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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Results (1-50 of 96 matches)

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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
1700.1.d.a	$1700$	$1$	1700.d	340.d	$2$	$2$	$2$	$0.848$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-17}) $	None		✓			1700.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$
1700.1.d.b	$1700$	$1$	1700.d	340.d	$2$	$2$	$2$	$0.848$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $					68.1.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}+q^{9}+iq^{13}+\cdots$
1700.1.d.c	$1700$	$1$	1700.d	340.d	$2$	$2$	$2$	$0.848$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-17}) $	None		✓			1700.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots$
1700.1.d.d	$1700$	$1$	1700.d	340.d	$2$	$4$	$4$	$0.848$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-17}) $	None		✓	✓		1700.1.h.f	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+\cdots$
1700.1.h.a	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	$\Q$	$D_{3}$	$\Q(\sqrt{-17}) $	None	✓	✓			1700.1.h.a	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
1700.1.h.b	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	$\Q$	$D_{3}$	$\Q(\sqrt{-17}) $	None	✓	✓			1700.1.h.a	$2$	$0$	$-1$	$1$	$0$	$1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
1700.1.h.c	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	$\Q$	$D_{3}$	$\Q(\sqrt{-17}) $	None	✓	✓			1700.1.h.a	$2$	$0$	$1$	$-1$	$0$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
1700.1.h.d	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $	✓				68.1.d.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}+2q^{13}+q^{16}+\cdots$
1700.1.h.e	$1700$	$1$	1700.h	68.d	$2$	$1$	$1$	$0.848$	$\Q$	$D_{3}$	$\Q(\sqrt{-17}) $	None	✓	✓			1700.1.h.a	$2$	$0$	$1$	$1$	$0$	$1$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
1700.1.h.f	$1700$	$1$	1700.h	68.d	$2$	$2$	$2$	$0.848$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-17}) $	None	✓	✓			1700.1.h.f	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots$
1700.1.h.g	$1700$	$1$	1700.h	68.d	$2$	$2$	$2$	$0.848$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-17}) $	None	✓	✓			1700.1.h.f	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{8}+\cdots$
1700.1.n.a	$1700$	$1$	1700.n	340.n	$4$	$2$	$1$	$0.848$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					68.1.f.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+iq^{9}+q^{16}+iq^{17}+\cdots$
1700.1.n.b	$1700$	$1$	1700.n	340.n	$4$	$2$	$1$	$0.848$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					68.1.f.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+iq^{9}+q^{16}-iq^{17}+\cdots$
1700.1.p.a	$1700$	$1$	1700.p	68.f	$4$	$2$	$1$	$0.848$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	68.1.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-q^{4}-iq^{8}-iq^{9}+q^{16}+\cdots$
1700.1.w.a	$1700$	$1$	1700.w	68.g	$8$	$4$	$1$	$0.848$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None					340.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{8}+\zeta_{8}^{3}q^{9}+\cdots$
1700.1.w.b	$1700$	$1$	1700.w	68.g	$8$	$4$	$1$	$0.848$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None					340.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+\zeta_{8}^{3}q^{9}+\cdots$
1700.1.bd.a	$1700$	$1$	1700.bd	1700.ad	$10$	$4$	$1$	$0.848$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓			1700.1.bd.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}-\zeta_{10}^{4}q^{8}+\cdots$
