Space of modular forms of level 19663, weight 2, and trivial character

• Label: 19663.2.a
• Level: $19663$
• Weight: $2$
• Character orbit: 19663.a
• Rep. character: $\chi_{19663}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1377$
• Newform subspaces: $27$
• Sturm bound: $3816$

Defining parameters

Level:	\( N \)	\(=\)	\( 19663 = 7 \cdot 53^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19663.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 27 \)
Sturm bound:			\(3816\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(19663))\).

	Total	New	Old
Modular forms	1962	1377	585
Cusp forms	1855	1377	478
Eisenstein series	107	0	107

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

\(7\)	\(53\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(477\)	\(338\)	\(139\)		\(451\)	\(338\)	\(113\)		\(26\)	\(0\)	\(26\)
\(+\)	\(-\)	\(-\)		\(503\)	\(351\)	\(152\)		\(476\)	\(351\)	\(125\)		\(27\)	\(0\)	\(27\)
\(-\)	\(+\)	\(-\)		\(504\)	\(363\)	\(141\)		\(477\)	\(363\)	\(114\)		\(27\)	\(0\)	\(27\)
\(-\)	\(-\)	\(+\)		\(478\)	\(325\)	\(153\)		\(451\)	\(325\)	\(126\)		\(27\)	\(0\)	\(27\)
Plus space		\(+\)		\(955\)	\(663\)	\(292\)		\(902\)	\(663\)	\(239\)		\(53\)	\(0\)	\(53\)
Minus space		\(-\)		\(1007\)	\(714\)	\(293\)		\(953\)	\(714\)	\(239\)		\(54\)	\(0\)	\(54\)

