Space of modular forms of level 9386, weight 2, and trivial character

• Label: 9386.2.a
• Level: $9386$
• Weight: $2$
• Character orbit: 9386.a
• Rep. character: $\chi_{9386}(1,\cdot)$
• Character field: $\Q$
• Dimension: $341$
• Newform subspaces: $56$
• Sturm bound: $2660$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 9386 = 2 \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9386.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(2660\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9386))\).

	Total	New	Old
Modular forms	1370	341	1029
Cusp forms	1291	341	950
Eisenstein series	79	0	79

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

\(2\)	\(13\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(160\)	\(39\)	\(121\)		\(151\)	\(39\)	\(112\)		\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)		\(182\)	\(45\)	\(137\)		\(172\)	\(45\)	\(127\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)		\(180\)	\(50\)	\(130\)		\(170\)	\(50\)	\(120\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)		\(163\)	\(36\)	\(127\)		\(153\)	\(36\)	\(117\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)		\(175\)	\(50\)	\(125\)		\(165\)	\(50\)	\(115\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(-\)	\(+\)		\(167\)	\(36\)	\(131\)		\(157\)	\(36\)	\(121\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)		\(165\)	\(31\)	\(134\)		\(155\)	\(31\)	\(124\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)		\(178\)	\(54\)	\(124\)		\(168\)	\(54\)	\(114\)		\(10\)	\(0\)	\(10\)
Plus space			\(+\)		\(655\)	\(142\)	\(513\)		\(616\)	\(142\)	\(474\)		\(39\)	\(0\)	\(39\)
Minus space			\(-\)		\(715\)	\(199\)	\(516\)		\(675\)	\(199\)	\(476\)		\(40\)	\(0\)	\(40\)

