LMFDB - Space of modular forms of level 8330, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 8330 = 2 \cdot 5 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8330.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 75 $
Sturm bound:			$3024$
Trace bound:			$13$
Distinguishing $T_p$:			$3$, $11$, $13$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8330))$.

	Total	New	Old
Modular forms	1544	216	1328
Cusp forms	1481	216	1265
Eisenstein series	63	0	63

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

$2$	$5$	$7$	$17$	Fricke	Total			Cusp			Eisenstein
$2$	$5$	$7$	$17$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$90$	$10$	$80$	$87$	$10$	$77$	$3$	$0$	$3$
$+$	$+$	$+$	$-$	$-$	$102$	$16$	$86$	$98$	$16$	$82$	$4$	$0$	$4$
$+$	$+$	$-$	$+$	$-$	$102$	$17$	$85$	$98$	$17$	$81$	$4$	$0$	$4$
$+$	$+$	$-$	$-$	$+$	$92$	$11$	$81$	$88$	$11$	$77$	$4$	$0$	$4$
$+$	$-$	$+$	$+$	$-$	$98$	$14$	$84$	$94$	$14$	$80$	$4$	$0$	$4$
$+$	$-$	$+$	$-$	$+$	$94$	$12$	$82$	$90$	$12$	$78$	$4$	$0$	$4$
$+$	$-$	$-$	$+$	$+$	$94$	$14$	$80$	$90$	$14$	$76$	$4$	$0$	$4$
$+$	$-$	$-$	$-$	$-$	$100$	$14$	$86$	$96$	$14$	$82$	$4$	$0$	$4$
$-$	$+$	$+$	$+$	$-$	$100$	$15$	$85$	$96$	$15$	$81$	$4$	$0$	$4$
$-$	$+$	$+$	$-$	$+$	$92$	$9$	$83$	$88$	$9$	$79$	$4$	$0$	$4$
$-$	$+$	$-$	$+$	$+$	$94$	$14$	$80$	$90$	$14$	$76$	$4$	$0$	$4$
$-$	$+$	$-$	$-$	$-$	$100$	$17$	$83$	$96$	$17$	$79$	$4$	$0$	$4$
$-$	$-$	$+$	$+$	$+$	$96$	$9$	$87$	$92$	$9$	$83$	$4$	$0$	$4$
$-$	$-$	$+$	$-$	$-$	$96$	$19$	$77$	$92$	$19$	$73$	$4$	$0$	$4$
$-$	$-$	$-$	$+$	$-$	$98$	$17$	$81$	$94$	$17$	$77$	$4$	$0$	$4$
$-$	$-$	$-$	$-$	$+$	$96$	$8$	$88$	$92$	$8$	$84$	$4$	$0$	$4$
Plus space				$+$	$748$	$87$	$661$	$717$	$87$	$630$	$31$	$0$	$31$
Minus space				$-$	$796$	$129$	$667$	$764$	$129$	$635$	$32$	$0$	$32$

Trace form

$ 216 q - 4 q^{3} + 216 q^{4} - 2 q^{5} - 4 q^{6} + 204 q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 216 q^{16} - 4 q^{17} - 8 q^{18} - 20 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} - 4 q^{24} + 216 q^{25}+ \cdots + 4 q^{99}+O(q^{100}) $

