LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1536.1.e.a	$1536$	$1$	1536.e	3.b	$2$	$4$	$4$	$0.767$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			1536.1.e.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
1536.1.e.b	$1536$	$1$	1536.e	3.b	$2$	$4$	$4$	$0.767$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-2}) $	None		✓			1536.1.e.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$
1536.1.h.a	$1536$	$1$	1536.h	24.h	$2$	$2$	$2$	$0.767$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-6}) $	None	✓	✓			1536.1.e.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots$
1536.1.h.b	$1536$	$1$	1536.h	24.h	$2$	$2$	$2$	$0.767$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-6}) $	None	✓	✓			1536.1.e.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots$
1536.1.h.c	$1536$	$1$	1536.h	24.h	$2$	$4$	$4$	$0.767$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-2}) $	None		✓	✓		1536.1.e.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$
1536.2.a.a	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.a	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+\beta q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
1536.2.a.b	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.b	$1$	$0$	$0$	$-2$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots$
1536.2.a.c	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.c	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-2q^{11}+\cdots$
1536.2.a.d	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.d	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+3\beta q^{7}+q^{9}+6q^{11}+\cdots$
1536.2.a.e	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.b	$1$	$1$	$0$	$-2$	$4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots$
1536.2.a.f	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.a	$1$	$0$	$0$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}+\beta q^{7}+q^{9}+(2+2\beta )q^{11}+\cdots$
1536.2.a.g	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.b	$1$	$1$	$0$	$2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+(-2-\beta )q^{7}+\cdots$
1536.2.a.h	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.a	$1$	$1$	$0$	$2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}-\beta q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
1536.2.a.i	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.d	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}-3\beta q^{7}+q^{9}-6q^{11}+\cdots$
1536.2.a.j	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.c	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots$
1536.2.a.k	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.a	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
1536.2.a.l	$1536$	$2$	1536.a	1.a	$1$	$2$	$2$	$12.265$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1536.2.a.b	$1$	$0$	$0$	$2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots$
1536.2.a.m	$1536$	$2$	1536.a	1.a	$1$	$4$	$4$	$12.265$	$\Q(\sqrt{10 +4 \sqrt{2}})$	$_{}$	None	None	✓	✓	✓		1536.2.a.m	$2$	$0$	$0$	$-4$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
1536.2.a.n	$1536$	$2$	1536.a	1.a	$1$	$4$	$4$	$12.265$	$\Q(\sqrt{10 +4 \sqrt{2}})$	$_{}$	None	None	✓	✓	✓		1536.2.a.m	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}+(2+\beta _{2}+\cdots)q^{11}+\cdots$
1536.2.c.a	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1536.2.c.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
1536.2.c.b	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1536.2.c.a	$2$	$1$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
1536.2.c.c	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1536.2.c.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1-2\beta )q^{9}+\cdots$
1536.2.c.d	$1536$	$2$	1536.c	12.b	$2$	$2$	$2$	$12.265$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1536.2.c.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots$
1536.2.c.e	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	None	None		✓			1536.2.c.e	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$
1536.2.c.f	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1536.2.c.f	$4$	$0$	$0$	$-4$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta_{2}-1)q^{3}+(\beta_{3}+2\beta_{2}-\beta_1)q^{9}+\cdots$
1536.2.c.g	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		✓			1536.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-2\beta _{2}q^{5}+(2+\beta _{3})q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots$
