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 59 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
3267.1.b.a	$3267$	$1$	3267.b	3.b	$2$	$1$	$1$	$1.630$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			3267.1.b.a	$2$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+q^{4}-q^{7}-q^{13}+q^{16}+2q^{19}+\cdots$
3267.1.b.b	$3267$	$1$	3267.b	3.b	$2$	$1$	$1$	$1.630$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			3267.1.b.a	$2$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{4}+q^{7}+q^{13}+q^{16}-2q^{19}+\cdots$
3267.1.b.c	$3267$	$1$	3267.b	3.b	$2$	$2$	$2$	$1.630$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		✓			3267.1.b.c	$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\beta q^{2}-q^{4}-\beta q^{5}-q^{7}+2q^{10}+\cdots$
3267.1.b.d	$3267$	$1$	3267.b	3.b	$2$	$2$	$2$	$1.630$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		✓			3267.1.b.c	$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\beta q^{2}-q^{4}-\beta q^{5}+q^{7}-2q^{10}+\cdots$
3267.1.b.e	$3267$	$1$	3267.b	3.b	$2$	$2$	$2$	$1.630$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None	✓	✓			3267.1.b.e	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}+q^{25}+\cdots$
3267.1.c.a	$3267$	$1$	3267.c	11.b	$2$	$4$	$4$	$1.630$	$\Q(\sqrt{-2}, \sqrt{3})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3267.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-\beta _{1}q^{7}-\beta _{3}q^{13}+q^{16}+(\beta _{1}+\cdots)q^{19}+\cdots$
3267.1.h.a	$3267$	$1$	3267.h	99.h	$6$	$4$	$2$	$1.630$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None			✓	✓	1089.1.h.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}+\cdots$
3267.1.i.a	$3267$	$1$	3267.i	9.d	$6$	$2$	$1$	$1.630$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None			✓	✓	1089.1.i.a	$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{16}+\cdots$
3267.1.l.a	$3267$	$1$	3267.l	11.d	$10$	$16$	$4$	$1.630$	16.0.$\cdots$.7	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	3267.1.c.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{4}q^{4}-\beta _{12}q^{7}+\beta _{3}q^{13}-\beta _{8}q^{16}+\cdots$
3267.1.m.a	$3267$	$1$	3267.m	33.h	$10$	$4$	$1$	$1.630$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			3267.1.b.a	$8$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{10}^{2}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}q^{13}+\cdots$
3267.1.m.b	$3267$	$1$	3267.m	33.h	$10$	$4$	$1$	$1.630$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			3267.1.b.a	$8$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{10}^{2}q^{4}-\zeta_{10}^{2}q^{7}+\zeta_{10}q^{13}+\cdots$
3267.1.m.c	$3267$	$1$	3267.m	33.h	$10$	$8$	$2$	$1.630$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3267.1.b.e	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{4}+\beta _{3}q^{7}+\cdots$
3267.1.m.d	$3267$	$1$	3267.m	33.h	$10$	$8$	$2$	$1.630$	8.0.64000000.1	$S_{4}$	None	None		✓			3267.1.b.c	$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta _{7}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+\beta _{4}q^{7}+\cdots$
3267.1.m.e	$3267$	$1$	3267.m	33.h	$10$	$8$	$2$	$1.630$	8.0.64000000.1	$S_{4}$	None	None		✓			3267.1.b.c	$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{7}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}-\beta _{4}q^{7}+\cdots$
3267.1.q.a	$3267$	$1$	3267.q	27.f	$18$	$6$	$1$	$1.630$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	3267.1.q.a	$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q+\zeta_{18}^{7}q^{3}+\zeta_{18}^{4}q^{4}+(\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots$
3267.1.v.a	$3267$	$1$	3267.v	99.n	$30$	$8$	$1$	$1.630$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-11}) $	None			✓	✓	1089.1.i.a	$16$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{30}^{11}q^{4}+(-\zeta_{30}^{7}-\zeta_{30}^{12})q^{5}+\cdots$
3267.1.w.a	$3267$	$1$	3267.w	99.o	$30$	$8$	$1$	$1.630$	$\Q(\zeta_{15})$	$D_{3}$	$\Q(\sqrt{-11}) $	None					99.1.h.a	$16$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{30}^{13}q^{4}-\zeta_{30}q^{5}-\zeta_{30}^{11}q^{16}+\cdots$
3267.1.w.b	$3267$	$1$	3267.w	99.o	$30$	$16$	$2$	$1.630$	16.0.$\cdots$.1	$S_{4}$	None	None			✓		1089.1.h.a	$16$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{2}-\beta _{8}-\beta _{10}+\cdots)q^{5}+\cdots$
3267.1.be.a	$3267$	$1$	3267.be	297.v	$90$	$24$	$1$	$1.630$	$\Q(\zeta_{45})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	3267.1.q.a	$16$	$0$	$0$	$0$	$3$	$0$		$1$		$q+\zeta_{90}^{11}q^{3}+\zeta_{90}^{14}q^{4}+(-\zeta_{90}^{3}+\cdots)q^{5}+\cdots$
3267.1.bf.a	$3267$	$1$	3267.bf	297.w	$90$	$24$	$1$	$1.630$	$\Q(\zeta_{45})$	$D_{9}$	$\Q(\sqrt{-11}) $	None			✓	✓	297.1.q.a	$16$	$0$	$0$	$0$	$3$	$0$		$1$		$q+\zeta_{90}^{34}q^{3}-\zeta_{90}^{31}q^{4}+(\zeta_{90}^{32}+\cdots)q^{5}+\cdots$
3267.2.a.a	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓				297.2.a.a	$1$	$1$	$-2$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{5}-q^{7}-4q^{10}+\cdots$
3267.2.a.b	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓	✓			3267.2.a.b	$1$	$1$	$-1$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}+2q^{10}+\cdots$