216 * q - 4 * q^3 + 216 * q^4 - 2 * q^5 - 4 * q^6 + 204 * q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 216 * q^16 - 4 * q^17 - 8 * q^18 - 20 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 - 4 * q^24 + 216 * q^25 - 4 * q^26 + 8 * q^27 + 20 * q^29 - 4 * q^30 - 8 * q^31 + 16 * q^33 + 204 * q^36 + 84 * q^37 + 16 * q^38 + 112 * q^39 - 2 * q^40 + 8 * q^41 + 88 * q^43 - 4 * q^44 - 10 * q^45 - 8 * q^46 + 32 * q^47 - 4 * q^48 - 16 * q^52 - 16 * q^54 + 80 * q^57 + 28 * q^58 - 36 * q^59 - 20 * q^61 + 216 * q^64 + 12 * q^65 - 8 * q^66 + 72 * q^67 - 4 * q^68 - 32 * q^71 - 8 * q^72 - 32 * q^73 + 4 * q^74 - 4 * q^75 - 20 * q^76 - 24 * q^78 + 120 * q^79 - 2 * q^80 + 192 * q^81 + 8 * q^82 + 16 * q^83 + 2 * q^85 + 16 * q^87 + 4 * q^88 + 28 * q^89 + 6 * q^90 + 8 * q^92 + 120 * q^93 - 4 * q^94 - 4 * q^96 - 24 * q^97 + 4 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8330))$ 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	5	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8330.2.a.a	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				170.2.a.d	$1$	$1$	$-1$	$-3$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{8}+\cdots$
8330.2.a.b	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.f	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
8330.2.a.c	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.a.b	$1$	$0$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
8330.2.a.d	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				170.2.a.c	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
8330.2.a.e	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.g	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
8330.2.a.f	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.a.c	$1$	$0$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
8330.2.a.g	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓	✓			8330.2.a.g	$1$	$0$	$-1$	$0$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots$
8330.2.a.h	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.a.a	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots$
8330.2.a.i	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓	✓			8330.2.a.g	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots$
8330.2.a.j	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.f	$1$	$0$	$-1$	$1$	$1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
8330.2.a.k	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.g	$1$	$0$	$-1$	$1$	$1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
8330.2.a.l	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				170.2.a.b	$1$	$0$	$-1$	$2$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots$
8330.2.a.m	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				170.2.a.a	$1$	$1$	$-1$	$2$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-q^{8}+\cdots$
8330.2.a.n	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.a	$1$	$1$	$1$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+q^{8}+\cdots$
8330.2.a.o	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.e	$1$	$0$	$1$	$-1$	$-1$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
8330.2.a.p	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.d	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8330.2.a.q	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				170.2.a.e	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8330.2.a.r	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.b	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8330.2.a.s	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.c	$1$	$1$	$1$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots$
8330.2.a.t	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.a.f	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
8330.2.a.u	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.c	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
8330.2.a.v	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.d	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
8330.2.a.w	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.a.e	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
8330.2.a.x	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.b	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
8330.2.a.y	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.e	$1$	$1$	$1$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
8330.2.a.z	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.i.a	$1$	$0$	$1$	$2$	$-1$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots$
8330.2.a.ba	$8330$	$2$	8330.a	1.a	$1$	$1$	$1$	$66.515$	$\Q$	None	✓				1190.2.a.d	$1$	$0$	$1$	$3$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}+q^{8}+\cdots$
8330.2.a.bb	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{2}) $	None	✓	✓			8330.2.a.bb	$1$	$0$	$-2$	$-4$	$-2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{8}+\cdots$
8330.2.a.bc	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{2}) $	None	✓				1190.2.i.h	$1$	$1$	$-2$	$-4$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-2+\beta )q^{3}+q^{4}+q^{5}+(2+\cdots)q^{6}+\cdots$
8330.2.a.bd	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{17}) $	None	✓				1190.2.i.i	$1$	$1$	$-2$	$-1$	$-2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{8}+\cdots$
8330.2.a.be	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{5}) $	None	✓				1190.2.a.h	$1$	$1$	$-2$	$-1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{8}+\cdots$
8330.2.a.bf	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{17}) $	None	✓				1190.2.i.i	$1$	$0$	$-2$	$1$	$2$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots$
8330.2.a.bg	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{17}) $	None	✓				1190.2.a.g	$1$	$0$	$-2$	$1$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots$
8330.2.a.bh	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{2}) $	None	✓				1190.2.i.h	$1$	$0$	$-2$	$4$	$-2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(2+\beta )q^{3}+q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots$
8330.2.a.bi	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{2}) $	None	✓	✓			8330.2.a.bb	$1$	$0$	$-2$	$4$	$2$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-q^{8}+\cdots$
8330.2.a.bj	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{5}) $	None	✓	✓			8330.2.a.bj	$1$	$1$	$2$	$-1$	$2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+q^{8}+\cdots$
8330.2.a.bk	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{21}) $	None	✓				1190.2.a.i	$1$	$1$	$2$	$-1$	$2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+q^{8}+\cdots$
8330.2.a.bl	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{21}) $	None	✓	✓			8330.2.a.bl	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots$
