LMFDB - Space of modular forms of level 8281, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 78 $
Sturm bound:			$1698$
Trace bound:			$17$
Distinguishing $T_p$:			$2$, $3$, $5$, $11$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8281))$.

	Total	New	Old
Modular forms	904	557	347
Cusp forms	793	502	291
Eisenstein series	111	55	56

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

$7$	$13$	Fricke	Dim
$+$	$+$	$+$	$118$
$+$	$-$	$-$	$130$
$-$	$+$	$-$	$131$
$-$	$-$	$+$	$123$
Plus space		$+$	$241$
Minus space		$-$	$261$

Trace form

$ 502 q - 4 q^{3} + 472 q^{4} + 2 q^{5} + 12 q^{8} + 442 q^{9} + O(q^{10}) $

$ 502 q - 4 q^{3} + 472 q^{4} + 2 q^{5} + 12 q^{8} + 442 q^{9} + 6 q^{10} - 4 q^{11} - 4 q^{12} - 4 q^{15} + 416 q^{16} + 4 q^{18} - 12 q^{19} - 2 q^{20} + 14 q^{22} + 6 q^{23} - 4 q^{24} + 404 q^{25} + 2 q^{27} + 20 q^{29} + 58 q^{30} - 4 q^{31} + 44 q^{32} - 4 q^{33} + 2 q^{34} + 354 q^{36} + 16 q^{37} - 20 q^{38} + 14 q^{40} + 2 q^{41} + 22 q^{43} + 28 q^{44} + 22 q^{45} + 8 q^{46} + 8 q^{47} + 46 q^{48} + 40 q^{50} + 6 q^{51} + 16 q^{53} + 48 q^{54} + 16 q^{55} + 16 q^{57} + 40 q^{58} + 16 q^{59} - 24 q^{61} - 10 q^{62} + 318 q^{64} + 26 q^{66} + 90 q^{68} - 16 q^{69} - 28 q^{71} + 40 q^{72} - 22 q^{73} + 70 q^{74} - 54 q^{75} + 16 q^{76} + 34 q^{79} - 38 q^{80} + 246 q^{81} + 52 q^{82} + 24 q^{83} + 24 q^{85} - 52 q^{86} + 16 q^{87} + 42 q^{88} + 26 q^{89} + 28 q^{90} - 140 q^{92} + 28 q^{93} - 2 q^{94} + 22 q^{95} - 4 q^{96} - 6 q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8281))$ 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8281.2.a.a	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
8281.2.a.b	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-2$	$2$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
8281.2.a.c	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$-3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}-3q^{5}+3q^{6}+3q^{8}+\cdots$
8281.2.a.d	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}-4q^{11}+\cdots$
8281.2.a.e	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots$
8281.2.a.f	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots$
8281.2.a.g	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-q^{4}+3q^{5}-3q^{6}+3q^{8}+\cdots$
8281.2.a.h	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-3q^{5}+q^{9}-4q^{12}+\cdots$
8281.2.a.i	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-q^{4}+3q^{5}-3q^{6}-3q^{8}+\cdots$
8281.2.a.j	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-q^{4}-3q^{5}+3q^{6}-3q^{8}+\cdots$
8281.2.a.k	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$2$	$-2$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
8281.2.a.l	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-3q^{5}-3q^{9}-6q^{10}+\cdots$
8281.2.a.m	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$2$	$2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
8281.2.a.n	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-3$	$3$	$3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots$
8281.2.a.o	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots$
8281.2.a.p	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots$
8281.2.a.q	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-2q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$
8281.2.a.r	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots$
8281.2.a.s	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots$
8281.2.a.t	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots$
8281.2.a.u	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{13}) $	$\Q(\sqrt{-91}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	$q-2q^{4}-\beta q^{5}-3q^{9}+4q^{16}-\beta q^{19}+\cdots$
8281.2.a.v	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+(3-\beta )q^{5}-2q^{6}-2\beta q^{8}+\cdots$
8281.2.a.w	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-\beta q^{8}+\cdots$
8281.2.a.x	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
8281.2.a.y	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots$
8281.2.a.z	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$3$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots$
8281.2.a.ba	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots$
8281.2.a.bb	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$3$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots$
8281.2.a.bc	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bd	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-3$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots$
8281.2.a.be	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓	$1$	$1$	$-2$	$0$	$3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bf	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-2$	$2$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bg	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.316.1	None	✓	$1$	$0$	$-1$	$2$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
8281.2.a.bh	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.404.1	None	✓	$1$	$0$	$2$	$-4$	$5$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bi	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓	$1$	$1$	$2$	$0$	$-3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bj	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$2$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bk	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.404.1	None	✓	$1$	$0$	$2$	$4$	$-5$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bl	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$3$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots$
8281.2.a.bm	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{8}+\cdots$
8281.2.a.bn	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{2}, \sqrt{23})$	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
8281.2.a.bo	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.105456.1	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