1536.2.c.h	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		✓			1536.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{3}-2\beta _{2}q^{5}+(2-\beta _{3})q^{9}+\cdots$
1536.2.c.i	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	None	None		✓			1536.2.c.e	$4$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$
1536.2.c.j	$1536$	$2$	1536.c	12.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1536.2.c.f	$4$	$0$	$0$	$4$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta_{2}+1)q^{3}+(\beta_{3}+2\beta_{2}-\beta_1)q^{9}+\cdots$
1536.2.c.k	$1536$	$2$	1536.c	12.b	$2$	$8$	$8$	$12.265$	$\Q(i, \sqrt{2}, \sqrt{5})$	$_{}$	None	None		✓			1536.2.c.k	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$
1536.2.c.l	$1536$	$2$	1536.c	12.b	$2$	$8$	$8$	$12.265$	$\Q(\zeta_{24})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			1536.2.c.l	$8$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta_1 q^{3}+\beta_{3} q^{5}+\beta_{2} q^{7}+3 q^{9}+\cdots$
1536.2.c.m	$1536$	$2$	1536.c	12.b	$2$	$16$	$16$	$12.265$	16.0.$\cdots$.7	$_{}$	None	None		✓	✓		1536.2.c.m	$8$	$0$	$0$	$0$	$0$	$0$		$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{3}+\beta _{2}q^{5}-\beta _{6}q^{7}+\beta _{13}q^{9}+\cdots$
1536.2.d.a	$1536$	$2$	1536.d	8.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.a.b	$2$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+(-\beta_{2}+2\beta_1)q^{5}+(-\beta_{3}-2)q^{7}+\cdots$
1536.2.d.b	$1536$	$2$	1536.d	8.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+(-\beta_{2}+2\beta_1)q^{5}+\beta_{3} q^{7}+\cdots$
1536.2.d.c	$1536$	$2$	1536.d	8.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.a.d	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+\beta_{2} q^{5}-3\beta_{3} q^{7}-q^{9}+\cdots$
1536.2.d.d	$1536$	$2$	1536.d	8.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.a.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+\beta_{2} q^{5}-\beta_{3} q^{7}-q^{9}+\cdots$
1536.2.d.e	$1536$	$2$	1536.d	8.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+(-\beta_{2}+2\beta_1)q^{5}-\beta_{3} q^{7}+\cdots$
1536.2.d.f	$1536$	$2$	1536.d	8.b	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.a.b	$2$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+(-\beta_{2}+2\beta_1)q^{5}+(\beta_{3}+2)q^{7}+\cdots$
1536.2.d.g	$1536$	$2$	1536.d	8.b	$2$	$8$	$8$	$12.265$	8.0.18939904.2	$_{}$	None	None		✓	✓		1536.2.a.m	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-q^{9}+(2\beta _{4}+\cdots)q^{11}+\cdots$
1536.2.f.a	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1536.2.c.f	$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{9}+\cdots$
1536.2.f.b	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			1536.2.c.l	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
1536.2.f.c	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		✓			1536.2.c.k	$4$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-2q^{5}+(2+\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots$
1536.2.f.d	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	None	None		✓			1536.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-2\beta _{2}q^{5}+(-2+\beta _{3})q^{9}+\cdots$
1536.2.f.e	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	None	None		✓			1536.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-2\beta _{2}q^{5}+(-2+\beta _{3})q^{9}+\cdots$
1536.2.f.f	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}+\beta_1)q^{3}-\beta_{3} q^{5}+3\beta_{2} q^{7}+\cdots$
1536.2.f.g	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1536.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{3}+\beta_1)q^{3}-\beta_{3} q^{5}+3\beta_{2} q^{7}+\cdots$
1536.2.f.h	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			1536.2.c.l	$4$	$0$	$0$	$0$	$8$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+(2+\beta _{3})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots$
1536.2.f.i	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		✓			1536.2.c.k	$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+2q^{5}+(2+\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots$
1536.2.f.j	$1536$	$2$	1536.f	24.f	$2$	$4$	$4$	$12.265$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			1536.2.c.f	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2}-2\zeta_{8}^{3})q^{9}+\cdots$
1536.2.f.k	$1536$	$2$	1536.f	24.f	$2$	$8$	$8$	$12.265$	$\Q(i, \sqrt{2}, \sqrt{7})$	$_{}$	None	None		✓			1536.2.c.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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L-functions

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