8330.2.a.bm	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{2}) $	None	✓	✓			8330.2.a.bm	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2\beta q^{3}+q^{4}-q^{5}+2\beta q^{6}+\cdots$
8330.2.a.bn	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{21}) $	None	✓	✓			8330.2.a.bl	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
8330.2.a.bo	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{2}) $	None	✓	✓			8330.2.a.bm	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2\beta q^{3}+q^{4}+q^{5}+2\beta q^{6}+\cdots$
8330.2.a.bp	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{5}) $	None	✓	✓			8330.2.a.bj	$1$	$1$	$2$	$1$	$-2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{8}+\cdots$
8330.2.a.bq	$8330$	$2$	8330.a	1.a	$1$	$2$	$2$	$66.515$	$\Q(\sqrt{17}) $	None	✓				170.2.a.f	$1$	$1$	$2$	$1$	$-2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{8}+\cdots$
8330.2.a.br	$8330$	$2$	8330.a	1.a	$1$	$3$	$3$	$66.515$	3.3.469.1	None	✓	✓			8330.2.a.br	$1$	$1$	$-3$	$-1$	$3$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8330.2.a.bs	$8330$	$2$	8330.a	1.a	$1$	$3$	$3$	$66.515$	3.3.837.1	None	✓				1190.2.a.l	$1$	$0$	$-3$	$0$	$3$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8330.2.a.bt	$8330$	$2$	8330.a	1.a	$1$	$3$	$3$	$66.515$	3.3.469.1	None	✓	✓			8330.2.a.br	$1$	$1$	$-3$	$1$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.bu	$8330$	$2$	8330.a	1.a	$1$	$3$	$3$	$66.515$	3.3.2597.1	None	✓				1190.2.a.j	$1$	$1$	$-3$	$1$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.bv	$8330$	$2$	8330.a	1.a	$1$	$3$	$3$	$66.515$	3.3.3229.1	None	✓				1190.2.a.k	$1$	$0$	$-3$	$1$	$-3$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.bw	$8330$	$2$	8330.a	1.a	$1$	$3$	$3$	$66.515$	3.3.229.1	None	✓				1190.2.a.m	$1$	$1$	$3$	$-3$	$-3$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
8330.2.a.bx	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.44688.2	None	✓				1190.2.i.l	$1$	$1$	$-4$	$-2$	$-4$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8330.2.a.by	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.44496.1	None	✓				1190.2.i.m	$1$	$0$	$-4$	$-2$	$-4$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots$
8330.2.a.bz	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.176652.1	None	✓	✓			8330.2.a.bz	$1$	$0$	$-4$	$-1$	$-4$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8330.2.a.ca	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.176652.1	None	✓	✓			8330.2.a.bz	$1$	$0$	$-4$	$1$	$4$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.cb	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.44688.2	None	✓				1190.2.i.l	$1$	$0$	$-4$	$2$	$4$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.cc	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.44496.1	None	✓		✓		1190.2.i.m	$1$	$1$	$-4$	$2$	$4$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
8330.2.a.cd	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.11344.1	None	✓				1190.2.i.k	$1$	$1$	$4$	$-2$	$-4$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}-q^{5}+\beta _{2}q^{6}+\cdots$
8330.2.a.ce	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓			8330.2.a.ce	$1$	$1$	$4$	$-2$	$4$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots$
8330.2.a.cf	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.16448.2	None	✓				1190.2.i.j	$1$	$1$	$4$	$-2$	$4$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.cg	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.109621.1	None	✓				1190.2.a.n	$1$	$0$	$4$	$-2$	$4$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
8330.2.a.ch	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.43820.1	None	✓	✓			8330.2.a.ch	$1$	$0$	$4$	$-1$	$-4$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{1}+\beta _{3})q^{3}+q^{4}-q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots$
8330.2.a.ci	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.43820.1	None	✓	✓			8330.2.a.ch	$1$	$0$	$4$	$1$	$4$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+q^{5}+\cdots$
8330.2.a.cj	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓			8330.2.a.ce	$1$	$1$	$4$	$2$	$-4$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}-q^{5}+\beta _{2}q^{6}+\cdots$
8330.2.a.ck	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.16448.2	None	✓				1190.2.i.j	$1$	$0$	$4$	$2$	$-4$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8330.2.a.cl	$8330$	$2$	8330.a	1.a	$1$	$4$	$4$	$66.515$	4.4.11344.1	None	✓				1190.2.i.k	$1$	$0$	$4$	$2$	$4$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots$
8330.2.a.cm	$8330$	$2$	8330.a	1.a	$1$	$5$	$5$	$66.515$	5.5.9251432.1	None	✓		✓		1190.2.a.o	$1$	$0$	$5$	$-2$	$-5$	$0$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.cn	$8330$	$2$	8330.a	1.a	$1$	$6$	$6$	$66.515$	6.6.12694016.1	None	✓	✓			8330.2.a.cn	$1$	$1$	$-6$	$-2$	$6$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots$
8330.2.a.co	$8330$	$2$	8330.a	1.a	$1$	$6$	$6$	$66.515$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓				1190.2.i.n	$1$	$1$	$-6$	$-1$	$6$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8330.2.a.cp	$8330$	$2$	8330.a	1.a	$1$	$6$	$6$	$66.515$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓		✓		1190.2.i.n	$1$	$0$	$-6$	$1$	$-6$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.cq	$8330$	$2$	8330.a	1.a	$1$	$6$	$6$	$66.515$	6.6.12694016.1	None	✓	✓	✓		8330.2.a.cn	$1$	$1$	$-6$	$2$	$-6$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}+\beta _{2}q^{6}+\cdots$
8330.2.a.cr	$8330$	$2$	8330.a	1.a	$1$	$7$	$7$	$66.515$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1190.2.i.o	$1$	$1$	$7$	$-1$	$-7$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.cs	$8330$	$2$	8330.a	1.a	$1$	$7$	$7$	$66.515$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				1190.2.i.o	$1$	$0$	$7$	$1$	$7$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8330.2.a.ct	$8330$	$2$	8330.a	1.a	$1$	$8$	$8$	$66.515$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		8330.2.a.ct	$1$	$0$	$-8$	$-2$	$8$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$
8330.2.a.cu	$8330$	$2$	8330.a	1.a	$1$	$8$	$8$	$66.515$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		8330.2.a.ct	$1$	$0$	$-8$	$2$	$-8$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots$
8330.2.a.cv	$8330$	$2$	8330.a	1.a	$1$	$10$	$10$	$66.515$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		8330.2.a.cv	$1$	$0$	$10$	$-2$	$-10$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8330.2.a.cw	$8330$	$2$	8330.a	1.a	$1$	$10$	$10$	$66.515$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		8330.2.a.cv	$1$	$0$	$10$	$2$	$10$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8330))$ 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:	\( N \)	\(=\)	\( 8330 = 2 \cdot 5 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8330.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 75 \)
Sturm bound:			\(3024\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\), \(19\)

