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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(3\)	\(3\)	\(0\)		\(3\)	\(3\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(7\)	\(5\)	\(2\)		\(6\)	\(5\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(5\)	\(3\)	\(2\)		\(4\)	\(3\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(8\)	\(5\)	\(3\)		\(7\)	\(5\)	\(2\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(12\)	\(8\)	\(4\)		\(10\)	\(8\)	\(2\)		\(2\)	\(0\)	\(2\)

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 + 6 * q^10 - 3 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^14 - 2 * q^15 + 31 * q^16 + q^17 - 17 * q^18 - 18 * q^20 - 24 * q^21 + q^22 - 18 * q^23 - 16 * q^24 + 21 * q^25 + 26 * q^26 - 14 * q^27 + 4 * q^28 - 2 * q^29 - 22 * q^31 - 5 * q^32 + 2 * q^33 - q^34 + 8 * q^35 - q^36 - 20 * q^38 - 8 * q^39 + 26 * q^40 + 22 * q^41 + 16 * q^42 - 8 * q^43 - 3 * q^44 + 14 * q^45 + 6 * q^47 - 8 * q^48 - 9 * q^49 + q^50 + 4 * q^51 - 70 * q^52 + 12 * q^53 + 52 * q^54 - 8 * q^56 - 8 * q^57 + 22 * q^58 + 8 * q^59 - 20 * q^60 - 14 * q^61 + 32 * q^62 + 44 * q^63 + 39 * q^64 + 20 * q^65 - 8 * q^66 - 12 * q^67 + 7 * q^68 + 26 * q^69 - 48 * q^70 + 18 * q^71 - 49 * q^72 + 10 * q^73 + 46 * q^74 + 20 * q^75 - 24 * q^76 + 6 * q^77 + 12 * q^78 - 12 * q^79 - 98 * q^80 - 35 * q^81 - 34 * q^82 + 40 * q^83 - 76 * q^84 + 6 * q^85 - 28 * q^86 + 8 * q^87 - 15 * q^88 + 2 * q^89 - 2 * q^90 - 8 * q^91 - 48 * q^92 + 26 * q^93 - 8 * q^94 + 28 * q^95 - 32 * q^96 + 12 * q^97 + 7 * q^98 - 9 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	17
187.2.a.a	$187$	$2$	187.a	1.a	$1$	$1$	$1$	$1.493$	\(\Q\)	None	✓	✓			187.2.a.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}+2q^{7}-2q^{9}+\cdots\)
187.2.a.b	$187$	$2$	187.a	1.a	$1$	$1$	$1$	$1.493$	\(\Q\)	None	✓	✓			187.2.a.b	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+4q^{5}-5q^{7}-3q^{9}+\cdots\)
187.2.a.c	$187$	$2$	187.a	1.a	$1$	$2$	$2$	$1.493$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	187.2.a.c	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-\beta q^{3}+(2-2\beta )q^{4}+\cdots\)
187.2.a.d	$187$	$2$	187.a	1.a	$1$	$2$	$2$	$1.493$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		187.2.a.d	$1$	$0$	\(4\)	\(-1\)	\(1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+\beta )q^{3}+2q^{4}+(1-\beta )q^{5}+\cdots\)
187.2.a.e	$187$	$2$	187.a	1.a	$1$	$3$	$3$	$1.493$	3.3.148.1	None	✓	✓	✓	✓	187.2.a.e	$1$	$1$	\(-2\)	\(-3\)	\(-7\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
187.2.a.f	$187$	$2$	187.a	1.a	$1$	$4$	$4$	$1.493$	4.4.33844.1	None	✓	✓	✓		187.2.a.f	$1$	$0$	\(1\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)

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

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