LMFDB - Space of modular forms of level 8085, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 68 $
Sturm bound:			$2688$
Trace bound:			$17$
Distinguishing $T_p$:			$2$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8085))$.

	Total	New	Old
Modular forms	1376	272	1104
Cusp forms	1313	272	1041
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.

$3$	$5$	$7$	$11$	Fricke	Dim
$+$	$+$	$+$	$+$	$+$	$19$
$+$	$+$	$+$	$-$	$-$	$17$
$+$	$+$	$-$	$+$	$-$	$14$
$+$	$+$	$-$	$-$	$+$	$20$
$+$	$-$	$+$	$+$	$-$	$15$
$+$	$-$	$+$	$-$	$+$	$13$
$+$	$-$	$-$	$+$	$+$	$20$
$+$	$-$	$-$	$-$	$-$	$20$
$-$	$+$	$+$	$+$	$-$	$18$
$-$	$+$	$+$	$-$	$+$	$12$
$-$	$+$	$-$	$+$	$+$	$15$
$-$	$+$	$-$	$-$	$-$	$21$
$-$	$-$	$+$	$+$	$+$	$14$
$-$	$-$	$+$	$-$	$-$	$24$
$-$	$-$	$-$	$+$	$-$	$21$
$-$	$-$	$-$	$-$	$+$	$9$
Plus space				$+$	$122$
Minus space				$-$	$150$

