Space of modular forms of level 9126, weight 2, and trivial character

• Label: 9126.2.a
• Level: $9126$
• Weight: $2$
• Character orbit: 9126.a
• Rep. character: $\chi_{9126}(1,\cdot)$
• Character field: $\Q$
• Dimension: $206$
• Newform subspaces: $80$
• Sturm bound: $3276$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9126 = 2 \cdot 3^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9126.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 80 \)
Sturm bound:			\(3276\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9126))\).

	Total	New	Old
Modular forms	1722	206	1516
Cusp forms	1555	206	1349
Eisenstein series	167	0	167

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

\(2\)	\(3\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(23\)
\(+\)	\(+\)	\(-\)	$-$	\(28\)
\(+\)	\(-\)	\(+\)	$-$	\(28\)
\(+\)	\(-\)	\(-\)	$+$	\(24\)
\(-\)	\(+\)	\(+\)	$-$	\(30\)
\(-\)	\(+\)	\(-\)	$+$	\(22\)
\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(-\)	\(-\)	$-$	\(30\)
Plus space			\(+\)	\(90\)
Minus space			\(-\)	\(116\)

Trace form

\( 206 q + 206 q^{4} + 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9126))\) 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	13
9126.2.a.a	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
9126.2.a.b	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-4q^{7}-q^{8}+2q^{10}+\cdots\)
9126.2.a.c	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-4q^{7}-q^{8}+2q^{10}+\cdots\)
9126.2.a.d	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots\)
9126.2.a.e	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
9126.2.a.f	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots\)
9126.2.a.g	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots\)
9126.2.a.h	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{7}-q^{8}+3q^{11}+3q^{14}+\cdots\)
9126.2.a.i	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{11}+2q^{14}+\cdots\)
9126.2.a.j	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-6q^{11}+q^{16}-6q^{17}+\cdots\)
9126.2.a.k	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-6q^{11}+q^{16}+6q^{17}+\cdots\)
9126.2.a.l	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}-q^{14}+\cdots\)
9126.2.a.m	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}-3q^{11}-2q^{14}+\cdots\)
9126.2.a.n	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{7}-q^{8}+3q^{11}-3q^{14}+\cdots\)
9126.2.a.o	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+5q^{7}-q^{8}-q^{10}+\cdots\)
9126.2.a.p	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-4q^{7}-q^{8}-2q^{10}+\cdots\)
9126.2.a.q	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+5q^{7}-q^{8}-2q^{10}+\cdots\)
9126.2.a.r	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
9126.2.a.s	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
9126.2.a.t	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
9126.2.a.u	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
9126.2.a.v	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-2q^{10}+\cdots\)
9126.2.a.w	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+5q^{7}+q^{8}-2q^{10}+\cdots\)
9126.2.a.x	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+5q^{7}+q^{8}-q^{10}+\cdots\)
9126.2.a.y	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{7}+q^{8}-3q^{11}-3q^{14}+\cdots\)
9126.2.a.z	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+3q^{11}-2q^{14}+\cdots\)
9126.2.a.ba	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+6q^{11}+q^{16}-6q^{17}+\cdots\)
9126.2.a.bb	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+6q^{11}+q^{16}+6q^{17}+\cdots\)
9126.2.a.bc	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+3q^{11}+q^{14}+\cdots\)
9126.2.a.bd	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}+2q^{14}+\cdots\)
9126.2.a.be	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{7}+q^{8}-3q^{11}+3q^{14}+\cdots\)
9126.2.a.bf	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-4q^{7}+q^{8}+2q^{10}+\cdots\)
9126.2.a.bg	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-4q^{7}+q^{8}+2q^{10}+\cdots\)
9126.2.a.bh	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots\)
9126.2.a.bi	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
9126.2.a.bj	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots\)
9126.2.a.bk	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots\)
9126.2.a.bl	$9126$	$2$	9126.a	1.a	$1$	$1$	$1$	$72.871$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
9126.2.a.bm	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{13}) \)	None	✓	$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+\beta q^{7}-q^{8}+2q^{10}+\cdots\)
9126.2.a.bn	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
9126.2.a.bo	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
9126.2.a.bp	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots\)
9126.2.a.bq	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\)
9126.2.a.br	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-2q^{7}-q^{8}-\beta q^{10}+\cdots\)
9126.2.a.bs	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots\)
9126.2.a.bt	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots\)
9126.2.a.bu	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\)
9126.2.a.bv	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta q^{5}+(-1-\beta )q^{7}+q^{8}+\cdots\)
