LMFDB - Space of modular forms of level 8670, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 65 $
Sturm bound:			$3672$
Trace bound:			$13$
Distinguishing $T_p$:			$7$, $11$, $13$, $23$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8670))$.

	Total	New	Old
Modular forms	1908	182	1726
Cusp forms	1765	182	1583
Eisenstein series	143	0	143

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

$2$	$3$	$5$	$17$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$17$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$108$	$11$	$97$	$100$	$11$	$89$	$8$	$0$	$8$
$+$	$+$	$+$	$-$	$-$	$129$	$12$	$117$	$120$	$12$	$108$	$9$	$0$	$9$
$+$	$+$	$-$	$+$	$-$	$126$	$10$	$116$	$117$	$10$	$107$	$9$	$0$	$9$
$+$	$+$	$-$	$-$	$+$	$114$	$12$	$102$	$105$	$12$	$93$	$9$	$0$	$9$
$+$	$-$	$+$	$+$	$-$	$126$	$16$	$110$	$117$	$16$	$101$	$9$	$0$	$9$
$+$	$-$	$+$	$-$	$+$	$114$	$7$	$107$	$105$	$7$	$98$	$9$	$0$	$9$
$+$	$-$	$-$	$+$	$+$	$117$	$8$	$109$	$108$	$8$	$100$	$9$	$0$	$9$
$+$	$-$	$-$	$-$	$-$	$120$	$15$	$105$	$111$	$15$	$96$	$9$	$0$	$9$
$-$	$+$	$+$	$+$	$-$	$117$	$10$	$107$	$108$	$10$	$98$	$9$	$0$	$9$
$-$	$+$	$+$	$-$	$+$	$121$	$12$	$109$	$112$	$12$	$100$	$9$	$0$	$9$
$-$	$+$	$-$	$+$	$+$	$126$	$11$	$115$	$117$	$11$	$106$	$9$	$0$	$9$
$-$	$+$	$-$	$-$	$-$	$113$	$12$	$101$	$104$	$12$	$92$	$9$	$0$	$9$
$-$	$-$	$+$	$+$	$+$	$117$	$8$	$109$	$108$	$8$	$100$	$9$	$0$	$9$
$-$	$-$	$+$	$-$	$-$	$122$	$15$	$107$	$113$	$15$	$98$	$9$	$0$	$9$
$-$	$-$	$-$	$+$	$-$	$117$	$16$	$101$	$108$	$16$	$92$	$9$	$0$	$9$
$-$	$-$	$-$	$-$	$+$	$121$	$7$	$114$	$112$	$7$	$105$	$9$	$0$	$9$
Plus space				$+$	$938$	$76$	$862$	$867$	$76$	$791$	$71$	$0$	$71$
Minus space				$-$	$970$	$106$	$864$	$898$	$106$	$792$	$72$	$0$	$72$

Trace form

$ 182 q + 2 q^{3} + 182 q^{4} + 4 q^{7} + 182 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 8 q^{13} - 4 q^{14} + 182 q^{16} + 4 q^{21} - 4 q^{22} - 8 q^{23} + 182 q^{25} + 12 q^{26} + 2 q^{27} + 4 q^{28} - 24 q^{29}+ \cdots - 4 q^{99}+O(q^{100}) $

