Space of modular forms of level 10002, weight 2, and trivial character

• Label: 10002.2.a
• Level: $10002$
• Weight: $2$
• Character orbit: 10002.a
• Rep. character: $\chi_{10002}(1,\cdot)$
• Character field: $\Q$
• Dimension: $279$
• Newform subspaces: $14$
• Sturm bound: $3336$

Defining parameters

Level:	\( N \)	\(=\)	\( 10002 = 2 \cdot 3 \cdot 1667 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	10002.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(3336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(10002))\).

	Total	New	Old
Modular forms	1672	279	1393
Cusp forms	1665	279	1386
Eisenstein series	7	0	7

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

\(2\)	\(3\)	\(1667\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(190\)	\(39\)	\(151\)		\(190\)	\(39\)	\(151\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(227\)	\(30\)	\(197\)		\(226\)	\(30\)	\(196\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(208\)	\(38\)	\(170\)		\(207\)	\(38\)	\(169\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(210\)	\(32\)	\(178\)		\(209\)	\(32\)	\(177\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(199\)	\(40\)	\(159\)		\(198\)	\(40\)	\(158\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(220\)	\(30\)	\(190\)		\(219\)	\(30\)	\(189\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(200\)	\(23\)	\(177\)		\(199\)	\(23\)	\(176\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(218\)	\(47\)	\(171\)		\(217\)	\(47\)	\(170\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(820\)	\(124\)	\(696\)		\(817\)	\(124\)	\(693\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(852\)	\(155\)	\(697\)		\(848\)	\(155\)	\(693\)		\(4\)	\(0\)	\(4\)

Trace form

279 * q + q^2 + q^3 + 279 * q^4 + 6 * q^5 - q^6 + 4 * q^7 + q^8 + 279 * q^9 + 2 * q^10 + 12 * q^11 + q^12 + 14 * q^13 + 8 * q^14 + 2 * q^15 + 279 * q^16 + 10 * q^17 + q^18 + 12 * q^19 + 6 * q^20 + 4 * q^21 - 4 * q^22 - 8 * q^23 - q^24 + 281 * q^25 + 6 * q^26 + q^27 + 4 * q^28 - 10 * q^29 - 2 * q^30 - 4 * q^31 + q^32 + 10 * q^34 + 279 * q^36 + 10 * q^37 - 12 * q^38 + 14 * q^39 + 2 * q^40 + 18 * q^41 + 4 * q^42 + 4 * q^43 + 12 * q^44 + 6 * q^45 + 16 * q^47 + q^48 + 299 * q^49 - q^50 - 6 * q^51 + 14 * q^52 + 30 * q^53 - q^54 + 32 * q^55 + 8 * q^56 + 12 * q^57 + 18 * q^58 + 4 * q^59 + 2 * q^60 + 22 * q^61 + 8 * q^62 + 4 * q^63 + 279 * q^64 + 52 * q^65 + 4 * q^66 + 40 * q^67 + 10 * q^68 - 8 * q^70 - 32 * q^71 + q^72 + 14 * q^73 + 22 * q^74 + 15 * q^75 + 12 * q^76 + 72 * q^77 + 10 * q^78 - 4 * q^79 + 6 * q^80 + 279 * q^81 + 2 * q^82 + 36 * q^83 + 4 * q^84 + 68 * q^85 - 4 * q^86 + 2 * q^87 - 4 * q^88 + 10 * q^89 + 2 * q^90 + 16 * q^91 - 8 * q^92 + 24 * q^93 + 8 * q^94 - 32 * q^95 - q^96 + 54 * q^97 + 9 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(10002))\) 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	3	1667
10002.2.a.a	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	\(\Q\)	None	✓	✓			10002.2.a.a	$1$		\(-1\)	\(-1\)	\(-2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
10002.2.a.b	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	\(\Q\)	None	✓	✓			10002.2.a.b	$1$		\(-1\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
10002.2.a.c	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	\(\Q\)	None	✓	✓			10002.2.a.c	$1$		\(-1\)	\(-1\)	\(2\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
10002.2.a.d	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	\(\Q\)	None	✓	✓			10002.2.a.d	$1$		\(1\)	\(-1\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
10002.2.a.e	$10002$	$2$	10002.a	1.a	$1$	$1$	$1$	$79.866$	\(\Q\)	None	✓	✓			10002.2.a.e	$1$		\(1\)	\(1\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
10002.2.a.f	$10002$	$2$	10002.a	1.a	$1$	$3$	$3$	$79.866$	3.3.148.1	None	✓	✓			10002.2.a.f	$1$		\(3\)	\(3\)	\(-6\)	\(-4\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
10002.2.a.g	$10002$	$2$	10002.a	1.a	$1$	$19$	$19$	$79.866$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓		10002.2.a.g	$1$		\(19\)	\(19\)	\(-5\)	\(-13\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
10002.2.a.h	$10002$	$2$	10002.a	1.a	$1$	$28$	$28$	$79.866$		None	✓	✓	✓		10002.2.a.h	$1$		\(-28\)	\(-28\)	\(3\)	\(5\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
10002.2.a.i	$10002$	$2$	10002.a	1.a	$1$	$29$	$29$	$79.866$		None	✓	✓	✓		10002.2.a.i	$1$		\(29\)	\(-29\)	\(-10\)	\(-5\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
10002.2.a.j	$10002$	$2$	10002.a	1.a	$1$	$32$	$32$	$79.866$		None	✓	✓	✓	✓	10002.2.a.j	$1$		\(-32\)	\(32\)	\(0\)	\(-26\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
10002.2.a.k	$10002$	$2$	10002.a	1.a	$1$	$38$	$38$	$79.866$		None	✓	✓	✓		10002.2.a.k	$1$		\(-38\)	\(-38\)	\(-3\)	\(-12\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
10002.2.a.l	$10002$	$2$	10002.a	1.a	$1$	$38$	$38$	$79.866$		None	✓	✓	✓	✓	10002.2.a.l	$1$		\(-38\)	\(38\)	\(2\)	\(25\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
10002.2.a.m	$10002$	$2$	10002.a	1.a	$1$	$40$	$40$	$79.866$		None	✓	✓	✓	✓	10002.2.a.m	$1$		\(40\)	\(-40\)	\(14\)	\(8\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
10002.2.a.n	$10002$	$2$	10002.a	1.a	$1$	$47$	$47$	$79.866$		None	✓	✓	✓	✓	10002.2.a.n	$1$		\(47\)	\(47\)	\(11\)	\(24\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(10002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(10002)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1667))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5001))\)\(^{\oplus 2}\)