Trace form

$ 272 q - 4 q^{3} + 272 q^{4} + 4 q^{6} + 272 q^{9} + O(q^{10}) $

$ 272 q - 4 q^{3} + 272 q^{4} + 4 q^{6} + 272 q^{9} + 4 q^{10} - 12 q^{12} - 16 q^{13} + 4 q^{15} + 264 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{20} + 4 q^{22} + 16 q^{23} + 12 q^{24} + 272 q^{25} - 40 q^{26} - 4 q^{27} - 40 q^{32} - 4 q^{33} - 8 q^{34} + 272 q^{36} + 40 q^{37} - 16 q^{38} + 40 q^{39} + 12 q^{40} + 16 q^{41} + 32 q^{43} - 8 q^{44} - 32 q^{46} + 16 q^{47} - 28 q^{48} - 8 q^{51} - 40 q^{52} + 16 q^{53} + 4 q^{54} - 8 q^{55} + 16 q^{57} - 64 q^{58} + 12 q^{60} + 16 q^{61} + 24 q^{62} + 304 q^{64} + 8 q^{65} + 56 q^{67} - 16 q^{68} + 16 q^{69} + 16 q^{71} + 80 q^{74} - 4 q^{75} + 8 q^{76} - 8 q^{78} + 64 q^{79} + 16 q^{80} + 272 q^{81} + 24 q^{83} + 8 q^{85} - 56 q^{86} + 24 q^{87} + 12 q^{88} + 16 q^{89} + 4 q^{90} + 32 q^{92} + 40 q^{93} + 16 q^{94} - 32 q^{95} + 28 q^{96} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8085))$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8085.2.a.a	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots$
8085.2.a.b	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$-2$	$-1$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots$
8085.2.a.c	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots$
8085.2.a.d	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$-1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
8085.2.a.e	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots$
8085.2.a.f	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots$
8085.2.a.g	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots$
8085.2.a.h	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots$
8085.2.a.i	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots$
8085.2.a.j	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots$
8085.2.a.k	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots$
8085.2.a.l	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{9}+q^{11}+2q^{12}+\cdots$
8085.2.a.m	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}+2q^{12}+\cdots$
8085.2.a.n	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}-2q^{12}+\cdots$
8085.2.a.o	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}-2q^{12}+\cdots$
8085.2.a.p	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}-2q^{12}+\cdots$
8085.2.a.q	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}-2q^{12}+\cdots$
8085.2.a.r	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots$
8085.2.a.s	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots$
8085.2.a.t	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots$
8085.2.a.u	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots$
8085.2.a.v	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots$
8085.2.a.w	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots$
8085.2.a.x	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$-1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
8085.2.a.y	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$1$	$2$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots$
8085.2.a.z	$8085$	$2$	8085.a	1.a	$1$	$1$	$1$	$64.559$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots$
8085.2.a.ba	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$2$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots$
8085.2.a.bb	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-1$	$2$	$-2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
8085.2.a.bc	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-2\beta q^{8}+\cdots$
8085.2.a.bd	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}-\beta q^{8}+\cdots$
8085.2.a.be	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+4q^{4}-q^{5}-\beta q^{6}+2\beta q^{8}+\cdots$
8085.2.a.bf	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots$
8085.2.a.bg	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots$
8085.2.a.bh	$8085$	$2$	8085.a	1.a	$1$	$2$	$2$	$64.559$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+q^{5}+\cdots$
8085.2.a.bi	$8085$	$2$	8085.a	1.a	$1$	$3$	$3$	$64.559$	3.3.148.1	None	✓	$1$	$1$	$-2$	$-3$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8085.2.a.bj	$8085$	$2$	8085.a	1.a	$1$	$3$	$3$	$64.559$	3.3.148.1	None	✓	$1$	$1$	$-2$	$3$	$3$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8085.2.a.bk	$8085$	$2$	8085.a	1.a	$1$	$3$	$3$	$64.559$	3.3.148.1	None	✓	$1$	$1$	$-1$	$-3$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
8085.2.a.bl	$8085$	$2$	8085.a	1.a	$1$	$3$	$3$	$64.559$	3.3.316.1	None	✓	$1$	$1$	$1$	$-3$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.bm	$8085$	$2$	8085.a	1.a	$1$	$3$	$3$	$64.559$	3.3.316.1	None	✓	$1$	$1$	$1$	$3$	$-3$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.bn	$8085$	$2$	8085.a	1.a	$1$	$4$	$4$	$64.559$	4.4.13448.1	None	✓	$1$	$1$	$0$	$-4$	$4$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.bo	$8085$	$2$	8085.a	1.a	$1$	$4$	$4$	$64.559$	4.4.34196.1	None	✓	$1$	$0$	$1$	$-4$	$-4$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}-q^{3}+(2-\beta _{2})q^{4}+\cdots$
8085.2.a.bp	$8085$	$2$	8085.a	1.a	$1$	$4$	$4$	$64.559$	4.4.34196.1	None	✓	$1$	$0$	$1$	$4$	$4$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+q^{3}+(2-\beta _{2})q^{4}+\cdots$
8085.2.a.bq	$8085$	$2$	8085.a	1.a	$1$	$4$	$4$	$64.559$	4.4.7232.1	None	✓	$1$	$0$	$2$	$4$	$-4$	$0$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots$
8085.2.a.br	$8085$	$2$	8085.a	1.a	$1$	$5$	$5$	$64.559$	5.5.833376.1	None	✓	$1$	$0$	$0$	$-5$	$5$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.bs	$8085$	$2$	8085.a	1.a	$1$	$5$	$5$	$64.559$	5.5.833376.1	None	✓	$1$	$1$	$0$	$-5$	$5$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.bt	$8085$	$2$	8085.a	1.a	$1$	$5$	$5$	$64.559$	5.5.833376.1	None	✓	$1$	$1$	$0$	$5$	$-5$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.bu	$8085$	$2$	8085.a	1.a	$1$	$5$	$5$	$64.559$	5.5.833376.1	None	✓	$1$	$1$	$0$	$5$	$-5$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.bv	$8085$	$2$	8085.a	1.a	$1$	$5$	$5$	$64.559$	5.5.352076.1	None	✓	$1$	$0$	$1$	$-5$	$5$	$0$	$+$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.bw	$8085$	$2$	8085.a	1.a	$1$	$6$	$6$	$64.559$	6.6.2803712.1	None	✓	$1$	$1$	$0$	$-6$	$6$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.bx	$8085$	$2$	8085.a	1.a	$1$	$6$	$6$	$64.559$	6.6.127775712.1	None	✓	$1$	$0$	$0$	$-6$	$6$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.by	$8085$	$2$	8085.a	1.a	$1$	$6$	$6$	$64.559$	6.6.2803712.1	None	✓	$1$	$1$	$0$	$6$	$-6$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.bz	$8085$	$2$	8085.a	1.a	$1$	$6$	$6$	$64.559$	6.6.127775712.1	None	✓	$1$	$1$	$0$	$6$	$-6$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.ca	$8085$	$2$	8085.a	1.a	$1$	$7$	$7$	$64.559$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$-7$	$7$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.cb	$8085$	$2$	8085.a	1.a	$1$	$7$	$7$	$64.559$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-7$	$7$	$0$	$+$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.cc	$8085$	$2$	8085.a	1.a	$1$	$7$	$7$	$64.559$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$7$	$-7$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.cd	$8085$	$2$	8085.a	1.a	$1$	$7$	$7$	$64.559$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$7$	$-7$	$0$	$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.ce	$8085$	$2$	8085.a	1.a	$1$	$8$	$8$	$64.559$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-8$	$8$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.cf	$8085$	$2$	8085.a	1.a	$1$	$8$	$8$	$64.559$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$8$	$-8$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.cg	$8085$	$2$	8085.a	1.a	$1$	$9$	$9$	$64.559$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-9$	$-9$	$0$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.ch	$8085$	$2$	8085.a	1.a	$1$	$9$	$9$	$64.559$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$9$	$9$	$0$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.ci	$8085$	$2$	8085.a	1.a	$1$	$10$	$10$	$64.559$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-4$	$-10$	$-10$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
8085.2.a.cj	$8085$	$2$	8085.a	1.a	$1$	$10$	$10$	$64.559$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-4$	$10$	$10$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
8085.2.a.ck	$8085$	$2$	8085.a	1.a	$1$	$10$	$10$	$64.559$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$-10$	$-10$	$0$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.cl	$8085$	$2$	8085.a	1.a	$1$	$10$	$10$	$64.559$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$-10$	$10$	$0$	$+$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.cm	$8085$	$2$	8085.a	1.a	$1$	$10$	$10$	$64.559$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$10$	$-10$	$0$	$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8085.2.a.cn	$8085$	$2$	8085.a	1.a	$1$	$10$	$10$	$64.559$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$10$	$10$	$0$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.co	$8085$	$2$	8085.a	1.a	$1$	$14$	$14$	$64.559$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$4$	$-14$	$-14$	$0$	$+$	$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8085.2.a.cp	$8085$	$2$	8085.a	1.a	$1$	$14$	$14$	$64.559$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$4$	$14$	$14$	$0$	$-$	$-$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8085))$ 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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 68 \)
Sturm bound:			\(2688\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(13\), \(17\)

\(3\)	\(5\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(19\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(17\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(14\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(20\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(15\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(13\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(20\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(20\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(15\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(14\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(24\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(21\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(9\)
Plus space				\(+\)	\(122\)
Minus space				\(-\)	\(150\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8085))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8085))\) 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	8085.2.a

Level	$8085$
Weight	$2$
Character orbit	8085.a
Rep. character	$\chi_{8085}(1,\cdot)$
Character field	$\Q$
Dimension	$272$
Newform subspaces	$68$
Sturm bound	$2688$
Trace bound	$17$