Space of modular forms of level 39326, weight 2, and trivial character

• Label: 39326.2.a
• Level: $39326$
• Weight: $2$
• Character orbit: 39326.a
• Rep. character: $\chi_{39326}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1378$
• Newform subspaces: $68$
• Sturm bound: $11448$

Defining parameters

Level:	\( N \)	\(=\)	\( 39326 = 2 \cdot 7 \cdot 53^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	39326.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 68 \)
Sturm bound:			\(11448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(39326))\).

	Total	New	Old
Modular forms	5832	1378	4454
Cusp forms	5617	1378	4239
Eisenstein series	215	0	215

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

\(2\)	\(7\)	\(53\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(702\)	\(162\)	\(540\)		\(676\)	\(162\)	\(514\)		\(26\)	\(0\)	\(26\)
\(+\)	\(+\)	\(-\)	\(-\)		\(755\)	\(182\)	\(573\)		\(728\)	\(182\)	\(546\)		\(27\)	\(0\)	\(27\)
\(+\)	\(-\)	\(+\)	\(-\)		\(756\)	\(189\)	\(567\)		\(729\)	\(189\)	\(540\)		\(27\)	\(0\)	\(27\)
\(+\)	\(-\)	\(-\)	\(+\)		\(703\)	\(156\)	\(547\)		\(676\)	\(156\)	\(520\)		\(27\)	\(0\)	\(27\)
\(-\)	\(+\)	\(+\)	\(-\)		\(729\)	\(176\)	\(553\)		\(702\)	\(176\)	\(526\)		\(27\)	\(0\)	\(27\)
\(-\)	\(+\)	\(-\)	\(+\)		\(728\)	\(169\)	\(559\)		\(701\)	\(169\)	\(532\)		\(27\)	\(0\)	\(27\)
\(-\)	\(-\)	\(+\)	\(+\)		\(729\)	\(149\)	\(580\)		\(702\)	\(149\)	\(553\)		\(27\)	\(0\)	\(27\)
\(-\)	\(-\)	\(-\)	\(-\)		\(730\)	\(195\)	\(535\)		\(703\)	\(195\)	\(508\)		\(27\)	\(0\)	\(27\)
Plus space			\(+\)		\(2862\)	\(636\)	\(2226\)		\(2755\)	\(636\)	\(2119\)		\(107\)	\(0\)	\(107\)
Minus space			\(-\)		\(2970\)	\(742\)	\(2228\)		\(2862\)	\(742\)	\(2120\)		\(108\)	\(0\)	\(108\)

