Space of modular forms of level 5032, weight 2, and trivial character

• Label: 5032.2.a
• Level: $5032$
• Weight: $2$
• Character orbit: 5032.a
• Rep. character: $\chi_{5032}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $11$
• Sturm bound: $1368$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 5032 = 2^{3} \cdot 17 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5032.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1368\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5032))\).

	Total	New	Old
Modular forms	692	144	548
Cusp forms	677	144	533
Eisenstein series	15	0	15

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

\(2\)	\(17\)	\(37\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(84\)	\(17\)	\(67\)		\(83\)	\(17\)	\(66\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(87\)	\(20\)	\(67\)		\(85\)	\(20\)	\(65\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(89\)	\(22\)	\(67\)		\(87\)	\(22\)	\(65\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(86\)	\(13\)	\(73\)		\(84\)	\(13\)	\(71\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(89\)	\(16\)	\(73\)		\(87\)	\(16\)	\(71\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)		\(86\)	\(21\)	\(65\)		\(84\)	\(21\)	\(63\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)		\(84\)	\(18\)	\(66\)		\(82\)	\(18\)	\(64\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)		\(87\)	\(17\)	\(70\)		\(85\)	\(17\)	\(68\)		\(2\)	\(0\)	\(2\)
Plus space			\(+\)		\(340\)	\(69\)	\(271\)		\(333\)	\(69\)	\(264\)		\(7\)	\(0\)	\(7\)
Minus space			\(-\)		\(352\)	\(75\)	\(277\)		\(344\)	\(75\)	\(269\)		\(8\)	\(0\)	\(8\)

Trace form

144 * q - 4 * q^5 - 8 * q^7 + 136 * q^9 - 24 * q^15 - 4 * q^17 + 8 * q^21 - 24 * q^23 + 168 * q^25 + 12 * q^29 - 16 * q^31 - 8 * q^33 - 2 * q^37 - 16 * q^39 - 12 * q^41 - 12 * q^45 - 8 * q^47 + 144 * q^49 + 12 * q^51 - 12 * q^53 - 16 * q^55 + 40 * q^57 - 52 * q^61 - 48 * q^63 + 24 * q^67 + 40 * q^69 - 8 * q^71 + 4 * q^73 - 20 * q^75 - 32 * q^79 + 184 * q^81 - 36 * q^83 + 16 * q^87 + 48 * q^89 + 8 * q^91 - 16 * q^93 + 32 * q^95 + 16 * q^97 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5032))\) 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	17	37
5032.2.a.a	$5032$	$2$	5032.a	1.a	$1$	$2$	$2$	$40.181$	\(\Q(\sqrt{2}) \)	None	✓	✓			5032.2.a.a	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+(-1+2\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
5032.2.a.b	$5032$	$2$	5032.a	1.a	$1$	$4$	$4$	$40.181$	4.4.6809.1	None	✓	✓			5032.2.a.b	$1$	$1$	\(0\)	\(-4\)	\(-6\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}+\cdots\)
5032.2.a.c	$5032$	$2$	5032.a	1.a	$1$	$4$	$4$	$40.181$	4.4.215761.1	None	✓	✓			5032.2.a.c	$1$	$1$	\(0\)	\(4\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+(-1+\beta _{1})q^{7}-2q^{9}+\cdots\)
5032.2.a.d	$5032$	$2$	5032.a	1.a	$1$	$9$	$9$	$40.181$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓		5032.2.a.d	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$5$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
5032.2.a.e	$5032$	$2$	5032.a	1.a	$1$	$11$	$11$	$40.181$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓		5032.2.a.e	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{7}q^{3}-\beta _{1}q^{5}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
5032.2.a.f	$5032$	$2$	5032.a	1.a	$1$	$16$	$16$	$40.181$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	5032.2.a.f	$1$	$0$	\(0\)	\(1\)	\(0\)	\(10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{10}q^{5}+(1-\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
5032.2.a.g	$5032$	$2$	5032.a	1.a	$1$	$17$	$17$	$40.181$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	5032.2.a.g	$1$	$0$	\(0\)	\(4\)	\(3\)	\(10\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(1+\beta _{6})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
5032.2.a.h	$5032$	$2$	5032.a	1.a	$1$	$18$	$18$	$40.181$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓	✓	5032.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{7}q^{5}+(-1+\beta _{13})q^{7}+\cdots\)
5032.2.a.i	$5032$	$2$	5032.a	1.a	$1$	$20$	$20$	$40.181$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	5032.2.a.i	$1$	$0$	\(0\)	\(2\)	\(5\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{14}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
5032.2.a.j	$5032$	$2$	5032.a	1.a	$1$	$21$	$21$	$40.181$		None	✓	✓	✓	✓	5032.2.a.j	$1$	$1$	\(0\)	\(-5\)	\(-2\)	\(-12\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
5032.2.a.k	$5032$	$2$	5032.a	1.a	$1$	$22$	$22$	$40.181$		None	✓	✓	✓	✓	5032.2.a.k	$1$	$0$	\(0\)	\(5\)	\(2\)	\(-5\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5032)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(629))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1258))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2516))\)\(^{\oplus 2}\)