Space of modular forms of level 17689, weight 2, and trivial character

• Label: 17689.2.a
• Level: $17689$
• Weight: $2$
• Character orbit: 17689.a
• Rep. character: $\chi_{17689}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1122$
• Newform subspaces: $86$
• Sturm bound: $3546$

Defining parameters

Level:	\( N \)	\(=\)	\( 17689 = 7^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	17689.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 86 \)
Sturm bound:			\(3546\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(17689))\).

	Total	New	Old
Modular forms	1852	1207	645
Cusp forms	1693	1122	571
Eisenstein series	159	85	74

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

\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(453\)	\(281\)	\(172\)		\(414\)	\(265\)	\(149\)		\(39\)	\(16\)	\(23\)
\(+\)	\(-\)	\(-\)		\(473\)	\(303\)	\(170\)		\(433\)	\(285\)	\(148\)		\(40\)	\(18\)	\(22\)
\(-\)	\(+\)	\(-\)		\(473\)	\(317\)	\(156\)		\(433\)	\(293\)	\(140\)		\(40\)	\(24\)	\(16\)
\(-\)	\(-\)	\(+\)		\(453\)	\(306\)	\(147\)		\(413\)	\(279\)	\(134\)		\(40\)	\(27\)	\(13\)
Plus space		\(+\)		\(906\)	\(587\)	\(319\)		\(827\)	\(544\)	\(283\)		\(79\)	\(43\)	\(36\)
Minus space		\(-\)		\(946\)	\(620\)	\(326\)		\(866\)	\(578\)	\(288\)		\(80\)	\(42\)	\(38\)

