Space of modular forms of level 9310, weight 2, and trivial character

• Label: 9310.2.a
• Level: $9310$
• Weight: $2$
• Character orbit: 9310.a
• Rep. character: $\chi_{9310}(1,\cdot)$
• Character field: $\Q$
• Dimension: $246$
• Newform subspaces: $69$
• Sturm bound: $3360$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9310 = 2 \cdot 5 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9310.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 69 \)
Sturm bound:			\(3360\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9310))\).

	Total	New	Old
Modular forms	1712	246	1466
Cusp forms	1649	246	1403
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.

\(2\)	\(5\)	\(7\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(15\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(14\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(15\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(18\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(13\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(12\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(18\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(14\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(15\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(18\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(15\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(13\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(18\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(12\)
Plus space				\(+\)	\(116\)
Minus space				\(-\)	\(130\)

Trace form

\( 246 q + 246 q^{4} - 2 q^{5} - 4 q^{6} + 234 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9310))\) 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	5	7	19
9310.2.a.a	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{8}+\cdots\)
9310.2.a.b	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
9310.2.a.c	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
9310.2.a.d	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
9310.2.a.e	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
9310.2.a.f	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
9310.2.a.g	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
9310.2.a.h	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
9310.2.a.i	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
9310.2.a.j	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
9310.2.a.k	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
9310.2.a.l	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-q^{8}+\cdots\)
9310.2.a.m	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(-1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}-q^{8}+\cdots\)
9310.2.a.n	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
9310.2.a.o	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
9310.2.a.p	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
9310.2.a.q	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
9310.2.a.r	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
9310.2.a.s	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\)
9310.2.a.t	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\)
9310.2.a.u	$9310$	$2$	9310.a	1.a	$1$	$1$	$1$	$74.341$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}+q^{8}+\cdots\)
9310.2.a.v	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
9310.2.a.w	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
9310.2.a.x	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
9310.2.a.y	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
9310.2.a.z	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots\)
9310.2.a.ba	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots\)
9310.2.a.bb	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-2\)	\(1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
9310.2.a.bc	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-2\)	\(1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
9310.2.a.bd	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.be	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.bf	$9310$	$2$	9310.a	1.a	$1$	$2$	$2$	$74.341$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(2\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{8}+\cdots\)
9310.2.a.bg	$9310$	$2$	9310.a	1.a	$1$	$3$	$3$	$74.341$	3.3.321.1	None	✓	$1$	$1$	\(-3\)	\(-2\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
9310.2.a.bh	$9310$	$2$	9310.a	1.a	$1$	$3$	$3$	$74.341$	3.3.756.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9310.2.a.bi	$9310$	$2$	9310.a	1.a	$1$	$3$	$3$	$74.341$	3.3.756.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.bj	$9310$	$2$	9310.a	1.a	$1$	$3$	$3$	$74.341$	3.3.321.1	None	✓	$1$	$0$	\(-3\)	\(2\)	\(3\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.bk	$9310$	$2$	9310.a	1.a	$1$	$3$	$3$	$74.341$	3.3.148.1	None	✓	$1$	$1$	\(3\)	\(-4\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.bl	$9310$	$2$	9310.a	1.a	$1$	$3$	$3$	$74.341$	3.3.940.1	None	✓	$1$	$1$	\(3\)	\(-3\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.bm	$9310$	$2$	9310.a	1.a	$1$	$3$	$3$	$74.341$	3.3.148.1	None	✓	$1$	$1$	\(3\)	\(4\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
