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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (42 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3204.1.b.a	$3204$	$1$	3204.b	267.b	$2$	$2$	$2$	$1.599$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{5}-\beta q^{7}-\beta q^{13}-\beta q^{17}-q^{23}+\cdots$
3204.1.b.b	$3204$	$1$	3204.b	267.b	$2$	$2$	$2$	$1.599$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}-\beta q^{7}-\beta q^{13}+\beta q^{17}+q^{23}+\cdots$
3204.1.h.a	$3204$	$1$	3204.h	356.d	$2$	$1$	$1$	$1.599$	$\Q$	$D_{3}$	$\Q(\sqrt{-89}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$-2$		$1$		$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
3204.1.h.b	$3204$	$1$	3204.h	356.d	$2$	$1$	$1$	$1.599$	$\Q$	$D_{3}$	$\Q(\sqrt{-89}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$2$		$1$		$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
3204.1.h.c	$3204$	$1$	3204.h	356.d	$2$	$1$	$1$	$1.599$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-89}) $	$\Q(\sqrt{89}) $	✓	$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{16}+\cdots$
3204.1.h.d	$3204$	$1$	3204.h	356.d	$2$	$2$	$2$	$1.599$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-89}) $	None	✓	$4$	$0$	$2$	$0$	$2$	$0$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{16}+\cdots$
3204.1.j.a	$3204$	$1$	3204.j	356.e	$4$	$2$	$1$	$1.599$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-iq^{5}-q^{8}+2iq^{10}+\cdots$
3204.1.j.b	$3204$	$1$	3204.j	356.e	$4$	$2$	$1$	$1.599$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+iq^{5}+q^{8}+2iq^{10}+\cdots$
3204.1.l.a	$3204$	$1$	3204.l	267.e	$4$	$4$	$2$	$1.599$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q+(1-\zeta_{8}^{2})q^{7}+(-\zeta_{8}-\zeta_{8}^{3})q^{11}+\cdots$
3204.1.n.a	$3204$	$1$	3204.n	3204.n	$6$	$6$	$3$	$1.599$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-89}) $	None		$4$	$0$	$-3$	$0$	$0$	$-3$		$1$		$q-\zeta_{18}^{3}q^{2}-\zeta_{18}^{2}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
3204.1.n.b	$3204$	$1$	3204.n	3204.n	$6$	$6$	$3$	$1.599$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-89}) $	None		$4$	$0$	$-3$	$0$	$0$	$3$		$1$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
3204.1.n.c	$3204$	$1$	3204.n	3204.n	$6$	$12$	$6$	$1.599$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-89}) $	None		$8$	$0$	$6$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{6}q^{2}-\zeta_{36}q^{3}+\zeta_{36}^{12}q^{4}+\cdots$
3204.1.u.a	$3204$	$1$	3204.u	1068.m	$8$	$4$	$1$	$1.599$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{2}q^{8}+(-1-\zeta_{8}^{3}+\cdots)q^{13}+\cdots$
3204.1.u.b	$3204$	$1$	3204.u	1068.m	$8$	$4$	$1$	$1.599$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{2}q^{8}+(-1-\zeta_{8}^{3}+\cdots)q^{13}+\cdots$
3204.1.bd.a	$3204$	$1$	3204.bd	356.j	$22$	$10$	$1$	$1.599$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$		$1$		$q-\zeta_{22}^{7}q^{2}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}^{4}+\zeta_{22}^{5}+\cdots)q^{5}+\cdots$
3204.1.bf.a	$3204$	$1$	3204.bf	356.l	$22$	$10$	$1$	$1.599$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q-\zeta_{22}^{8}q^{2}-\zeta_{22}^{5}q^{4}+(\zeta_{22}+\zeta_{22}^{3}+\cdots)q^{5}+\cdots$
3204.1.bs.a	$3204$	$1$	3204.bs	356.n	$44$	$20$	$1$	$1.599$	$\Q(\zeta_{44})$	$D_{44}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{44}^{8}q^{2}+\zeta_{44}^{16}q^{4}+(\zeta_{44}-\zeta_{44}^{3}+\cdots)q^{5}+\cdots$
3204.1.bs.b	$3204$	$1$	3204.bs	356.n	$44$	$20$	$1$	$1.599$	$\Q(\zeta_{44})$	$D_{44}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{44}^{8}q^{2}+\zeta_{44}^{16}q^{4}+(-\zeta_{44}+\zeta_{44}^{3}+\cdots)q^{5}+\cdots$
3204.1.cd.a	$3204$	$1$	3204.cd	1068.af	$88$	$40$	$1$	$1.599$	$\Q(\zeta_{88})$	$D_{88}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{88}^{42}q^{2}-\zeta_{88}^{40}q^{4}+(-\zeta_{88}^{19}+\cdots)q^{5}+\cdots$