Trace form

341 * q + q^2 - 2 * q^3 + 341 * q^4 - 2 * q^5 - 4 * q^6 + q^8 + 335 * q^9 - 4 * q^10 + 4 * q^11 - 2 * q^12 + q^13 - 2 * q^14 + 341 * q^16 + 24 * q^17 + 5 * q^18 - 2 * q^20 - 4 * q^21 + 12 * q^22 - 4 * q^23 - 4 * q^24 + 341 * q^25 - 3 * q^26 - 14 * q^27 - 2 * q^29 - 2 * q^30 - 32 * q^31 + q^32 - 20 * q^33 + 18 * q^34 + 18 * q^35 + 335 * q^36 + 2 * q^37 - 4 * q^40 - 14 * q^41 + 14 * q^42 + 26 * q^43 + 4 * q^44 + 18 * q^45 + 4 * q^46 - 2 * q^48 + 331 * q^49 + 39 * q^50 - 2 * q^51 + q^52 + 10 * q^53 - 4 * q^54 + 8 * q^55 - 2 * q^56 - 2 * q^58 + 28 * q^59 - 2 * q^61 + 4 * q^62 + 40 * q^63 + 341 * q^64 + 8 * q^65 + 48 * q^66 - 8 * q^67 + 24 * q^68 - 12 * q^69 - 12 * q^70 + 16 * q^71 + 5 * q^72 + 2 * q^73 + 4 * q^74 + 8 * q^75 + 48 * q^77 + 2 * q^78 - 20 * q^79 - 2 * q^80 + 357 * q^81 + 26 * q^82 + 44 * q^83 - 4 * q^84 + 40 * q^85 + 24 * q^86 + 56 * q^87 + 12 * q^88 - 6 * q^89 + 46 * q^90 - 6 * q^91 - 4 * q^92 + 64 * q^93 - 26 * q^94 - 4 * q^96 + 22 * q^97 + 41 * q^98 + 104 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9386))\) 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	13	19
9386.2.a.a	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.d	$1$	$1$	\(-1\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots\)
9386.2.a.b	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.c	$1$	$1$	\(-1\)	\(-1\)	\(4\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+2q^{7}+\cdots\)
9386.2.a.c	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.a.d	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
9386.2.a.d	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.b	$1$	$1$	\(-1\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots\)
9386.2.a.e	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.a	$1$	$1$	\(-1\)	\(3\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-4q^{5}-3q^{6}-2q^{7}+\cdots\)
9386.2.a.f	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				26.2.a.b	$1$	$1$	\(-1\)	\(3\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
9386.2.a.g	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.a	$1$	$2$	\(1\)	\(-3\)	\(-4\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-4q^{5}-3q^{6}-2q^{7}+\cdots\)
9386.2.a.h	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.a.c	$1$	$0$	\(1\)	\(-3\)	\(-3\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-3q^{5}-3q^{6}+3q^{7}+\cdots\)
9386.2.a.i	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.b	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
9386.2.a.j	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				26.2.a.a	$1$	$1$	\(1\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
9386.2.a.k	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.a.b	$1$	$0$	\(1\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots\)
9386.2.a.l	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.a.a	$1$	$0$	\(1\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
9386.2.a.m	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.c	$1$	$0$	\(1\)	\(1\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+2q^{7}+\cdots\)
9386.2.a.n	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	\(\Q\)	None	✓				494.2.f.d	$1$	$0$	\(1\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
9386.2.a.o	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	\(\Q(\sqrt{6}) \)	None	✓				494.2.f.g	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}+2\beta q^{7}+\cdots\)
9386.2.a.p	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	\(\Q(\sqrt{3}) \)	None	✓				494.2.f.e	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
9386.2.a.q	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	\(\Q(\sqrt{6}) \)	None	✓				494.2.f.f	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+2q^{7}+\cdots\)
9386.2.a.r	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	\(\Q(\sqrt{6}) \)	None	✓				494.2.f.f	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+2q^{7}+\cdots\)
9386.2.a.s	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	\(\Q(\sqrt{3}) \)	None	✓				494.2.f.e	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}+\beta q^{6}+\cdots\)
9386.2.a.t	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	\(\Q(\sqrt{6}) \)	None	✓				494.2.f.g	$1$	$0$	\(2\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+2\beta q^{7}+\cdots\)
9386.2.a.u	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	\(\Q(\zeta_{14})^+\)	None	✓				494.2.a.g	$1$	$1$	\(-3\)	\(-5\)	\(5\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-2-\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
9386.2.a.v	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.316.1	None	✓				494.2.f.h	$1$	$1$	\(-3\)	\(-2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
9386.2.a.w	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.148.1	None	✓				494.2.f.i	$1$	$0$	\(-3\)	\(-1\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
9386.2.a.x	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	\(\Q(\zeta_{18})^+\)	None	✓				494.2.x.a	$1$	$0$	\(-3\)	\(0\)	\(-6\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
9386.2.a.y	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	\(\Q(\zeta_{18})^+\)	None	✓	✓			9386.2.a.y	$1$	$1$	\(-3\)	\(3\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
9386.2.a.z	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	\(\Q(\zeta_{18})^+\)	None	✓	✓			9386.2.a.y	$1$	$1$	\(3\)	\(-3\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
9386.2.a.ba	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	\(\Q(\zeta_{18})^+\)	None	✓				494.2.x.a	$1$	$1$	\(3\)	\(0\)	\(-6\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
