Space of modular forms of level 87, weight 2, and Character 87.g

• Label: 87.2.g
• Level: $87$
• Weight: $2$
• Character orbit: 87.g
• Rep. character: $\chi_{87}(7,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(20\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(87, [\chi])\).

	Total	New	Old
Modular forms	72	36	36
Cusp forms	48	36	12
Eisenstein series	24	0	24

Trace form

36 * q - 6 * q^2 - 12 * q^4 - 8 * q^5 - 2 * q^6 - 8 * q^7 - 18 * q^8 - 6 * q^9 - 8 * q^10 + 20 * q^11 - 2 * q^13 - 12 * q^14 + 6 * q^15 + 4 * q^16 - 28 * q^17 - 6 * q^18 - 8 * q^19 + 50 * q^20 + 12 * q^22 - 14 * q^23 - 12 * q^24 + 20 * q^25 + 2 * q^26 + 32 * q^28 - 2 * q^29 + 8 * q^30 - 4 * q^31 + 64 * q^32 - 24 * q^33 - 16 * q^34 + 40 * q^35 - 12 * q^36 + 4 * q^37 - 52 * q^38 - 8 * q^39 - 26 * q^40 - 44 * q^41 - 22 * q^42 - 34 * q^43 - 62 * q^44 + 20 * q^45 - 56 * q^46 + 24 * q^47 + 24 * q^48 - 30 * q^49 + 16 * q^50 + 22 * q^51 + 76 * q^52 + 4 * q^53 - 2 * q^54 - 14 * q^55 + 52 * q^56 + 16 * q^57 + 24 * q^58 - 12 * q^59 + 74 * q^60 - 4 * q^61 + 148 * q^62 + 6 * q^63 - 98 * q^64 + 28 * q^65 + 84 * q^66 - 8 * q^67 + 30 * q^68 + 12 * q^69 + 16 * q^70 + 18 * q^71 - 4 * q^72 + 42 * q^73 - 82 * q^74 - 16 * q^75 - 26 * q^76 - 10 * q^77 - 62 * q^78 - 6 * q^79 - 160 * q^80 - 6 * q^81 + 30 * q^82 - 8 * q^83 - 40 * q^84 - 2 * q^85 - 24 * q^86 + 32 * q^87 - 4 * q^88 - 78 * q^89 - 8 * q^90 - 62 * q^91 - 110 * q^92 - 20 * q^93 - 16 * q^94 - 88 * q^95 + 24 * q^96 - 38 * q^97 + 20 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(87, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
87.2.g.a	$87$	$2$	87.g	29.d	$7$	$18$	$3$	$0.695$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			87.2.g.a	$2$	$0$	\(-4\)	\(-3\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-\beta _{3}+\beta _{9})q^{2}-\beta _{10}q^{3}+(2\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)
87.2.g.b	$87$	$2$	87.g	29.d	$7$	$18$	$3$	$0.695$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			87.2.g.b	$2$	$0$	\(-2\)	\(3\)	\(-7\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{3}q^{2}+\beta _{14}q^{3}+(-\beta _{10}-\beta _{16}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(87, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(87, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)