Space of modular forms of level 8732, weight 2, and trivial character

• Label: 8732.2.a
• Level: $8732$
• Weight: $2$
• Character orbit: 8732.a
• Rep. character: $\chi_{8732}(1,\cdot)$
• Character field: $\Q$
• Dimension: $174$
• Newform subspaces: $6$
• Sturm bound: $2280$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 8732 = 2^{2} \cdot 37 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8732.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2280\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8732))\).

	Total	New	Old
Modular forms	1146	174	972
Cusp forms	1135	174	961
Eisenstein series	11	0	11

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

\(2\)	\(37\)	\(59\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(122\)	\(0\)	\(122\)		\(121\)	\(0\)	\(121\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(164\)	\(0\)	\(164\)		\(162\)	\(0\)	\(162\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(165\)	\(0\)	\(165\)		\(163\)	\(0\)	\(163\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(123\)	\(0\)	\(123\)		\(121\)	\(0\)	\(121\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(133\)	\(42\)	\(91\)		\(132\)	\(42\)	\(90\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(154\)	\(45\)	\(109\)		\(153\)	\(45\)	\(108\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(153\)	\(42\)	\(111\)		\(152\)	\(42\)	\(110\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(132\)	\(45\)	\(87\)		\(131\)	\(45\)	\(86\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(552\)	\(87\)	\(465\)		\(547\)	\(87\)	\(460\)		\(5\)	\(0\)	\(5\)
Minus space			\(-\)		\(594\)	\(87\)	\(507\)		\(588\)	\(87\)	\(501\)		\(6\)	\(0\)	\(6\)

Trace form

174 * q - 4 * q^7 + 174 * q^9 - 12 * q^11 - 8 * q^13 - 22 * q^15 - 2 * q^17 - 4 * q^19 + 18 * q^21 + 16 * q^23 + 162 * q^25 - 6 * q^27 + 12 * q^29 + 8 * q^31 + 32 * q^33 + 6 * q^35 + 8 * q^39 + 4 * q^41 - 32 * q^43 + 18 * q^45 + 178 * q^49 - 4 * q^53 - 4 * q^55 - 14 * q^57 + 6 * q^59 + 32 * q^61 - 52 * q^63 - 12 * q^65 + 48 * q^67 - 4 * q^69 - 2 * q^71 - 4 * q^73 + 36 * q^75 + 20 * q^77 - 24 * q^79 + 174 * q^81 - 16 * q^83 - 56 * q^85 + 10 * q^87 - 12 * q^89 - 8 * q^91 + 12 * q^93 + 12 * q^95 + 4 * q^97 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8732))\) 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	37	59
8732.2.a.a	$8732$	$2$	8732.a	1.a	$1$	$1$	$1$	$69.725$	\(\Q\)	None	✓	✓			8732.2.a.a	$1$	$2$	\(0\)	\(-1\)	\(2\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-3q^{7}-2q^{9}-5q^{11}+\cdots\)
8732.2.a.b	$8732$	$2$	8732.a	1.a	$1$	$1$	$1$	$69.725$	\(\Q\)	None	✓	✓			8732.2.a.b	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
8732.2.a.c	$8732$	$2$	8732.a	1.a	$1$	$41$	$41$	$69.725$		None	✓	✓	✓		8732.2.a.c	$1$	$0$	\(0\)	\(7\)	\(5\)	\(13\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8732.2.a.d	$8732$	$2$	8732.a	1.a	$1$	$42$	$42$	$69.725$		None	✓	✓	✓	✓	8732.2.a.d	$1$	$1$	\(0\)	\(-9\)	\(-3\)	\(-24\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8732.2.a.e	$8732$	$2$	8732.a	1.a	$1$	$44$	$44$	$69.725$		None	✓	✓	✓		8732.2.a.e	$1$	$0$	\(0\)	\(10\)	\(1\)	\(25\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
8732.2.a.f	$8732$	$2$	8732.a	1.a	$1$	$45$	$45$	$69.725$		None	✓	✓	✓	✓	8732.2.a.f	$1$	$1$	\(0\)	\(-7\)	\(-3\)	\(-14\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8732))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8732)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(236))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2183))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4366))\)\(^{\oplus 2}\)