3204.1.cd.b	$3204$	$1$	3204.cd	1068.af	$88$	$40$	$1$	$1.599$	$\Q(\zeta_{88})$	$D_{88}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{88}^{42}q^{2}-\zeta_{88}^{40}q^{4}+(\zeta_{88}^{19}+\cdots)q^{5}+\cdots$
3204.2.a.a	$3204$	$2$	3204.a	1.a	$1$	$1$	$1$	$25.584$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+6q^{11}-4q^{13}-2q^{17}+4q^{19}+\cdots$
3204.2.a.b	$3204$	$2$	3204.a	1.a	$1$	$1$	$1$	$25.584$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{13}+q^{17}-5q^{19}+q^{23}+\cdots$
3204.2.a.c	$3204$	$2$	3204.a	1.a	$1$	$1$	$1$	$25.584$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-6q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots$
3204.2.a.d	$3204$	$2$	3204.a	1.a	$1$	$3$	$3$	$25.584$	3.3.321.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots$
3204.2.a.e	$3204$	$2$	3204.a	1.a	$1$	$3$	$3$	$25.584$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{1}-\beta _{2})q^{7}+\cdots$
3204.2.a.f	$3204$	$2$	3204.a	1.a	$1$	$4$	$4$	$25.584$	4.4.17417.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
3204.2.a.g	$3204$	$2$	3204.a	1.a	$1$	$4$	$4$	$25.584$	4.4.33097.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+(2-\beta _{1}+\beta _{3})q^{7}+(1+\cdots)q^{11}+\cdots$
3204.2.a.h	$3204$	$2$	3204.a	1.a	$1$	$6$	$6$	$25.584$	6.6.223378112.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-6$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{5})q^{5}+(1-\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots$
3204.2.a.i	$3204$	$2$	3204.a	1.a	$1$	$6$	$6$	$25.584$	6.6.223378112.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$6$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{5})q^{5}+(1-\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
3204.2.a.j	$3204$	$2$	3204.a	1.a	$1$	$7$	$7$	$25.584$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{5}+(\beta _{2}+\beta _{5})q^{7}+(-2-\beta _{3}+\cdots)q^{11}+\cdots$
3204.2.g.a	$3204$	$2$	3204.g	89.b	$2$	$4$	$4$	$25.584$	$\Q(i, \sqrt{89})$	$_{}$	$\Q(\sqrt{-267}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{23}-5q^{25}+(-\beta _{1}+2\beta _{2})q^{29}+\cdots$
3204.2.g.b	$3204$	$2$	3204.g	89.b	$2$	$6$	$6$	$25.584$	6.0.4227136.1	$_{}$	None	None		$2$	$1$	$0$	$0$	$-10$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{2}+\beta _{3})q^{5}+(-\beta _{4}+2\beta _{5})q^{7}+\cdots$
3204.2.g.c	$3204$	$2$	3204.g	89.b	$2$	$6$	$6$	$25.584$	6.0.4227136.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{2}-\beta _{3})q^{5}+(\beta _{4}-2\beta _{5})q^{7}+\cdots$
3204.2.g.d	$3204$	$2$	3204.g	89.b	$2$	$8$	$8$	$25.584$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{5}q^{11}-\beta _{7}q^{13}+\cdots$
3204.2.g.e	$3204$	$2$	3204.g	89.b	$2$	$14$	$14$	$25.584$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}-\beta _{11}q^{7}+(1-\beta _{6})q^{11}+(\beta _{5}+\cdots)q^{13}+\cdots$
3204.2.k.a	$3204$	$2$	3204.k	89.c	$4$	$2$	$1$	$25.584$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2i)q^{7}-4q^{11}+(1-i)q^{13}+\cdots$
3204.2.k.b	$3204$	$2$	3204.k	89.c	$4$	$4$	$2$	$25.584$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+(-2-2\zeta_{8}^{2})q^{7}+\cdots$
3204.2.k.c	$3204$	$2$	3204.k	89.c	$4$	$12$	$6$	$25.584$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{4}-\beta _{11})q^{5}+(1-\beta _{1}-\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots$
3204.2.k.d	$3204$	$2$	3204.k	89.c	$4$	$24$	$12$	$25.584$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
3204.2.k.e	$3204$	$2$	3204.k	89.c	$4$	$32$	$16$	$25.584$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
3204.3.b.a	$3204$	$3$	3204.b	267.b	$2$	$60$	$60$	$87.303$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3204.3.d.a	$3204$	$3$	3204.d	3.b	$2$	$60$	$60$	$87.303$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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 $\F_{q}$

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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.