9126.2.a.bw	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
9126.2.a.bx	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}-2q^{7}+q^{8}+\beta q^{10}+\cdots\)
9126.2.a.by	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots\)
9126.2.a.bz	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+(-1-\beta )q^{7}+q^{8}+\cdots\)
9126.2.a.ca	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
9126.2.a.cb	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
9126.2.a.cc	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
9126.2.a.cd	$9126$	$2$	9126.a	1.a	$1$	$2$	$2$	$72.871$	\(\Q(\sqrt{13}) \)	None	✓	$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+\beta q^{7}+q^{8}+2q^{10}+\cdots\)
9126.2.a.ce	$9126$	$2$	9126.a	1.a	$1$	$3$	$3$	$72.871$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9126.2.a.cf	$9126$	$2$	9126.a	1.a	$1$	$3$	$3$	$72.871$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9126.2.a.cg	$9126$	$2$	9126.a	1.a	$1$	$3$	$3$	$72.871$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9126.2.a.ch	$9126$	$2$	9126.a	1.a	$1$	$3$	$3$	$72.871$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9126.2.a.ci	$9126$	$2$	9126.a	1.a	$1$	$4$	$4$	$72.871$	4.4.21312.1	None	✓	$1$	$1$	\(-4\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
9126.2.a.cj	$9126$	$2$	9126.a	1.a	$1$	$4$	$4$	$72.871$	4.4.21312.1	None	✓	$1$	$0$	\(-4\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}-q^{8}+\cdots\)
9126.2.a.ck	$9126$	$2$	9126.a	1.a	$1$	$4$	$4$	$72.871$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	$2$	$0$	\(-4\)	\(0\)	\(6\)	\(0\)		$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(2+\beta _{2})q^{5}-\beta _{3}q^{7}-q^{8}+\cdots\)
9126.2.a.cl	$9126$	$2$	9126.a	1.a	$1$	$4$	$4$	$72.871$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	$2$	$1$	\(4\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-2-\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots\)
9126.2.a.cm	$9126$	$2$	9126.a	1.a	$1$	$4$	$4$	$72.871$	4.4.21312.1	None	✓	$1$	$1$	\(4\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
9126.2.a.cn	$9126$	$2$	9126.a	1.a	$1$	$4$	$4$	$72.871$	4.4.21312.1	None	✓	$1$	$0$	\(4\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{3})q^{7}+q^{8}+\cdots\)
9126.2.a.co	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.11498389.1	None	✓	$1$	$0$	\(-6\)	\(0\)	\(-2\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta _{2}+\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots\)
9126.2.a.cp	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.2041751232.1	None	✓	$2$	$1$	\(-6\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{7}-q^{8}+\cdots\)
9126.2.a.cq	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.11498389.1	None	✓	$1$	$1$	\(-6\)	\(0\)	\(-2\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta _{2}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots\)
9126.2.a.cr	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.2624293.1	None	✓	$1$	$0$	\(-6\)	\(0\)	\(0\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
9126.2.a.cs	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.2624293.1	None	✓	$1$	$1$	\(-6\)	\(0\)	\(0\)	\(5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
9126.2.a.ct	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.2624293.1	None	✓	$1$	$1$	\(6\)	\(0\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
9126.2.a.cu	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.2624293.1	None	✓	$1$	$0$	\(6\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
9126.2.a.cv	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.11498389.1	None	✓	$1$	$1$	\(6\)	\(0\)	\(2\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta _{2}-\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots\)
9126.2.a.cw	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.2041751232.1	None	✓	$2$	$0$	\(6\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}+q^{8}+\cdots\)
9126.2.a.cx	$9126$	$2$	9126.a	1.a	$1$	$6$	$6$	$72.871$	6.6.11498389.1	None	✓	$1$	$0$	\(6\)	\(0\)	\(2\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta _{2}-\beta _{4})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
9126.2.a.cy	$9126$	$2$	9126.a	1.a	$1$	$9$	$9$	$72.871$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(-9\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{5}q^{7}-q^{8}+\cdots\)
9126.2.a.cz	$9126$	$2$	9126.a	1.a	$1$	$9$	$9$	$72.871$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(-9\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+\beta _{5}q^{7}-q^{8}+\cdots\)
9126.2.a.da	$9126$	$2$	9126.a	1.a	$1$	$9$	$9$	$72.871$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(9\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{5}q^{7}+q^{8}+\cdots\)
9126.2.a.db	$9126$	$2$	9126.a	1.a	$1$	$9$	$9$	$72.871$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(9\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{5}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9126))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9126)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(702))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1521))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3042))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4563))\)\(^{\oplus 2}\)