182 * q + 2 * q^3 + 182 * q^4 + 4 * q^7 + 182 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 8 * q^13 - 4 * q^14 + 182 * q^16 + 4 * q^21 - 4 * q^22 - 8 * q^23 + 182 * q^25 + 12 * q^26 + 2 * q^27 + 4 * q^28 - 24 * q^29 - 2 * q^30 - 16 * q^31 - 12 * q^33 - 4 * q^35 + 182 * q^36 - 8 * q^37 + 8 * q^38 + 8 * q^39 + 2 * q^40 + 4 * q^41 - 12 * q^42 - 4 * q^44 - 16 * q^47 + 2 * q^48 + 150 * q^49 - 8 * q^52 - 16 * q^53 - 12 * q^55 - 4 * q^56 + 16 * q^57 + 4 * q^58 - 20 * q^59 + 4 * q^61 + 8 * q^62 + 4 * q^63 + 182 * q^64 + 12 * q^65 + 4 * q^66 - 8 * q^67 - 8 * q^69 - 4 * q^70 + 24 * q^71 + 44 * q^73 + 20 * q^74 + 2 * q^75 - 16 * q^77 - 4 * q^78 - 16 * q^79 + 182 * q^81 + 32 * q^82 + 16 * q^83 + 4 * q^84 + 16 * q^86 + 8 * q^87 - 4 * q^88 - 36 * q^89 + 2 * q^90 + 40 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 - 24 * q^95 + 4 * q^97 + 48 * q^98 - 4 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8670))$ 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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8670.2.a.a	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.a	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
8670.2.a.b	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.b	$1$	$0$	$-1$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
8670.2.a.c	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.a.b	$1$	$1$	$-1$	$-1$	$-1$	$2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
8670.2.a.d	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.c.b	$1$	$1$	$-1$	$-1$	$-1$	$2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
8670.2.a.e	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.e	$1$	$1$	$-1$	$-1$	$1$	$-3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
8670.2.a.f	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.f	$1$	$1$	$-1$	$-1$	$1$	$3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$
8670.2.a.g	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				30.2.a.a	$1$	$0$	$-1$	$-1$	$1$	$4$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
8670.2.a.h	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.f	$1$	$2$	$-1$	$1$	$-1$	$-3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots$
8670.2.a.i	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.e	$1$	$0$	$-1$	$1$	$-1$	$3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots$
8670.2.a.j	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.c.b	$1$	$1$	$-1$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
8670.2.a.k	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.a.a	$1$	$1$	$-1$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
8670.2.a.l	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.b	$1$	$1$	$-1$	$1$	$1$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
8670.2.a.m	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.a	$1$	$0$	$-1$	$1$	$1$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
8670.2.a.n	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.a.g	$1$	$0$	$1$	$-1$	$-1$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
8670.2.a.o	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.o	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
8670.2.a.p	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.p	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
8670.2.a.q	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.q	$1$	$1$	$1$	$-1$	$1$	$-3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots$
8670.2.a.r	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.a.f	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8670.2.a.s	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.c.a	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8670.2.a.t	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.t	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
8670.2.a.u	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.t	$1$	$1$	$1$	$1$	$-1$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots$
8670.2.a.v	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.a.e	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
8670.2.a.w	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.c.a	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
8670.2.a.x	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.q	$1$	$0$	$1$	$1$	$-1$	$3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots$
8670.2.a.y	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.a.d	$1$	$0$	$1$	$1$	$1$	$-2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
8670.2.a.z	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.p	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
8670.2.a.ba	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓	✓			8670.2.a.o	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
8670.2.a.bb	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	$\Q$	None	✓				510.2.a.c	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
8670.2.a.bc	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{2}) $	None	✓				510.2.p.b	$1$	$1$	$-2$	$-2$	$-2$	$4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(2+2\beta )q^{7}+\cdots$
8670.2.a.bd	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{2}) $	None	✓				510.2.c.d	$1$	$0$	$-2$	$-2$	$2$	$-4$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
8670.2.a.be	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{6}) $	None	✓				510.2.a.h	$1$	$0$	$-2$	$2$	$-2$	$0$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots$
8670.2.a.bf	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{2}) $	None	✓				510.2.c.d	$1$	$0$	$-2$	$2$	$-2$	$4$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta )q^{7}+\cdots$
8670.2.a.bg	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{2}) $	None	✓				510.2.p.b	$1$	$1$	$-2$	$2$	$2$	$-4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
8670.2.a.bh	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{13}) $	None	✓				510.2.c.c	$1$	$0$	$2$	$-2$	$-2$	$2$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots$
8670.2.a.bi	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{2}) $	None	✓				510.2.p.a	$1$	$1$	$2$	$-2$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2\beta q^{7}+\cdots$
8670.2.a.bj	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{2}) $	None	✓				510.2.p.a	$1$	$1$	$2$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2\beta q^{7}+\cdots$
8670.2.a.bk	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	$\Q(\sqrt{13}) $	None	✓				510.2.c.c	$1$	$0$	$2$	$2$	$2$	$-2$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
8670.2.a.bl	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓			8670.2.a.bl	$1$	$0$	$-3$	$-3$	$-3$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta _{1}q^{7}+\cdots$
8670.2.a.bm	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓			8670.2.a.bm	$1$	$0$	$-3$	$-3$	$3$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$
8670.2.a.bn	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓			8670.2.a.bm	$1$	$1$	$-3$	$3$	$-3$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-\beta _{1}q^{7}+\cdots$
8670.2.a.bo	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		8670.2.a.bl	$1$	$1$	$-3$	$3$	$3$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
8670.2.a.bp	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓			8670.2.a.bp	$1$	$0$	$3$	$-3$	$-3$	$6$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
8670.2.a.bq	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓			8670.2.a.bq	$1$	$0$	$3$	$-3$	$3$	$6$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots$
8670.2.a.br	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓	✓		8670.2.a.bq	$1$	$1$	$3$	$3$	$-3$	$-6$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
8670.2.a.bs	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	$\Q(\zeta_{18})^+$	None	✓	✓			8670.2.a.bp	$1$	$1$	$3$	$3$	$3$	$-6$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
8670.2.a.bt	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\zeta_{16})^+$	None	✓		✓		510.2.p.d	$1$	$0$	$-4$	$-4$	$4$	$0$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$
8670.2.a.bu	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\zeta_{16})^+$	None	✓				510.2.u.b	$1$	$1$	$-4$	$-4$	$4$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(\beta _{1}+\beta _{3})q^{7}+\cdots$
8670.2.a.bv	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\zeta_{16})^+$	None	✓		✓		510.2.u.b	$1$	$1$	$-4$	$4$	$-4$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(\beta _{1}+\beta _{3})q^{7}+\cdots$
8670.2.a.bw	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\zeta_{16})^+$	None	✓				510.2.p.d	$1$	$0$	$-4$	$4$	$-4$	$0$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
8670.2.a.bx	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\sqrt{10 +4 \sqrt{2}})$	None	✓		✓		510.2.p.c	$1$	$0$	$4$	$-4$	$-4$	$-4$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
8670.2.a.by	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\zeta_{16})^+$	None	✓				510.2.u.a	$1$	$1$	$4$	$-4$	$-4$	$8$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots$
8670.2.a.bz	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\zeta_{16})^+$	None	✓		✓		510.2.u.a	$1$	$1$	$4$	$4$	$4$	$-8$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
8670.2.a.ca	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	$\Q(\sqrt{10 +4 \sqrt{2}})$	None	✓				510.2.p.c	$1$	$0$	$4$	$4$	$4$	$4$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{3})q^{7}+\cdots$
8670.2.a.cb	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.204493248.1	None	✓	✓	✓		8670.2.a.cb	$1$	$1$	$-6$	$-6$	$-6$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$
8670.2.a.cc	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.46609344.1	None	✓	✓	✓		8670.2.a.cc	$1$	$1$	$-6$	$-6$	$6$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{5}q^{7}+\cdots$
8670.2.a.cd	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.46609344.1	None	✓	✓	✓		8670.2.a.cc	$1$	$0$	$-6$	$6$	$-6$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{5}q^{7}+\cdots$
8670.2.a.ce	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.204493248.1	None	✓	✓			8670.2.a.cb	$1$	$0$	$-6$	$6$	$6$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
8670.2.a.cf	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.30652992.1	None	✓	✓	✓		8670.2.a.cf	$1$	$1$	$6$	$-6$	$-6$	$-6$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
8670.2.a.cg	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.45769536.1	None	✓	✓	✓		8670.2.a.cg	$1$	$1$	$6$	$-6$	$6$	$-6$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
8670.2.a.ch	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.45769536.1	None	✓	✓			8670.2.a.cg	$1$	$0$	$6$	$6$	$-6$	$6$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
8670.2.a.ci	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.30652992.1	None	✓	✓	✓		8670.2.a.cf	$1$	$0$	$6$	$6$	$6$	$6$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
8670.2.a.cj	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.$\cdots$.1	None	✓		✓		510.2.u.c	$1$	$0$	$-8$	$-8$	$-8$	$-8$	$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
8670.2.a.ck	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.$\cdots$.1	None	✓		✓		510.2.u.c	$1$	$0$	$-8$	$8$	$8$	$8$	$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
8670.2.a.cl	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.$\cdots$.1	None	✓		✓		510.2.u.d	$1$	$0$	$8$	$-8$	$8$	$0$	$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
8670.2.a.cm	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.$\cdots$.1	None	✓		✓		510.2.u.d	$1$	$0$	$8$	$8$	$-8$	$0$	$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8670))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 65 \)
Sturm bound:			\(3672\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(23\)

