Space of modular forms of level 87, weight 2, and trivial character

• Label: 87.2.a
• Level: $87$
• Weight: $2$
• Character orbit: 87.a
• Rep. character: $\chi_{87}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(20\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(87))\).

	Total	New	Old
Modular forms	12	5	7
Cusp forms	9	5	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.

\(3\)	\(29\)	Fricke	Dim
\(+\)	\(-\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(2\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(5\)

Trace form

5 * q + 3 * q^2 - q^3 + 5 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 10 * q^10 - 4 * q^11 - 7 * q^12 + 2 * q^13 - 12 * q^14 + 2 * q^15 - 7 * q^16 + 10 * q^17 + 3 * q^18 - 12 * q^19 - 22 * q^20 - 8 * q^21 - 6 * q^22 + 4 * q^23 - 3 * q^24 + 19 * q^25 - 2 * q^26 - q^27 + 10 * q^28 + q^29 + 2 * q^30 - q^32 + 12 * q^33 + 4 * q^34 - 4 * q^35 + 5 * q^36 + 14 * q^37 + 20 * q^38 - 6 * q^39 - 22 * q^40 + 2 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 + 2 * q^45 + 12 * q^46 - 16 * q^47 + q^48 + q^49 + 45 * q^50 + 2 * q^51 + 8 * q^52 + 26 * q^53 - q^54 - 16 * q^55 + 24 * q^56 - 8 * q^57 + q^58 - 20 * q^59 + 10 * q^60 - 2 * q^61 - 20 * q^62 - q^64 + 20 * q^66 - 4 * q^67 + 26 * q^68 - 8 * q^69 - 20 * q^70 - 20 * q^71 + 3 * q^72 + 10 * q^73 - 18 * q^74 - 15 * q^75 + 12 * q^76 - 16 * q^77 + 20 * q^78 - 32 * q^79 - 26 * q^80 + 5 * q^81 - 30 * q^82 - 20 * q^83 - 16 * q^84 - 36 * q^85 + 32 * q^86 - 5 * q^87 - 8 * q^88 + 2 * q^89 - 10 * q^90 - 8 * q^91 + 12 * q^92 - 12 * q^93 - 2 * q^94 - 32 * q^95 - 17 * q^96 + 10 * q^97 - 9 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(87))\) 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	29
87.2.a.a	$87$	$2$	87.a	1.a	$1$	$2$	$2$	$0.695$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	87.2.a.a	$1$	$0$	\(1\)	\(2\)	\(2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
87.2.a.b	$87$	$2$	87.a	1.a	$1$	$3$	$3$	$0.695$	3.3.229.1	None	✓	✓	✓	✓	87.2.a.b	$1$	$0$	\(2\)	\(-3\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}-2\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(87))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(87)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)