9310.2.a.bn	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.7053.1	None	✓	$1$	$0$	\(-4\)	\(-1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}+\beta _{2}q^{6}+\cdots\)
9310.2.a.bo	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.14013.1	None	✓	$1$	$0$	\(-4\)	\(-1\)	\(-4\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}+\beta _{2}q^{6}+\cdots\)
9310.2.a.bp	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.37773.1	None	✓	$1$	$0$	\(-4\)	\(-1\)	\(4\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9310.2.a.bq	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.37773.1	None	✓	$1$	$1$	\(-4\)	\(1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.br	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.7053.1	None	✓	$1$	$1$	\(-4\)	\(1\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots\)
9310.2.a.bs	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.14013.1	None	✓	$1$	$1$	\(-4\)	\(1\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots\)
9310.2.a.bt	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.44648.1	None	✓	$1$	$1$	\(4\)	\(-3\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.bu	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.1957.1	None	✓	$1$	$1$	\(4\)	\(-3\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.bv	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.118616.1	None	✓	$1$	$0$	\(4\)	\(-1\)	\(-4\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.bw	$9310$	$2$	9310.a	1.a	$1$	$4$	$4$	$74.341$	4.4.1957.1	None	✓	$1$	$0$	\(4\)	\(3\)	\(-4\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
9310.2.a.bx	$9310$	$2$	9310.a	1.a	$1$	$5$	$5$	$74.341$	5.5.5073748.1	None	✓	$1$	$0$	\(-5\)	\(-1\)	\(5\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9310.2.a.by	$9310$	$2$	9310.a	1.a	$1$	$5$	$5$	$74.341$	5.5.5073748.1	None	✓	$1$	$0$	\(-5\)	\(1\)	\(-5\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.bz	$9310$	$2$	9310.a	1.a	$1$	$5$	$5$	$74.341$	5.5.320837.1	None	✓	$1$	$1$	\(5\)	\(-4\)	\(5\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.ca	$9310$	$2$	9310.a	1.a	$1$	$5$	$5$	$74.341$	5.5.24266516.1	None	✓	$1$	$0$	\(5\)	\(-1\)	\(5\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.cb	$9310$	$2$	9310.a	1.a	$1$	$5$	$5$	$74.341$	5.5.24266516.1	None	✓	$1$	$0$	\(5\)	\(1\)	\(-5\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9310.2.a.cc	$9310$	$2$	9310.a	1.a	$1$	$5$	$5$	$74.341$	5.5.320837.1	None	✓	$1$	$0$	\(5\)	\(4\)	\(-5\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
9310.2.a.cd	$9310$	$2$	9310.a	1.a	$1$	$6$	$6$	$74.341$	6.6.14895104.1	None	✓	$1$	$1$	\(-6\)	\(-4\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
9310.2.a.ce	$9310$	$2$	9310.a	1.a	$1$	$6$	$6$	$74.341$	6.6.14895104.1	None	✓	$1$	$1$	\(-6\)	\(4\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.cf	$9310$	$2$	9310.a	1.a	$1$	$7$	$7$	$74.341$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(-1\)	\(-7\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9310.2.a.cg	$9310$	$2$	9310.a	1.a	$1$	$7$	$7$	$74.341$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-7\)	\(1\)	\(7\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.ch	$9310$	$2$	9310.a	1.a	$1$	$7$	$7$	$74.341$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(7\)	\(-5\)	\(-7\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.ci	$9310$	$2$	9310.a	1.a	$1$	$7$	$7$	$74.341$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(5\)	\(7\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
9310.2.a.cj	$9310$	$2$	9310.a	1.a	$1$	$8$	$8$	$74.341$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(8\)	\(-4\)	\(-8\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.ck	$9310$	$2$	9310.a	1.a	$1$	$8$	$8$	$74.341$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(8\)	\(-2\)	\(8\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.cl	$9310$	$2$	9310.a	1.a	$1$	$8$	$8$	$74.341$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(8\)	\(2\)	\(-8\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9310.2.a.cm	$9310$	$2$	9310.a	1.a	$1$	$8$	$8$	$74.341$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(4\)	\(8\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
9310.2.a.cn	$9310$	$2$	9310.a	1.a	$1$	$10$	$10$	$74.341$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-10\)	\(-6\)	\(10\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
9310.2.a.co	$9310$	$2$	9310.a	1.a	$1$	$10$	$10$	$74.341$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-10\)	\(6\)	\(-10\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9310.2.a.cp	$9310$	$2$	9310.a	1.a	$1$	$10$	$10$	$74.341$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(10\)	\(-2\)	\(-10\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9310.2.a.cq	$9310$	$2$	9310.a	1.a	$1$	$10$	$10$	$74.341$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(10\)	\(2\)	\(10\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9310))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9310)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(665))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4655))\)\(^{\oplus 2}\)