3267.2.a.c	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓				297.2.a.b	$1$	$1$	$-1$	$0$	$-2$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+5q^{7}+3q^{8}+2q^{10}+\cdots$
3267.2.a.d	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓	✓			3267.2.a.b	$1$	$1$	$-1$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots$
3267.2.a.e	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			3267.2.a.e	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-4q^{7}-7q^{13}+4q^{16}-7q^{19}+\cdots$
3267.2.a.f	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				27.2.a.a	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+q^{7}-5q^{13}+4q^{16}+7q^{19}+\cdots$
3267.2.a.g	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			3267.2.a.e	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+4q^{7}+7q^{13}+4q^{16}+7q^{19}+\cdots$
3267.2.a.h	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓	✓			3267.2.a.b	$1$	$1$	$1$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}+q^{7}-3q^{8}-2q^{10}+\cdots$
3267.2.a.i	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓	✓			3267.2.a.b	$1$	$1$	$1$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots$
3267.2.a.j	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓				297.2.a.b	$1$	$0$	$1$	$0$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+5q^{7}-3q^{8}+2q^{10}+\cdots$
3267.2.a.k	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	$\Q$	$_{}$	None	None	✓				297.2.a.a	$1$	$1$	$2$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{5}-q^{7}-4q^{10}+\cdots$
3267.2.a.l	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				297.2.a.e	$1$	$0$	$-2$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(1+\beta )q^{5}+\cdots$
3267.2.a.m	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			3267.2.a.m	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$3$	$N(\mathrm{U}(1))$	$q-2q^{4}-\beta q^{7}+\beta q^{13}+4q^{16}+\beta q^{19}+\cdots$
3267.2.a.n	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			3267.2.a.n	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-2\beta q^{7}-\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots$
3267.2.a.o	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			3267.2.a.o	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{7}-\beta q^{8}+\beta q^{13}+\cdots$
3267.2.a.p	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			3267.2.a.o	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+\beta q^{7}-\beta q^{8}-\beta q^{13}+\cdots$
3267.2.a.q	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				297.2.a.e	$1$	$0$	$2$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
3267.2.a.r	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	$_{}$	None	None	✓	✓			3267.2.a.r	$1$	$1$	$-1$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2})q^{5}+\cdots$
3267.2.a.s	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	$_{}$	None	None	✓	✓			3267.2.a.r	$1$	$0$	$-1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{2})q^{5}+\cdots$
3267.2.a.t	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.564.1	$_{}$	None	None	✓				297.2.a.g	$1$	$1$	$-1$	$0$	$-2$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
3267.2.a.u	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	$_{}$	None	None	✓	✓			3267.2.a.r	$1$	$1$	$1$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2})q^{5}+\cdots$
3267.2.a.v	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	$_{}$	None	None	✓	✓			3267.2.a.r	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{2})q^{5}+\cdots$
3267.2.a.w	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.564.1	$_{}$	None	None	✓				297.2.a.g	$1$	$0$	$1$	$0$	$2$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
3267.2.a.x	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	✓			3267.2.a.x	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{2}q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$
3267.2.a.y	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	$\Q(\sqrt{2}, \sqrt{7})$	$_{}$	None	None	✓	✓			3267.2.a.y	$2$	$1$	$0$	$0$	$-4$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
3267.2.a.z	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	4.4.29952.1	$_{}$	None	None	✓	✓			3267.2.a.z	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
3267.2.a.ba	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	4.4.29952.1	$_{}$	None	None	✓	✓			3267.2.a.z	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(1-2\beta _{2}+\cdots)q^{7}+\cdots$
3267.2.a.bb	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	$\Q(\sqrt{2}, \sqrt{7})$	$_{}$	None	None	✓	✓			3267.2.a.y	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
3267.2.a.bc	$3267$	$2$	3267.a	1.a	$1$	$6$	$6$	$26.087$	6.6.19783872.1	$_{}$	None	None	✓	✓			3267.2.a.bc	$2$	$1$	$0$	$0$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$
3267.2.a.bd	$3267$	$2$	3267.a	1.a	$1$	$6$	$6$	$26.087$	6.6.19783872.1	$_{}$	None	None	✓	✓			3267.2.a.bc	$2$	$0$	$0$	$0$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots$

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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.