Space of modular forms of level 1587, weight 4, and trivial character

• Label: 1587.4.a
• Level: $1587$
• Weight: $4$
• Character orbit: 1587.a
• Rep. character: $\chi_{1587}(1,\cdot)$
• Character field: $\Q$
• Dimension: $252$
• Newform subspaces: $23$
• Sturm bound: $736$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1587.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(736\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1587))\).

	Total	New	Old
Modular forms	576	252	324
Cusp forms	528	252	276
Eisenstein series	48	0	48

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

\(3\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(64\)
\(+\)	\(-\)	\(-\)	\(62\)
\(-\)	\(+\)	\(-\)	\(56\)
\(-\)	\(-\)	\(+\)	\(70\)
Plus space		\(+\)	\(134\)
Minus space		\(-\)	\(118\)

Trace form

\( 252 q + 4 q^{2} + 1000 q^{4} + 16 q^{5} - 12 q^{6} + 20 q^{7} - 36 q^{8} + 2268 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1587))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	23
1587.4.a.a	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	\(\Q(\sqrt{2}) \)	None	✓	✓			1587.4.a.a	$2$	$1$	\(-6\)	\(6\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+3q^{3}+q^{4}-3\beta q^{5}-9q^{6}+\cdots\)
1587.4.a.b	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	\(\Q(\sqrt{5}) \)	None	✓				69.4.a.a	$1$	$0$	\(-4\)	\(6\)	\(26\)	\(10\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
1587.4.a.c	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	\(\Q(\sqrt{2}) \)	None	✓				69.4.a.b	$1$	$1$	\(-2\)	\(-6\)	\(-8\)	\(28\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
1587.4.a.d	$1587$	$4$	1587.a	1.a	$1$	$2$	$2$	$93.636$	\(\Q(\sqrt{2}) \)	None	✓	✓			1587.4.a.d	$2$	$1$	\(0\)	\(6\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-8q^{4}-9\beta q^{5}+4\beta q^{7}+9q^{9}+\cdots\)
1587.4.a.e	$1587$	$4$	1587.a	1.a	$1$	$4$	$4$	$93.636$	4.4.1140200.1	None	✓				69.4.a.c	$1$	$1$	\(-2\)	\(-12\)	\(2\)	\(-32\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots\)
1587.4.a.f	$1587$	$4$	1587.a	1.a	$1$	$4$	$4$	$93.636$	\(\Q(\zeta_{24})^+\)	None	✓	✓			1587.4.a.f	$2$	$1$	\(0\)	\(-12\)	\(0\)	\(0\)		$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}-2q^{4}+(-2\beta _{2}-2\beta _{3})q^{5}+\cdots\)
1587.4.a.g	$1587$	$4$	1587.a	1.a	$1$	$4$	$4$	$93.636$	4.4.2009704.1	None	✓				69.4.a.d	$1$	$0$	\(4\)	\(12\)	\(-4\)	\(14\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1587.4.a.h	$1587$	$4$	1587.a	1.a	$1$	$5$	$5$	$93.636$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			1587.4.a.h	$1$	$1$	\(-4\)	\(-15\)	\(-18\)	\(25\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1587.4.a.i	$1587$	$4$	1587.a	1.a	$1$	$5$	$5$	$93.636$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			1587.4.a.h	$1$	$1$	\(-4\)	\(-15\)	\(18\)	\(-25\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1587.4.a.j	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	6.6.\(\cdots\).1	None	✓	✓			1587.4.a.j	$2$	$1$	\(0\)	\(-18\)	\(0\)	\(0\)		$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-3q^{3}+(6-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
1587.4.a.k	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			1587.4.a.k	$2$	$1$	\(0\)	\(-18\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{1}+\beta _{4})q^{4}+\cdots\)
1587.4.a.l	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	6.6.52756992.1	None	✓	✓			1587.4.a.l	$2$	$1$	\(2\)	\(18\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+3q^{3}+(10-2\beta _{4}-\beta _{5})q^{4}+\cdots\)
1587.4.a.m	$1587$	$4$	1587.a	1.a	$1$	$6$	$6$	$93.636$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			1587.4.a.m	$2$	$0$	\(4\)	\(18\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(1+\beta _{5})q^{2}+3q^{3}+(4-\beta _{4}+\beta _{5})q^{4}+\cdots\)
1587.4.a.n	$1587$	$4$	1587.a	1.a	$1$	$7$	$7$	$93.636$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1587.4.a.n	$1$	$0$	\(0\)	\(21\)	\(-10\)	\(17\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1587.4.a.o	$1587$	$4$	1587.a	1.a	$1$	$7$	$7$	$93.636$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1587.4.a.n	$1$	$0$	\(0\)	\(21\)	\(10\)	\(-17\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1587.4.a.p	$1587$	$4$	1587.a	1.a	$1$	$10$	$10$	$93.636$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			1587.4.a.p	$2$	$0$	\(4\)	\(-30\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{7})q^{4}+(\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots\)
1587.4.a.q	$1587$	$4$	1587.a	1.a	$1$	$14$	$14$	$93.636$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓			1587.4.a.q	$2$	$0$	\(8\)	\(42\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{2}+3q^{3}+(6-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1587.4.a.r	$1587$	$4$	1587.a	1.a	$1$	$16$	$16$	$93.636$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓			1587.4.a.r	$2$	$1$	\(-8\)	\(48\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{8})q^{2}+3q^{3}+(1-\beta _{12})q^{4}+\cdots\)
1587.4.a.s	$1587$	$4$	1587.a	1.a	$1$	$24$	$24$	$93.636$		None	✓	✓			1587.4.a.s	$2$	$0$	\(8\)	\(-72\)	\(0\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1587.4.a.t	$1587$	$4$	1587.a	1.a	$1$	$30$	$30$	$93.636$		None	✓		✓		69.4.e.a	$1$	$1$	\(0\)	\(90\)	\(-44\)	\(-142\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1587.4.a.u	$1587$	$4$	1587.a	1.a	$1$	$30$	$30$	$93.636$		None	✓		✓		69.4.e.a	$1$	$0$	\(0\)	\(90\)	\(44\)	\(142\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
1587.4.a.v	$1587$	$4$	1587.a	1.a	$1$	$30$	$30$	$93.636$		None	✓		✓		69.4.e.b	$1$	$1$	\(2\)	\(-90\)	\(-52\)	\(2\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
1587.4.a.w	$1587$	$4$	1587.a	1.a	$1$	$30$	$30$	$93.636$		None	✓		✓		69.4.e.b	$1$	$0$	\(2\)	\(-90\)	\(52\)	\(-2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1587))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1587)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 2}\)