Space of modular forms of level 882, weight 2, and trivial character

• Label: 882.2.a
• Level: $882$
• Weight: $2$
• Character orbit: 882.a
• Rep. character: $\chi_{882}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $15$
• Sturm bound: $336$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(336\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(882))\).

	Total	New	Old
Modular forms	200	18	182
Cusp forms	137	18	119
Eisenstein series	63	0	63

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

\(2\)	\(3\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(22\)	\(3\)	\(19\)		\(15\)	\(3\)	\(12\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)		\(28\)	\(1\)	\(27\)		\(20\)	\(1\)	\(19\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)		\(26\)	\(3\)	\(23\)		\(18\)	\(3\)	\(15\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)		\(24\)	\(2\)	\(22\)		\(16\)	\(2\)	\(14\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)		\(26\)	\(3\)	\(23\)		\(18\)	\(3\)	\(15\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)		\(24\)	\(1\)	\(23\)		\(16\)	\(1\)	\(15\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)		\(26\)	\(1\)	\(25\)		\(18\)	\(1\)	\(17\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)		\(24\)	\(4\)	\(20\)		\(16\)	\(4\)	\(12\)		\(8\)	\(0\)	\(8\)
Plus space			\(+\)		\(96\)	\(7\)	\(89\)		\(65\)	\(7\)	\(58\)		\(31\)	\(0\)	\(31\)
Minus space			\(-\)		\(104\)	\(11\)	\(93\)		\(72\)	\(11\)	\(61\)		\(32\)	\(0\)	\(32\)

Trace form

18 * q + 18 * q^4 - 2 * q^5 + 2 * q^10 - 2 * q^13 + 18 * q^16 + 8 * q^17 + 2 * q^19 - 2 * q^20 + 8 * q^22 + 8 * q^23 + 26 * q^25 + 10 * q^26 - 8 * q^29 + 4 * q^31 + 4 * q^34 - 16 * q^37 - 6 * q^38 + 2 * q^40 - 32 * q^43 - 12 * q^47 + 28 * q^50 - 2 * q^52 + 36 * q^53 - 8 * q^55 + 20 * q^58 - 2 * q^59 - 14 * q^61 + 4 * q^62 + 18 * q^64 + 4 * q^65 - 32 * q^67 + 8 * q^68 + 8 * q^71 - 12 * q^73 + 4 * q^74 + 2 * q^76 - 56 * q^79 - 2 * q^80 + 12 * q^82 - 10 * q^83 + 12 * q^85 - 8 * q^86 + 8 * q^88 - 12 * q^89 + 8 * q^92 - 12 * q^94 + 8 * q^95 + 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(882))\) 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	7
882.2.a.a	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				126.2.g.a	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots\)
882.2.a.b	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				42.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots\)
882.2.a.c	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				42.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\cdots\)
882.2.a.d	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				42.2.e.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots\)
882.2.a.e	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓		✓	✓	126.2.g.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
882.2.a.f	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				294.2.a.b	$1$	$0$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\cdots\)
882.2.a.g	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓		✓	✓	42.2.e.b	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.h	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓		✓	✓	126.2.g.a	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.i	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				14.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots\)
882.2.a.j	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				126.2.g.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.k	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				42.2.e.b	$1$	$0$	\(1\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.l	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	\(\Q\)	None	✓				294.2.a.b	$1$	$0$	\(1\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots\)
882.2.a.m	$882$	$2$	882.a	1.a	$1$	$2$	$2$	$7.043$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		882.2.a.m	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-4q^{11}+\cdots\)
882.2.a.n	$882$	$2$	882.a	1.a	$1$	$2$	$2$	$7.043$	\(\Q(\sqrt{2}) \)	None	✓		✓		98.2.a.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
882.2.a.o	$882$	$2$	882.a	1.a	$1$	$2$	$2$	$7.043$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		882.2.a.m	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(882))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(882)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)