9386.2.a.bb	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.148.1	None	✓				494.2.f.i	$1$	$1$	\(3\)	\(1\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
9386.2.a.bc	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.361.1	None	✓				494.2.a.f	$1$	$1$	\(3\)	\(1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots\)
9386.2.a.bd	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.316.1	None	✓				494.2.f.h	$1$	$0$	\(3\)	\(2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
9386.2.a.be	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	\(\Q(\zeta_{18})^+\)	None	✓				494.2.a.e	$1$	$0$	\(3\)	\(3\)	\(3\)	\(-6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+2\beta _{1}-\beta _{2})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots\)
9386.2.a.bf	$9386$	$2$	9386.a	1.a	$1$	$4$	$4$	$74.948$	4.4.16609.1	None	✓				494.2.a.h	$1$	$0$	\(-4\)	\(-2\)	\(2\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
9386.2.a.bg	$9386$	$2$	9386.a	1.a	$1$	$4$	$4$	$74.948$	4.4.11344.1	None	✓				494.2.f.j	$1$	$0$	\(-4\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{2}q^{6}+\cdots\)
9386.2.a.bh	$9386$	$2$	9386.a	1.a	$1$	$4$	$4$	$74.948$	4.4.11344.1	None	✓				494.2.f.j	$1$	$1$	\(4\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{2}q^{6}+\cdots\)
9386.2.a.bi	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.980125.1	None	✓	✓			9386.2.a.bi	$1$	$1$	\(-6\)	\(-2\)	\(2\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
9386.2.a.bj	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.2235125.1	None	✓	✓			9386.2.a.bj	$1$	$1$	\(-6\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
9386.2.a.bk	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.784399964.1	None	✓	✓			9386.2.a.bk	$1$	$0$	\(-6\)	\(3\)	\(-1\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
9386.2.a.bl	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.784399964.1	None	✓	✓			9386.2.a.bk	$1$	$0$	\(6\)	\(-3\)	\(-1\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
9386.2.a.bm	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.2235125.1	None	✓	✓			9386.2.a.bj	$1$	$1$	\(6\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
9386.2.a.bn	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.980125.1	None	✓	✓			9386.2.a.bi	$1$	$1$	\(6\)	\(2\)	\(2\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1}+\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
9386.2.a.bo	$9386$	$2$	9386.a	1.a	$1$	$9$	$9$	$74.948$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				494.2.x.b	$1$	$0$	\(-9\)	\(3\)	\(-3\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
9386.2.a.bp	$9386$	$2$	9386.a	1.a	$1$	$9$	$9$	$74.948$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				494.2.x.b	$1$	$1$	\(9\)	\(-3\)	\(-3\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
9386.2.a.bq	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9386.2.a.bq	$1$	$0$	\(-12\)	\(-2\)	\(6\)	\(10\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{7})q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.br	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9386.2.a.br	$1$	$0$	\(-12\)	\(0\)	\(4\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.bs	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9386.2.a.bs	$1$	$1$	\(-12\)	\(2\)	\(-2\)	\(-10\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
9386.2.a.bt	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		9386.2.a.bs	$1$	$1$	\(12\)	\(-2\)	\(-2\)	\(-10\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
9386.2.a.bu	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9386.2.a.br	$1$	$0$	\(12\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.bv	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			9386.2.a.bq	$1$	$0$	\(12\)	\(2\)	\(6\)	\(10\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{7})q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.bw	$9386$	$2$	9386.a	1.a	$1$	$15$	$15$	$74.948$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		494.2.x.d	$1$	$1$	\(-15\)	\(-3\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.bx	$9386$	$2$	9386.a	1.a	$1$	$15$	$15$	$74.948$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				494.2.x.c	$1$	$0$	\(-15\)	\(3\)	\(-9\)	\(-9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
9386.2.a.by	$9386$	$2$	9386.a	1.a	$1$	$15$	$15$	$74.948$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		494.2.x.c	$1$	$1$	\(15\)	\(-3\)	\(-9\)	\(-9\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
9386.2.a.bz	$9386$	$2$	9386.a	1.a	$1$	$15$	$15$	$74.948$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓				494.2.x.d	$1$	$0$	\(15\)	\(3\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.ca	$9386$	$2$	9386.a	1.a	$1$	$18$	$18$	$74.948$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		494.2.x.e	$1$	$1$	\(-18\)	\(-3\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.cb	$9386$	$2$	9386.a	1.a	$1$	$18$	$18$	$74.948$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		494.2.x.e	$1$	$0$	\(18\)	\(3\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
9386.2.a.cc	$9386$	$2$	9386.a	1.a	$1$	$24$	$24$	$74.948$		None	✓	✓	✓		9386.2.a.cc	$1$	$0$	\(-24\)	\(2\)	\(6\)	\(14\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
9386.2.a.cd	$9386$	$2$	9386.a	1.a	$1$	$24$	$24$	$74.948$		None	✓	✓	✓		9386.2.a.cc	$1$	$0$	\(24\)	\(-2\)	\(6\)	\(14\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9386))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9386)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(494))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4693))\)\(^{\oplus 2}\)