q^{7}+q^{9}+\cdots\)
5808.2.a.bs	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.a	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+3\beta )q^{5}+3\beta q^{7}+q^{9}+\cdots\)
5808.2.a.bt	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{3}) \)	None	✓				2904.2.a.x	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+(2+\beta )q^{13}+\cdots\)
5808.2.a.bu	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{3}) \)	None	✓				2904.2.a.x	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{13}+\cdots\)
5808.2.a.bv	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.b	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(-3+2\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.bw	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.b	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.bx	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				363.2.a.g	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-\beta q^{7}+q^{9}-2q^{15}+\cdots\)
5808.2.a.by	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				66.2.e.b	$1$	$1$	\(0\)	\(-2\)	\(5\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(3-\beta )q^{5}-\beta q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
5808.2.a.bz	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				66.2.e.b	$1$	$0$	\(0\)	\(-2\)	\(5\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(3-\beta )q^{5}+\beta q^{7}+q^{9}+(2-2\beta )q^{13}+\cdots\)
5808.2.a.ca	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{3}) \)	None	✓				363.2.a.f	$2$	$1$	\(0\)	\(2\)	\(-6\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+2\beta q^{7}+q^{9}-\beta q^{13}+\cdots\)
5808.2.a.cb	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				66.2.e.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-3\beta )q^{5}+(-4+\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.cc	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				132.2.i.b	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-3\beta )q^{5}+(-3+2\beta )q^{7}+\cdots\)
5808.2.a.cd	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.d	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(-1+2\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.ce	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				264.2.q.d	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(1-2\beta )q^{7}+q^{9}+(3+\cdots)q^{13}+\cdots\)
5808.2.a.cf	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				132.2.i.b	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-3\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.cg	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				66.2.e.a	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-3\beta )q^{5}+(4-\beta )q^{7}+q^{9}+\cdots\)
5808.2.a.ch	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{3}) \)	None	✓				1452.2.a.k	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{7}+q^{9}+\beta q^{19}-\beta q^{21}+\cdots\)
5808.2.a.ci	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.b	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(1+2\beta )q^{13}+\cdots\)
5808.2.a.cj	$5808$	$2$	5808.a	1.a	$1$	$2$	$2$	$46.377$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.b	$1$	$1$	\(0\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(-1-2\beta )q^{13}+\cdots\)
5808.2.a.ck	$5808$	$2$	5808.a	1.a	$1$	$4$	$4$	$46.377$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓		✓		363.2.a.j	$2$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+q^{9}+(3\beta _{1}+\cdots)q^{13}+\cdots\)
5808.2.a.cl	$5808$	$2$	5808.a	1.a	$1$	$4$	$4$	$46.377$	4.4.13625.1	None	✓		✓		264.2.q.e	$1$	$1$	\(0\)	\(4\)	\(2\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(-2+\beta _{2}-2\beta _{3})q^{7}+\cdots\)
5808.2.a.cm	$5808$	$2$	5808.a	1.a	$1$	$4$	$4$	$46.377$	4.4.46224.1	None	✓				2904.2.a.bc	$1$	$0$	\(0\)	\(4\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
5808.2.a.cn	$5808$	$2$	5808.a	1.a	$1$	$4$	$4$	$46.377$	4.4.46224.1	None	✓				2904.2.a.bc	$1$	$0$	\(0\)	\(4\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
5808.2.a.co	$5808$	$2$	5808.a	1.a	$1$	$4$	$4$	$46.377$	4.4.13625.1	None	✓				264.2.q.e	$1$	$0$	\(0\)	\(4\)	\(2\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(2-\beta _{2}+2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5808))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5808)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2904))\)\(^{\oplus 2}\)