Trace form

1122 * q - 2 * q^3 + 1080 * q^4 - 4 * q^5 + 1040 * q^9 - 10 * q^10 - 2 * q^11 - 12 * q^12 - 10 * q^13 - 2 * q^15 + 1000 * q^16 - 6 * q^17 + 20 * q^18 + 14 * q^20 + 16 * q^22 - 8 * q^23 + 28 * q^24 + 940 * q^25 + 10 * q^26 - 8 * q^27 + 18 * q^29 + 40 * q^30 - 12 * q^31 + 20 * q^32 + 30 * q^33 + 18 * q^34 + 932 * q^36 - 6 * q^37 + 20 * q^39 + 6 * q^40 + 4 * q^41 - 2 * q^43 + 34 * q^44 - 20 * q^45 + 48 * q^46 + 2 * q^47 - 44 * q^48 - 8 * q^50 + 70 * q^51 - 6 * q^52 - 20 * q^53 + 18 * q^54 + 12 * q^55 + 10 * q^58 - 6 * q^59 + 12 * q^60 - 4 * q^61 + 10 * q^62 + 830 * q^64 - 24 * q^65 + 42 * q^66 + 28 * q^67 - 34 * q^68 + 28 * q^69 + 30 * q^71 - 16 * q^72 - 14 * q^73 + 28 * q^74 - 12 * q^75 + 12 * q^78 + 16 * q^79 + 72 * q^80 + 810 * q^81 + 28 * q^82 + 32 * q^83 - 52 * q^85 - 8 * q^86 + 38 * q^87 + 12 * q^88 - 2 * q^89 - 102 * q^90 + 16 * q^92 - 8 * q^93 - 12 * q^94 + 58 * q^96 - 2 * q^97 + 26 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(17689))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	19
17689.2.a.a	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}-2q^{5}+4q^{6}+\cdots\)
17689.2.a.b	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(3\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}+3q^{5}+4q^{6}+\cdots\)
17689.2.a.c	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(2\)	\(-3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{3}+2q^{4}-3q^{5}-4q^{6}+\cdots\)
17689.2.a.d	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(2\)	\(2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{3}+2q^{4}+2q^{5}-4q^{6}+\cdots\)
17689.2.a.e	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	not computed	✓	?				$-1$		\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$		\(q-q^{2}-q^{4}+3q^{8}-3q^{9}+4q^{11}+\cdots\)
17689.2.a.f	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(-2\)	\(-3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}-3q^{5}+q^{9}+3q^{11}+\cdots\)
17689.2.a.g	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$1$		\(q-2q^{4}+q^{5}-3q^{9}-5q^{11}+4q^{16}+\cdots\)
17689.2.a.h	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	None	✓	?				$-1$		\(2\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+2q^{4}+2q^{5}-4q^{6}+\cdots\)
17689.2.a.i	$17689$	$2$	17689.a	1.a	$1$	$1$	$1$	$141.247$	\(\Q\)	None	✓	?				$-1$		\(2\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{3}+2q^{4}-2q^{5}+4q^{6}+\cdots\)
17689.2.a.j	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.k	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(3\)	\(-2\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.l	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(-1\)	\(3\)	\(-2\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.m	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(-4\)	\(-1\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.n	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{57}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$
17689.2.a.o	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{57}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$+$
17689.2.a.p	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.q	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.r	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{7}) \)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$
17689.2.a.s	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(0\)	\(4\)	\(-1\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.t	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(-3\)	\(-2\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.u	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{13}) \)	None	✓	?				$-1$		\(1\)	\(-3\)	\(6\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.v	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.w	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.x	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{2}) \)	None	✓	?				$-1$		\(2\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.y	$17689$	$2$	17689.a	1.a	$1$	$2$	$2$	$141.247$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(3\)	\(-3\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.z	$17689$	$2$	17689.a	1.a	$1$	$3$	$3$	$141.247$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(-3\)	\(3\)	\(3\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.ba	$17689$	$2$	17689.a	1.a	$1$	$3$	$3$	$141.247$	3.3.321.1	None	✓	?				$-1$		\(-2\)	\(1\)	\(3\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bb	$17689$	$2$	17689.a	1.a	$1$	$3$	$3$	$141.247$	3.3.229.1	None	✓	?				$-1$		\(-2\)	\(3\)	\(2\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bc	$17689$	$2$	17689.a	1.a	$1$	$3$	$3$	$141.247$	3.3.321.1	None	✓	?				$-1$		\(2\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.bd	$17689$	$2$	17689.a	1.a	$1$	$3$	$3$	$141.247$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(3\)	\(-3\)	\(3\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.be	$17689$	$2$	17689.a	1.a	$1$	$4$	$4$	$141.247$	4.4.6125.1	not computed	✓	?				$-1$		\(-1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$
17689.2.a.bf	$17689$	$2$	17689.a	1.a	$1$	$4$	$4$	$141.247$	4.4.5744.1	None	✓	?				$-1$		\(0\)	\(-2\)	\(8\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bg	$17689$	$2$	17689.a	1.a	$1$	$4$	$4$	$141.247$	\(\Q(\zeta_{20})^+\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$
17689.2.a.bh	$17689$	$2$	17689.a	1.a	$1$	$4$	$4$	$141.247$	4.4.240944.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$
17689.2.a.bi	$17689$	$2$	17689.a	1.a	$1$	$4$	$4$	$141.247$	4.4.5744.1	None	✓	?				$-1$		\(0\)	\(2\)	\(-8\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bj	$17689$	$2$	17689.a	1.a	$1$	$4$	$4$	$141.247$	4.4.6125.1	not computed	✓	?				$-1$		\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$
17689.2.a.bk	$17689$	$2$	17689.a	1.a	$1$	$5$	$5$	$141.247$	5.5.210557.1	None	✓	?				$-1$		\(-1\)	\(3\)	\(-1\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.bl	$17689$	$2$	17689.a	1.a	$1$	$5$	$5$	$141.247$	5.5.210557.1	None	✓	?				$-1$		\(1\)	\(-3\)	\(-1\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bm	$17689$	$2$	17689.a	1.a	$1$	$6$	$6$	$141.247$	6.6.1416125.1	None	✓	?				$-1$		\(-1\)	\(-2\)	\(5\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bn	$17689$	$2$	17689.a	1.a	$1$	$6$	$6$	$141.247$	6.6.171932480.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$
17689.2.a.bo	$17689$	$2$	17689.a	1.a	$1$	$6$	$6$	$141.247$	6.6.1416125.1	None	✓	?				$-1$		\(1\)	\(2\)	\(5\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bp	$17689$	$2$	17689.a	1.a	$1$	$7$	$7$	$141.247$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bq	$17689$	$2$	17689.a	1.a	$1$	$7$	$7$	$141.247$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.br	$17689$	$2$	17689.a	1.a	$1$	$8$	$8$	$141.247$	8.8.\(\cdots\).1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$
