Space of modular forms of level 187, weight 2, and trivial character

• Label: 187.2.a
• Level: $187$
• Weight: $2$
• Character orbit: 187.a
• Rep. character: $\chi_{187}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $6$
• Sturm bound: $36$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(36\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(187))\).

	Total	New	Old
Modular forms	20	13	7
Cusp forms	17	13	4
Eisenstein series	3	0	3

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

\(11\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(5\)
Minus space		\(-\)	\(8\)

Trace form

\( 13 q + 3 q^{2} - 2 q^{3} + 15 q^{4} - 8 q^{6} - 4 q^{7} - 9 q^{8} + 11 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(187))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	17
187.2.a.a	$187$	$2$	187.a	1.a	$1$	$1$	$1$	$1.493$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}+2q^{7}-2q^{9}+\cdots\)
187.2.a.b	$187$	$2$	187.a	1.a	$1$	$1$	$1$	$1.493$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+4q^{5}-5q^{7}-3q^{9}+\cdots\)
187.2.a.c	$187$	$2$	187.a	1.a	$1$	$2$	$2$	$1.493$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-\beta q^{3}+(2-2\beta )q^{4}+\cdots\)
187.2.a.d	$187$	$2$	187.a	1.a	$1$	$2$	$2$	$1.493$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(4\)	\(-1\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+\beta )q^{3}+2q^{4}+(1-\beta )q^{5}+\cdots\)
187.2.a.e	$187$	$2$	187.a	1.a	$1$	$3$	$3$	$1.493$	3.3.148.1	None	✓	$1$	$1$	\(-2\)	\(-3\)	\(-7\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
187.2.a.f	$187$	$2$	187.a	1.a	$1$	$4$	$4$	$1.493$	4.4.33844.1	None	✓	$1$	$0$	\(1\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(187))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(187)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)