8281.2.a.bp	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.27004.1	None	✓	$1$	$0$	$-1$	$-1$	$7$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bq	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}-\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
8281.2.a.br	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{13})$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{8}-3q^{9}+\cdots$
8281.2.a.bs	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
8281.2.a.bt	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.27004.1	None	✓	$1$	$0$	$1$	$-1$	$-7$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bu	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.105456.1	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots$
8281.2.a.bv	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{2}, \sqrt{23})$	None	✓	$2$	$1$	$4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
8281.2.a.bw	$8281$	$2$	8281.a	1.a	$1$	$5$	$5$	$66.124$	5.5.746052.1	None	✓	$1$	$1$	$-4$	$0$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.bx	$8281$	$2$	8281.a	1.a	$1$	$5$	$5$	$66.124$	5.5.746052.1	None	✓	$1$	$0$	$-4$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.by	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.7674048.1	None	✓	$1$	$1$	$-4$	$0$	$6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
8281.2.a.bz	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓	$1$	$1$	$-2$	$-1$	$-1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots$
8281.2.a.ca	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓	$1$	$0$	$-2$	$1$	$1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots$
8281.2.a.cb	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.1279733.1	None	✓	$1$	$1$	$-2$	$4$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2}+\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots$
8281.2.a.cc	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.4507648.1	None	✓	$1$	$1$	$0$	$-8$	$6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.cd	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.4507648.1	None	✓	$1$	$1$	$0$	$8$	$-6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.ce	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓	$1$	$1$	$2$	$-1$	$1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots$
8281.2.a.cf	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓	$1$	$0$	$2$	$1$	$-1$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots$
8281.2.a.cg	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.1279733.1	None	✓	$1$	$0$	$2$	$4$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.ch	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.7674048.1	None	✓	$1$	$1$	$4$	$0$	$-6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
8281.2.a.ci	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	8.8.8446345216.1	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots$
8281.2.a.cj	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
8281.2.a.ck	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
8281.2.a.cl	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	8.8.8446345216.1	None	✓	$2$	$1$	$4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
8281.2.a.cm	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
8281.2.a.cn	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-3$	$-8$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
8281.2.a.co	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$-6$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots$
8281.2.a.cp	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$6$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots$
8281.2.a.cq	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$3$	$-8$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
8281.2.a.cr	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
8281.2.a.cs	$8281$	$2$	8281.a	1.a	$1$	$16$	$16$	$66.124$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{7}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
8281.2.a.ct	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓	$1$	$1$	$-1$	$0$	$-13$	$0$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8281.2.a.cu	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓	$1$	$0$	$-1$	$0$	$13$	$0$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8281.2.a.cv	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓	$1$	$1$	$1$	$0$	$-13$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8281.2.a.cw	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓	$1$	$0$	$1$	$0$	$13$	$0$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8281.2.a.cx	$8281$	$2$	8281.a	1.a	$1$	$32$	$32$	$66.124$		None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8281.2.a.cy	$8281$	$2$	8281.a	1.a	$1$	$36$	$36$	$66.124$		None	✓	$2$	$1$	$-14$	$0$	$0$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8281.2.a.cz	$8281$	$2$	8281.a	1.a	$1$	$36$	$36$	$66.124$		None	✓	$2$	$0$	$14$	$0$	$0$	$0$	$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8281))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(8281)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(49))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(91))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(169))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(637))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1183))$$^{\oplus 2}$

Overview	Random
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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:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 78 \)
Sturm bound:			\(1698\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\), \(11\), \(17\)

\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(118\)
\(+\)	\(-\)	$-$	\(130\)
\(-\)	\(+\)	$-$	\(131\)
\(-\)	\(-\)	$+$	\(123\)
Plus space		\(+\)	\(241\)
Minus space		\(-\)	\(261\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8281))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8281))\) 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	8281.2.a

Level	$8281$
Weight	$2$
Character orbit	8281.a
Rep. character	$\chi_{8281}(1,\cdot)$
Character field	$\Q$
Dimension	$502$
Newform subspaces	$78$
Sturm bound	$1698$
Trace bound	$17$