Space of modular forms of level 5166, weight 2, and trivial character

• Label: 5166.2.a
• Level: $5166$
• Weight: $2$
• Character orbit: 5166.a
• Rep. character: $\chi_{5166}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $55$
• Sturm bound: $2016$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5166.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 55 \)
Sturm bound:			\(2016\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5166))\).

	Total	New	Old
Modular forms	1024	100	924
Cusp forms	993	100	893
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(7\)	\(41\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(7\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(9\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(6\)
Plus space				\(+\)	\(38\)
Minus space				\(-\)	\(62\)

Trace form

\( 100 q + 100 q^{4} - 8 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5166))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	7	41
5166.2.a.a	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots\)
5166.2.a.b	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots\)
5166.2.a.c	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
5166.2.a.d	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
5166.2.a.e	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
5166.2.a.f	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
5166.2.a.g	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
5166.2.a.h	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
5166.2.a.i	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots\)
5166.2.a.j	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-4q^{13}+\cdots\)
5166.2.a.k	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.l	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.m	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.n	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.o	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
5166.2.a.p	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
5166.2.a.q	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
5166.2.a.r	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
5166.2.a.s	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
5166.2.a.t	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots\)
5166.2.a.u	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots\)
5166.2.a.v	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots\)
5166.2.a.w	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
5166.2.a.x	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
5166.2.a.y	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
5166.2.a.z	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
5166.2.a.ba	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bb	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bc	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bd	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.be	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
5166.2.a.bf	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{11}+4q^{13}+\cdots\)
5166.2.a.bg	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
5166.2.a.bh	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
5166.2.a.bi	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
5166.2.a.bj	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
5166.2.a.bk	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
5166.2.a.bl	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots\)
5166.2.a.bm	$5166$	$2$	5166.a	1.a	$1$	$1$	$1$	$41.251$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
5166.2.a.bn	$5166$	$2$	5166.a	1.a	$1$	$2$	$2$	$41.251$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.bo	$5166$	$2$	5166.a	1.a	$1$	$2$	$2$	$41.251$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.bp	$5166$	$2$	5166.a	1.a	$1$	$2$	$2$	$41.251$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
5166.2.a.bq	$5166$	$2$	5166.a	1.a	$1$	$2$	$2$	$41.251$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
5166.2.a.br	$5166$	$2$	5166.a	1.a	$1$	$2$	$2$	$41.251$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
5166.2.a.bs	$5166$	$2$	5166.a	1.a	$1$	$2$	$2$	$41.251$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
5166.2.a.bt	$5166$	$2$	5166.a	1.a	$1$	$3$	$3$	$41.251$	3.3.568.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{1}q^{5}-q^{7}-q^{8}+\beta _{1}q^{10}+\cdots\)
5166.2.a.bu	$5166$	$2$	5166.a	1.a	$1$	$3$	$3$	$41.251$	3.3.940.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}-q^{7}+q^{8}+\cdots\)
5166.2.a.bv	$5166$	$2$	5166.a	1.a	$1$	$3$	$3$	$41.251$	3.3.316.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots\)
5166.2.a.bw	$5166$	$2$	5166.a	1.a	$1$	$3$	$3$	$41.251$	3.3.940.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta _{1})q^{5}+q^{7}+q^{8}+\cdots\)
5166.2.a.bx	$5166$	$2$	5166.a	1.a	$1$	$4$	$4$	$41.251$	4.4.11348.1	None	✓	$1$	$1$	\(4\)	\(0\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
5166.2.a.by	$5166$	$2$	5166.a	1.a	$1$	$5$	$5$	$41.251$	5.5.2620729.1	None	✓	$1$	$0$	\(-5\)	\(0\)	\(-4\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.bz	$5166$	$2$	5166.a	1.a	$1$	$7$	$7$	$41.251$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-7\)	\(0\)	\(-4\)	\(7\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+q^{7}-q^{8}+\cdots\)
5166.2.a.ca	$5166$	$2$	5166.a	1.a	$1$	$7$	$7$	$41.251$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-7\)	\(0\)	\(2\)	\(-7\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{7}-q^{8}-\beta _{1}q^{10}+\cdots\)
5166.2.a.cb	$5166$	$2$	5166.a	1.a	$1$	$7$	$7$	$41.251$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(0\)	\(-2\)	\(-7\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}-q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\)
5166.2.a.cc	$5166$	$2$	5166.a	1.a	$1$	$7$	$7$	$41.251$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(0\)	\(4\)	\(7\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5166))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(738))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(861))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2583))\)\(^{\oplus 2}\)