\(2\)	\(5\)	\(7\)	\(17\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(5\)	\(7\)	\(17\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(90\)	\(10\)	\(80\)	\(87\)	\(10\)	\(77\)	\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(102\)	\(16\)	\(86\)	\(98\)	\(16\)	\(82\)	\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(102\)	\(17\)	\(85\)	\(98\)	\(17\)	\(81\)	\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(92\)	\(11\)	\(81\)	\(88\)	\(11\)	\(77\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(98\)	\(14\)	\(84\)	\(94\)	\(14\)	\(80\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(94\)	\(12\)	\(82\)	\(90\)	\(12\)	\(78\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(94\)	\(14\)	\(80\)	\(90\)	\(14\)	\(76\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(100\)	\(14\)	\(86\)	\(96\)	\(14\)	\(82\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(100\)	\(15\)	\(85\)	\(96\)	\(15\)	\(81\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(92\)	\(9\)	\(83\)	\(88\)	\(9\)	\(79\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(94\)	\(14\)	\(80\)	\(90\)	\(14\)	\(76\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(100\)	\(17\)	\(83\)	\(96\)	\(17\)	\(79\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(96\)	\(9\)	\(87\)	\(92\)	\(9\)	\(83\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(96\)	\(19\)	\(77\)	\(92\)	\(19\)	\(73\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(98\)	\(17\)	\(81\)	\(94\)	\(17\)	\(77\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(96\)	\(8\)	\(88\)	\(92\)	\(8\)	\(84\)	\(4\)	\(0\)	\(4\)
Plus space				\(+\)	\(748\)	\(87\)	\(661\)	\(717\)	\(87\)	\(630\)	\(31\)	\(0\)	\(31\)
Minus space				\(-\)	\(796\)	\(129\)	\(667\)	\(764\)	\(129\)	\(635\)	\(32\)	\(0\)	\(32\)

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8330))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8330))\) 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	8330.2.a

Level	$8330$
Weight	$2$
Character orbit	8330.a
Rep. character	$\chi_{8330}(1,\cdot)$
Character field	$\Q$
Dimension	$216$
Newform subspaces	$75$
Sturm bound	$3024$
Trace bound	$13$