Trace form

1378 * q + 2 * q^3 + 1378 * q^4 + 6 * q^5 - 2 * q^6 + 1378 * q^9 + 6 * q^10 + 2 * q^12 + 2 * q^13 - 2 * q^14 - 8 * q^15 + 1378 * q^16 - 4 * q^18 - 18 * q^19 + 6 * q^20 - 6 * q^21 - 12 * q^22 - 2 * q^24 + 1390 * q^25 + 2 * q^26 + 20 * q^27 + 20 * q^29 + 12 * q^31 + 24 * q^33 - 4 * q^34 + 2 * q^35 + 1378 * q^36 + 20 * q^37 + 10 * q^38 + 8 * q^39 + 6 * q^40 + 32 * q^41 + 2 * q^42 + 8 * q^43 + 38 * q^45 + 4 * q^47 + 2 * q^48 + 1378 * q^49 + 4 * q^50 - 12 * q^51 + 2 * q^52 + 4 * q^54 + 24 * q^55 - 2 * q^56 + 20 * q^57 + 12 * q^58 + 6 * q^59 - 8 * q^60 + 38 * q^61 + 20 * q^62 + 4 * q^63 + 1378 * q^64 - 4 * q^65 - 32 * q^66 + 16 * q^67 + 32 * q^69 - 2 * q^70 + 32 * q^71 - 4 * q^72 + 4 * q^73 - 20 * q^74 - 26 * q^75 - 18 * q^76 + 12 * q^77 + 16 * q^78 - 32 * q^79 + 6 * q^80 + 1390 * q^81 + 36 * q^82 - 2 * q^83 - 6 * q^84 + 12 * q^85 - 20 * q^86 - 36 * q^87 - 12 * q^88 + 44 * q^89 - 34 * q^90 - 6 * q^91 + 48 * q^93 - 4 * q^94 + 48 * q^95 - 2 * q^96 + 48 * q^97 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(39326))\) 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	7	53
39326.2.a.a	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-3\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{7}+\cdots\)
39326.2.a.b	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-3\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}+2q^{5}+3q^{6}-q^{7}+\cdots\)
39326.2.a.c	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
39326.2.a.d	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
39326.2.a.e	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(3\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}-q^{7}+\cdots\)
39326.2.a.f	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-3\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-2q^{5}-3q^{6}-q^{7}+\cdots\)
39326.2.a.g	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-3\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-3q^{6}+q^{7}+q^{8}+\cdots\)
39326.2.a.h	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-2\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-4q^{5}-2q^{6}-q^{7}+\cdots\)
39326.2.a.i	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(-2\)	\(4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+4q^{5}-2q^{6}+q^{7}+\cdots\)
39326.2.a.j	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
39326.2.a.k	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
39326.2.a.l	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
39326.2.a.m	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
39326.2.a.n	$39326$	$2$	39326.a	1.a	$1$	$1$	$1$	$314.020$	\(\Q\)	None	✓	?				$-1$		\(1\)	\(3\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}-q^{7}+\cdots\)
39326.2.a.o	$39326$	$2$	39326.a	1.a	$1$	$2$	$2$	$314.020$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.p	$39326$	$2$	39326.a	1.a	$1$	$2$	$2$	$314.020$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.q	$39326$	$2$	39326.a	1.a	$1$	$2$	$2$	$314.020$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.r	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	3.3.788.1	None	✓	?				$-1$		\(-3\)	\(-2\)	\(-2\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.s	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(-3\)	\(0\)	\(-6\)	\(3\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.t	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(-3\)	\(3\)	\(-3\)	\(-3\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.u	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(-3\)	\(3\)	\(3\)	\(3\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.v	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	3.3.316.1	None	✓	?				$-1$		\(-3\)	\(4\)	\(5\)	\(-3\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.w	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(3\)	\(-3\)	\(-3\)	\(3\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.x	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(3\)	\(-3\)	\(3\)	\(-3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.y	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(3\)	\(0\)	\(6\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.z	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	3.3.788.1	None	✓	?				$-1$		\(3\)	\(2\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.ba	$39326$	$2$	39326.a	1.a	$1$	$3$	$3$	$314.020$	3.3.940.1	None	✓	?				$-1$		\(3\)	\(3\)	\(2\)	\(-3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.bb	$39326$	$2$	39326.a	1.a	$1$	$4$	$4$	$314.020$	4.4.399092.1	None	✓	?				$-1$		\(-4\)	\(1\)	\(3\)	\(4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.bc	$39326$	$2$	39326.a	1.a	$1$	$4$	$4$	$314.020$	4.4.399092.1	None	✓	?				$-1$		\(4\)	\(-1\)	\(-3\)	\(4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.bd	$39326$	$2$	39326.a	1.a	$1$	$5$	$5$	$314.020$	5.5.240881.1	None	✓	?				$-1$		\(-5\)	\(1\)	\(-2\)	\(-5\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.be	$39326$	$2$	39326.a	1.a	$1$	$5$	$5$	$314.020$	5.5.2008889.1	None	✓	?				$-1$		\(-5\)	\(1\)	\(-2\)	\(-5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.bf	$39326$	$2$	39326.a	1.a	$1$	$5$	$5$	$314.020$	5.5.684609.1	None	✓	?				$-1$		\(-5\)	\(3\)	\(2\)	\(5\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.bg	$39326$	$2$	39326.a	1.a	$1$	$5$	$5$	$314.020$	5.5.684609.1	None	✓	?				$-1$		\(5\)	\(-3\)	\(-2\)	\(5\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.bh	$39326$	$2$	39326.a	1.a	$1$	$5$	$5$	$314.020$	5.5.240881.1	None	✓	?				$-1$		\(5\)	\(-1\)	\(2\)	\(-5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.bi	$39326$	$2$	39326.a	1.a	$1$	$5$	$5$	$314.020$	5.5.2008889.1	None	✓	?				$-1$		\(5\)	\(-1\)	\(2\)	\(-5\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.bj	$39326$	$2$	39326.a	1.a	$1$	$6$	$6$	$314.020$	6.6.111663536.1	None	✓	?				