\(2\)	\(3\)	\(5\)	\(17\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(17\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(108\)	\(11\)	\(97\)	\(100\)	\(11\)	\(89\)	\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(129\)	\(12\)	\(117\)	\(120\)	\(12\)	\(108\)	\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(126\)	\(10\)	\(116\)	\(117\)	\(10\)	\(107\)	\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(114\)	\(12\)	\(102\)	\(105\)	\(12\)	\(93\)	\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(126\)	\(16\)	\(110\)	\(117\)	\(16\)	\(101\)	\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(114\)	\(7\)	\(107\)	\(105\)	\(7\)	\(98\)	\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(117\)	\(8\)	\(109\)	\(108\)	\(8\)	\(100\)	\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(120\)	\(15\)	\(105\)	\(111\)	\(15\)	\(96\)	\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(117\)	\(10\)	\(107\)	\(108\)	\(10\)	\(98\)	\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(121\)	\(12\)	\(109\)	\(112\)	\(12\)	\(100\)	\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(126\)	\(11\)	\(115\)	\(117\)	\(11\)	\(106\)	\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(113\)	\(12\)	\(101\)	\(104\)	\(12\)	\(92\)	\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(117\)	\(8\)	\(109\)	\(108\)	\(8\)	\(100\)	\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(122\)	\(15\)	\(107\)	\(113\)	\(15\)	\(98\)	\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(117\)	\(16\)	\(101\)	\(108\)	\(16\)	\(92\)	\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(121\)	\(7\)	\(114\)	\(112\)	\(7\)	\(105\)	\(9\)	\(0\)	\(9\)
Plus space				\(+\)	\(938\)	\(76\)	\(862\)	\(867\)	\(76\)	\(791\)	\(71\)	\(0\)	\(71\)
Minus space				\(-\)	\(970\)	\(106\)	\(864\)	\(898\)	\(106\)	\(792\)	\(72\)	\(0\)	\(72\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8670))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8670))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	8670.2.a

Level	$8670$
Weight	$2$
Character orbit	8670.a
Rep. character	$\chi_{8670}(1,\cdot)$
Character field	$\Q$
Dimension	$182$
Newform subspaces	$65$
Sturm bound	$3672$
Trace bound	$13$