1700.1.bd.b	$1700$	$1$	1700.bd	1700.ad	$10$	$4$	$1$	$0.848$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓			1700.1.bd.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{4}q^{8}+\cdots$
1700.1.bk.a	$1700$	$1$	1700.bk	340.ac	$16$	$8$	$1$	$0.848$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None			✓	✓	340.1.bc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{7}q^{8}+\cdots$
1700.1.br.a	$1700$	$1$	1700.br	340.aj	$16$	$8$	$1$	$0.848$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None			✓	✓	340.1.bc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{7}q^{8}+\cdots$
1700.1.bw.a	$1700$	$1$	1700.bw	1700.aw	$20$	$8$	$1$	$0.848$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓			1700.1.bw.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}-\zeta_{20}^{7}q^{5}+\cdots$
1700.1.bw.b	$1700$	$1$	1700.bw	1700.aw	$20$	$8$	$1$	$0.848$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓			1700.1.bw.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+\zeta_{20}^{2}q^{5}+\cdots$
1700.1.cf.a	$1700$	$1$	1700.cf	1700.bf	$40$	$16$	$1$	$0.848$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		✓			1700.1.cf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{17}q^{2}-\zeta_{40}^{14}q^{4}-\zeta_{40}^{11}q^{5}+\cdots$
1700.1.cf.b	$1700$	$1$	1700.cf	1700.bf	$40$	$16$	$1$	$0.848$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		✓			1700.1.cf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{17}q^{2}-\zeta_{40}^{14}q^{4}+\zeta_{40}^{6}q^{5}+\cdots$
1700.1.cm.a	$1700$	$1$	1700.cm	1700.bm	$80$	$32$	$1$	$0.848$	$\Q(\zeta_{80})$	$D_{80}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1700.1.cm.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{80}^{23}q^{2}-\zeta_{80}^{6}q^{4}-\zeta_{80}^{9}q^{5}+\cdots$
1700.1.ct.a	$1700$	$1$	1700.ct	1700.bt	$80$	$32$	$1$	$0.848$	$\Q(\zeta_{80})$	$D_{80}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1700.1.cm.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{80}^{37}q^{2}-\zeta_{80}^{34}q^{4}-\zeta_{80}^{6}q^{5}+\cdots$
1700.2.a.a	$1700$	$2$	1700.a	1.a	$1$	$1$	$1$	$13.575$	$\Q$	$_{}$	None	None	✓	✓			1700.2.a.a	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+q^{13}+q^{17}-4q^{19}+\cdots$
1700.2.a.b	$1700$	$2$	1700.a	1.a	$1$	$1$	$1$	$13.575$	$\Q$	$_{}$	None	None	✓				340.2.a.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+2q^{11}+6q^{13}-q^{17}+\cdots$
1700.2.a.c	$1700$	$2$	1700.a	1.a	$1$	$1$	$1$	$13.575$	$\Q$	$_{}$	None	None	✓	✓			1700.2.a.a	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-q^{13}-q^{17}-4q^{19}+\cdots$
1700.2.a.d	$1700$	$2$	1700.a	1.a	$1$	$2$	$2$	$13.575$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		68.2.a.a	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1-\beta )q^{7}+(1-2\beta )q^{9}+\cdots$
1700.2.a.e	$1700$	$2$	1700.a	1.a	$1$	$3$	$3$	$13.575$	3.3.404.1	$_{}$	None	None	✓				340.2.a.b	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{2}q^{7}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots$
1700.2.a.f	$1700$	$2$	1700.a	1.a	$1$	$4$	$4$	$13.575$	4.4.11344.1	$_{}$	None	None	✓		✓		340.2.e.a	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{2}-\beta _{3})q^{7}+\cdots$
1700.2.a.g	$1700$	$2$	1700.a	1.a	$1$	$4$	$4$	$13.575$	4.4.11344.1	$_{}$	None	None	✓				340.2.e.a	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{2}+\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
1700.2.a.h	$1700$	$2$	1700.a	1.a	$1$	$5$	$5$	$13.575$	5.5.27977168.1	$_{}$	None	None	✓	✓	✓		1700.2.a.h	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{4}q^{7}+(3+\beta _{1}+\beta _{3}+\beta _{4})q^{9}+\cdots$