$-1$		\(-6\)	\(-2\)	\(1\)	\(6\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.bk	$39326$	$2$	39326.a	1.a	$1$	$7$	$7$	$314.020$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(-7\)	\(1\)	\(3\)	\(-7\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.bl	$39326$	$2$	39326.a	1.a	$1$	$7$	$7$	$314.020$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(7\)	\(-1\)	\(-3\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.bm	$39326$	$2$	39326.a	1.a	$1$	$8$	$8$	$314.020$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(-8\)	\(-2\)	\(0\)	\(8\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.bn	$39326$	$2$	39326.a	1.a	$1$	$8$	$8$	$314.020$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	?				$-1$		\(8\)	\(2\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.bo	$39326$	$2$	39326.a	1.a	$1$	$12$	$12$	$314.020$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-12\)	\(-3\)	\(0\)	\(12\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.bp	$39326$	$2$	39326.a	1.a	$1$	$12$	$12$	$314.020$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(12\)	\(3\)	\(0\)	\(12\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.bq	$39326$	$2$	39326.a	1.a	$1$	$18$	$18$	$314.020$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(-18\)	\(-3\)	\(0\)	\(-18\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.br	$39326$	$2$	39326.a	1.a	$1$	$18$	$18$	$314.020$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(-18\)	\(0\)	\(3\)	\(-18\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.bs	$39326$	$2$	39326.a	1.a	$1$	$18$	$18$	$314.020$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(18\)	\(0\)	\(-3\)	\(-18\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.bt	$39326$	$2$	39326.a	1.a	$1$	$18$	$18$	$314.020$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	?				$-1$		\(18\)	\(3\)	\(0\)	\(-18\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.bu	$39326$	$2$	39326.a	1.a	$1$	$21$	$21$	$314.020$		None	✓	?				$-1$		\(-21\)	\(0\)	\(3\)	\(21\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.bv	$39326$	$2$	39326.a	1.a	$1$	$21$	$21$	$314.020$		None	✓	?				$-1$		\(21\)	\(0\)	\(-3\)	\(21\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.bw	$39326$	$2$	39326.a	1.a	$1$	$36$	$36$	$314.020$		None	✓	?				$-1$		\(-36\)	\(-7\)	\(-8\)	\(-36\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.bx	$39326$	$2$	39326.a	1.a	$1$	$36$	$36$	$314.020$		None	✓	?				$-1$		\(-36\)	\(5\)	\(2\)	\(36\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.by	$39326$	$2$	39326.a	1.a	$1$	$36$	$36$	$314.020$		None	✓	?				$-1$		\(36\)	\(-5\)	\(-2\)	\(36\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.bz	$39326$	$2$	39326.a	1.a	$1$	$36$	$36$	$314.020$		None	✓	?				$-1$		\(36\)	\(7\)	\(8\)	\(-36\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.ca	$39326$	$2$	39326.a	1.a	$1$	$42$	$42$	$314.020$		None	✓	?				$-1$		\(-42\)	\(-5\)	\(-7\)	\(-42\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.cb	$39326$	$2$	39326.a	1.a	$1$	$42$	$42$	$314.020$		None	✓	?				$-1$		\(-42\)	\(7\)	\(7\)	\(42\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.cc	$39326$	$2$	39326.a	1.a	$1$	$42$	$42$	$314.020$		None	✓	?				$-1$		\(42\)	\(-7\)	\(-7\)	\(42\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.cd	$39326$	$2$	39326.a	1.a	$1$	$42$	$42$	$314.020$		None	✓	?				$-1$		\(42\)	\(5\)	\(7\)	\(-42\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.ce	$39326$	$2$	39326.a	1.a	$1$	$45$	$45$	$314.020$		None	✓	?				$-1$		\(-45\)	\(9\)	\(9\)	\(45\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.cf	$39326$	$2$	39326.a	1.a	$1$	$45$	$45$	$314.020$		None	✓	?	✓			$-1$		\(45\)	\(-9\)	\(-9\)	\(45\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.cg	$39326$	$2$	39326.a	1.a	$1$	$54$	$54$	$314.020$		None	✓	?	✓			$-1$		\(-54\)	\(9\)	\(9\)	\(-54\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
39326.2.a.ch	$39326$	$2$	39326.a	1.a	$1$	$54$	$54$	$314.020$		None	✓	?				$-1$		\(54\)	\(-9\)	\(-9\)	\(-54\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.ci	$39326$	$2$	39326.a	1.a	$1$	$63$	$63$	$314.020$		None	✓	?				$-1$		\(-63\)	\(-9\)	\(-9\)	\(-63\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.cj	$39326$	$2$	39326.a	1.a	$1$	$63$	$63$	$314.020$		None	✓	?	✓			$-1$		\(63\)	\(9\)	\(9\)	\(-63\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.ck	$39326$	$2$	39326.a	1.a	$1$	$72$	$72$	$314.020$		None	✓	?	✓			$-1$		\(-72\)	\(-9\)	\(-9\)	\(72\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
39326.2.a.cl	$39326$	$2$	39326.a	1.a	$1$	$72$	$72$	$314.020$		None	✓	?				$-1$		\(72\)	\(9\)	\(9\)	\(72\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.cm	$39326$	$2$	39326.a	1.a	$1$	$84$	$84$	$314.020$		None	✓	?	✓			$-1$		\(-84\)	\(-12\)	\(-14\)	\(84\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.cn	$39326$	$2$	39326.a	1.a	$1$	$84$	$84$	$314.020$		None	✓	?	✓			$-1$		\(-84\)	\(12\)	\(10\)	\(-84\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
39326.2.a.co	$39326$	$2$	39326.a	1.a	$1$	$84$	$84$	$314.020$		None	✓	?	✓			$-1$		\(84\)	\(-12\)	\(-10\)	\(-84\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
39326.2.a.cp	$39326$	$2$	39326.a	1.a	$1$	$84$	$84$	$314.020$		None	✓	?	✓			$-1$		\(84\)	\(12\)	\(14\)	\(84\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(39326))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(39326)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(371))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(742))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2809))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5618))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19663))\)\(^{\oplus 2}\)