17689.2.a.bs	$17689$	$2$	17689.a	1.a	$1$	$8$	$8$	$141.247$	8.8.\(\cdots\).1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(-10\)	\(0\)		$+$	$+$	$+$
17689.2.a.bt	$17689$	$2$	17689.a	1.a	$1$	$8$	$8$	$141.247$	8.8.9604000000.1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$
17689.2.a.bu	$17689$	$2$	17689.a	1.a	$1$	$8$	$8$	$141.247$	8.8.\(\cdots\).1	not computed	✓	?				$-1$		\(0\)	\(0\)	\(10\)	\(0\)		$-$	$+$	$-$
17689.2.a.bv	$17689$	$2$	17689.a	1.a	$1$	$10$	$10$	$141.247$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-11\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bw	$17689$	$2$	17689.a	1.a	$1$	$10$	$10$	$141.247$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	not computed	✓	?				$-1$		\(-2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$
17689.2.a.bx	$17689$	$2$	17689.a	1.a	$1$	$10$	$10$	$141.247$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(-4\)	\(16\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.by	$17689$	$2$	17689.a	1.a	$1$	$10$	$10$	$141.247$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(0\)	\(-11\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.bz	$17689$	$2$	17689.a	1.a	$1$	$10$	$10$	$141.247$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	not computed	✓	?				$-1$		\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$
17689.2.a.ca	$17689$	$2$	17689.a	1.a	$1$	$10$	$10$	$141.247$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(2\)	\(4\)	\(-16\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.cb	$17689$	$2$	17689.a	1.a	$1$	$12$	$12$	$141.247$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	not computed	✓	?				$-1$		\(-6\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$
17689.2.a.cc	$17689$	$2$	17689.a	1.a	$1$	$12$	$12$	$141.247$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
17689.2.a.cd	$17689$	$2$	17689.a	1.a	$1$	$12$	$12$	$141.247$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(3\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.ce	$17689$	$2$	17689.a	1.a	$1$	$12$	$12$	$141.247$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(-3\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.cf	$17689$	$2$	17689.a	1.a	$1$	$12$	$12$	$141.247$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.cg	$17689$	$2$	17689.a	1.a	$1$	$12$	$12$	$141.247$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	not computed	✓	?				$-1$		\(6\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$
17689.2.a.ch	$17689$	$2$	17689.a	1.a	$1$	$15$	$15$	$141.247$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(-9\)	\(6\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.ci	$17689$	$2$	17689.a	1.a	$1$	$15$	$15$	$141.247$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(-3\)	\(6\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.cj	$17689$	$2$	17689.a	1.a	$1$	$15$	$15$	$141.247$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(3\)	\(-6\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.ck	$17689$	$2$	17689.a	1.a	$1$	$15$	$15$	$141.247$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	?				$-1$		\(9\)	\(-6\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.cl	$17689$	$2$	17689.a	1.a	$1$	$16$	$16$	$141.247$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(16\)	\(0\)		$-$	$+$	$-$
17689.2.a.cm	$17689$	$2$	17689.a	1.a	$1$	$16$	$16$	$141.247$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$
17689.2.a.cn	$17689$	$2$	17689.a	1.a	$1$	$20$	$20$	$141.247$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	not computed	✓	?				$-1$		\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$
17689.2.a.co	$17689$	$2$	17689.a	1.a	$1$	$20$	$20$	$141.247$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	not computed	✓	?				$-1$		\(4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$
17689.2.a.cp	$17689$	$2$	17689.a	1.a	$1$	$24$	$24$	$141.247$		None	✓	?				$-1$		\(-1\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.cq	$17689$	$2$	17689.a	1.a	$1$	$24$	$24$	$141.247$		None	✓	?				$-1$		\(-1\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.cr	$17689$	$2$	17689.a	1.a	$1$	$24$	$24$	$141.247$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(-16\)	\(0\)		$-$	$+$	$-$
17689.2.a.cs	$17689$	$2$	17689.a	1.a	$1$	$24$	$24$	$141.247$		None	✓	?				$-1$		\(1\)	\(0\)	\(-6\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.ct	$17689$	$2$	17689.a	1.a	$1$	$24$	$24$	$141.247$		None	✓	?				$-1$		\(1\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.cu	$17689$	$2$	17689.a	1.a	$1$	$30$	$30$	$141.247$		not computed	✓	?				$-1$		\(-6\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$
17689.2.a.cv	$17689$	$2$	17689.a	1.a	$1$	$30$	$30$	$141.247$		not computed	✓	?				$-1$		\(6\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$
17689.2.a.cw	$17689$	$2$	17689.a	1.a	$1$	$32$	$32$	$141.247$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$
17689.2.a.cx	$17689$	$2$	17689.a	1.a	$1$	$33$	$33$	$141.247$		None	✓	?	✓			$-1$		\(0\)	\(-9\)	\(-3\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
17689.2.a.cy	$17689$	$2$	17689.a	1.a	$1$	$33$	$33$	$141.247$		None	✓	?				$-1$		\(0\)	\(-9\)	\(3\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
17689.2.a.cz	$17689$	$2$	17689.a	1.a	$1$	$33$	$33$	$141.247$		None	✓	?				$-1$		\(0\)	\(9\)	\(-3\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
17689.2.a.da	$17689$	$2$	17689.a	1.a	$1$	$33$	$33$	$141.247$		None	✓	?				$-1$		\(0\)	\(9\)	\(3\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
17689.2.a.db	$17689$	$2$	17689.a	1.a	$1$	$40$	$40$	$141.247$		not computed	✓	?				$-1$		\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$
17689.2.a.dc	$17689$	$2$	17689.a	1.a	$1$	$40$	$40$	$141.247$		not computed	✓	?				$-1$		\(2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$
17689.2.a.dd	$17689$	$2$	17689.a	1.a	$1$	$48$	$48$	$141.247$		not computed	✓	?				$-1$		\(0\)	\(0\)	\(-20\)	\(0\)		$+$	$+$	$+$
17689.2.a.de	$17689$	$2$	17689.a	1.a	$1$	$48$	$48$	$141.247$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(20\)	\(0\)		$-$	$+$	$-$
17689.2.a.df	$17689$	$2$	17689.a	1.a	$1$	$60$	$60$	$141.247$		not computed	✓	?				$-1$		\(-12\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$
17689.2.a.dg	$17689$	$2$	17689.a	1.a	$1$	$60$	$60$	$141.247$		not computed	✓	?	✓			$-1$		\(12\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$
17689.2.a.dh	$17689$	$2$	17689.a	1.a	$1$	$64$	$64$	$141.247$		not computed	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(17689))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(17689)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2527))\)\(^{\oplus 2}\)