1700.2.a.i	$1700$	$2$	1700.a	1.a	$1$	$5$	$5$	$13.575$	5.5.27977168.1	$_{}$	None	None	✓	✓	✓		1700.2.a.h	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{4}q^{7}+(3+\beta _{1}+\beta _{3}+\beta _{4})q^{9}+\cdots$
1700.2.c.a	$1700$	$2$	1700.c	17.b	$2$	$2$	$2$	$13.575$	$\Q(\sqrt{-2}) $	$_{}$	None	None					68.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-3\beta q^{7}+q^{9}+\beta q^{11}+4q^{13}+\cdots$
1700.2.c.b	$1700$	$2$	1700.c	17.b	$2$	$6$	$6$	$13.575$	6.0.37161216.1	$_{}$	None	None					340.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(-\beta _{2}+\beta _{4})q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots$
1700.2.c.c	$1700$	$2$	1700.c	17.b	$2$	$6$	$6$	$13.575$	6.0.336208896.1	$_{}$	None	None		✓			1700.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{4}-\beta _{5})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1700.2.c.d	$1700$	$2$	1700.c	17.b	$2$	$6$	$6$	$13.575$	6.0.336208896.1	$_{}$	None	None		✓			1700.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{4}-\beta _{5})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1700.2.c.e	$1700$	$2$	1700.c	17.b	$2$	$8$	$8$	$13.575$	8.0.$\cdots$.29	$_{}$	None	None			✓		340.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{4}q^{7}+\beta _{1}q^{9}-\beta _{7}q^{11}+\cdots$
1700.2.e.a	$1700$	$2$	1700.e	5.b	$2$	$2$	$2$	$13.575$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1700.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{7}+2q^{9}-iq^{13}+iq^{17}+\cdots$
1700.2.e.b	$1700$	$2$	1700.e	5.b	$2$	$2$	$2$	$13.575$	$\Q(\sqrt{-1}) $	$_{}$	None	None					340.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-4iq^{7}+3q^{9}+2q^{11}+6iq^{13}+\cdots$
1700.2.e.c	$1700$	$2$	1700.e	5.b	$2$	$4$	$4$	$13.575$	$\Q(\zeta_{12})$	$_{}$	None	None					68.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots$
1700.2.e.d	$1700$	$2$	1700.e	5.b	$2$	$6$	$6$	$13.575$	6.0.2611456.1	$_{}$	None	None					340.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{2}q^{7}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
1700.2.e.e	$1700$	$2$	1700.e	5.b	$2$	$10$	$10$	$13.575$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓	✓		1700.2.a.h	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{8}q^{7}+(-3+\beta _{4}-\beta _{6}+\cdots)q^{9}+\cdots$
1700.2.g.a	$1700$	$2$	1700.g	85.c	$2$	$4$	$4$	$13.575$	$\Q(\zeta_{8})$	$_{}$	None	None					68.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{3}q^{3}-3\zeta_{8}^{3}q^{7}-q^{9}+\zeta_{8}^{2}q^{11}+\cdots$
1700.2.g.b	$1700$	$2$	1700.g	85.c	$2$	$6$	$6$	$13.575$	6.0.37161216.1	$_{}$	None	None					340.2.c.a	$2$	$0$	$0$	$-4$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{3}+(-1-\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$
1700.2.g.c	$1700$	$2$	1700.g	85.c	$2$	$6$	$6$	$13.575$	6.0.37161216.1	$_{}$	None	None					340.2.c.a	$2$	$0$	$0$	$4$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{2})q^{3}+(1+\beta _{2})q^{7}+(3-\beta _{2}+\cdots)q^{9}+\cdots$
1700.2.g.d	$1700$	$2$	1700.g	85.c	$2$	$12$	$12$	$13.575$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		1700.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}+(\beta _{6}-\beta _{10})q^{7}+(1-\beta _{2})q^{9}+\cdots$
1700.2.m.a	$1700$	$2$	1700.m	85.j	$4$	$4$	$2$	$13.575$	$\Q(i, \sqrt{13})$	$_{}$	None	None					68.2.e.a	$2$	$0$	$0$	$-2$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{3})q^{7}+\cdots$

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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.