Trace form

1377 * q - q^2 + 1371 * q^4 - 6 * q^5 + 4 * q^6 - q^7 + 3 * q^8 + 1381 * q^9 - 2 * q^10 - 4 * q^11 + 12 * q^12 - 6 * q^13 + q^14 - 4 * q^15 + 1363 * q^16 - 2 * q^17 + 19 * q^18 + 4 * q^19 + 6 * q^20 + 4 * q^21 + 24 * q^22 + 8 * q^23 + 4 * q^24 + 1363 * q^25 - 2 * q^26 - 7 * q^28 - 22 * q^29 - 4 * q^30 - 8 * q^31 + 15 * q^32 - 6 * q^34 + 2 * q^35 + 1343 * q^36 - 26 * q^37 + 28 * q^38 + 28 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 8 * q^43 - 8 * q^44 - 58 * q^45 - 48 * q^46 - 16 * q^47 + 52 * q^48 + 1377 * q^49 + 29 * q^50 + 16 * q^51 + 6 * q^52 + 8 * q^54 + 16 * q^55 - 3 * q^56 + 12 * q^57 + 10 * q^58 + 12 * q^59 + 68 * q^60 - 54 * q^61 + 48 * q^62 - 5 * q^63 + 1367 * q^64 - 12 * q^65 + 64 * q^66 + 74 * q^68 - 48 * q^69 + 14 * q^70 + 4 * q^71 + 115 * q^72 - 10 * q^73 + 78 * q^74 + 68 * q^75 - 4 * q^76 - 12 * q^77 + 48 * q^78 + 30 * q^80 + 1409 * q^81 - 38 * q^82 + 40 * q^83 + 28 * q^84 - 32 * q^85 + 24 * q^86 + 76 * q^87 + 72 * q^88 - 26 * q^89 + 158 * q^90 - 2 * q^91 + 68 * q^92 - 24 * q^93 + 56 * q^94 - 20 * q^95 + 20 * q^96 - 18 * q^97 - q^98 - 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(19663))\) 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	53
19663.2.a.a	$19663$	$2$	19663.a	1.a	$1$	$1$	$1$	$157.010$	\(\Q\)	None	✓	?				$-1$		\(-2\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{5}+q^{7}-3q^{9}+\cdots\)
19663.2.a.b	$19663$	$2$	19663.a	1.a	$1$	$1$	$1$	$157.010$	\(\Q\)	None	✓	?				$-1$		\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
19663.2.a.c	$19663$	$2$	19663.a	1.a	$1$	$2$	$2$	$157.010$	\(\Q(\sqrt{5}) \)	None	✓	?				$-1$		\(1\)	\(1\)	\(3\)	\(2\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
19663.2.a.d	$19663$	$2$	19663.a	1.a	$1$	$3$	$3$	$157.010$	3.3.229.1	None	✓	?				$-1$		\(0\)	\(0\)	\(5\)	\(-3\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
19663.2.a.e	$19663$	$2$	19663.a	1.a	$1$	$4$	$4$	$157.010$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
19663.2.a.f	$19663$	$2$	19663.a	1.a	$1$	$9$	$9$	$157.010$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(-3\)	\(-9\)	\(-9\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
19663.2.a.g	$19663$	$2$	19663.a	1.a	$1$	$10$	$10$	$157.010$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-10\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
19663.2.a.h	$19663$	$2$	19663.a	1.a	$1$	$11$	$11$	$157.010$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(1\)	\(-2\)	\(11\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
19663.2.a.i	$19663$	$2$	19663.a	1.a	$1$	$12$	$12$	$157.010$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(12\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
19663.2.a.j	$19663$	$2$	19663.a	1.a	$1$	$13$	$13$	$157.010$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?				$-1$		\(-3\)	\(-3\)	\(-4\)	\(13\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
19663.2.a.k	$19663$	$2$	19663.a	1.a	$1$	$13$	$13$	$157.010$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?				$-1$		\(-1\)	\(-5\)	\(-4\)	\(-13\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
19663.2.a.l	$19663$	$2$	19663.a	1.a	$1$	$13$	$13$	$157.010$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?				$-1$		\(1\)	\(5\)	\(4\)	\(-13\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
19663.2.a.m	$19663$	$2$	19663.a	1.a	$1$	$13$	$13$	$157.010$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	?				$-1$		\(3\)	\(3\)	\(4\)	\(13\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
19663.2.a.n	$19663$	$2$	19663.a	1.a	$1$	$39$	$39$	$157.010$		None	✓	?				$-1$		\(-9\)	\(-3\)	\(-12\)	\(39\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
19663.2.a.o	$19663$	$2$	19663.a	1.a	$1$	$39$	$39$	$157.010$		None	✓	?				$-1$		\(-3\)	\(-3\)	\(-12\)	\(-39\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
19663.2.a.p	$19663$	$2$	19663.a	1.a	$1$	$39$	$39$	$157.010$		None	✓	?				$-1$		\(3\)	\(3\)	\(12\)	\(-39\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
19663.2.a.q	$19663$	$2$	19663.a	1.a	$1$	$39$	$39$	$157.010$		None	✓	?				$-1$		\(9\)	\(3\)	\(12\)	\(39\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
19663.2.a.r	$19663$	$2$	19663.a	1.a	$1$	$78$	$78$	$157.010$		None	✓	?				$-1$		\(-6\)	\(1\)	\(2\)	\(-78\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
19663.2.a.s	$19663$	$2$	19663.a	1.a	$1$	$78$	$78$	$157.010$		None	✓	?				$-1$		\(6\)	\(-1\)	\(-2\)	\(-78\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
19663.2.a.t	$19663$	$2$	19663.a	1.a	$1$	$90$	$90$	$157.010$		None	✓	?				$-1$		\(-5\)	\(1\)	\(4\)	\(90\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
19663.2.a.u	$19663$	$2$	19663.a	1.a	$1$	$90$	$90$	$157.010$		None	✓	?				$-1$		\(5\)	\(-1\)	\(-4\)	\(90\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
19663.2.a.v	$19663$	$2$	19663.a	1.a	$1$	$117$	$117$	$157.010$		None	✓	?				$-1$		\(-27\)	\(-18\)	\(-36\)	\(117\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
19663.2.a.w	$19663$	$2$	19663.a	1.a	$1$	$117$	$117$	$157.010$		None	✓	?	✓			$-1$		\(-9\)	\(-18\)	\(-36\)	\(-117\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
19663.2.a.x	$19663$	$2$	19663.a	1.a	$1$	$117$	$117$	$157.010$		None	✓	?				$-1$		\(9\)	\(18\)	\(36\)	\(-117\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
19663.2.a.y	$19663$	$2$	19663.a	1.a	$1$	$117$	$117$	$157.010$		None	✓	?	✓			$-1$		\(27\)	\(18\)	\(36\)	\(117\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
19663.2.a.z	$19663$	$2$	19663.a	1.a	$1$	$144$	$144$	$157.010$		None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(144\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
19663.2.a.ba	$19663$	$2$	19663.a	1.a	$1$	$168$	$168$	$157.010$		None	✓	?	✓			$-1$		\(0\)	\(0\)	\(0\)	\(-168\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(19663))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(19663)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(371))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2809))\)\(^{\oplus 2}\)