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 221 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
3600.1.c.a	$3600$	$1$	3600.c	15.d	$2$	$4$	$4$	$1.797$	$\Q(\zeta_{8})$	$S_{4}$	None	None			✓	✓	1800.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q-\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\zeta_{8}^{2}q^{13}+\cdots$
3600.1.e.a	$3600$	$1$	3600.e	4.b	$2$	$1$	$1$	$1.797$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓				80.1.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+2q^{29}+2q^{41}+q^{49}-2q^{61}+2q^{89}+\cdots$
3600.1.e.b	$3600$	$1$	3600.e	4.b	$2$	$1$	$1$	$1.797$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $	✓				144.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+2q^{13}-2q^{37}+q^{49}+2q^{61}+2q^{73}+\cdots$
3600.1.e.c	$3600$	$1$	3600.e	4.b	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3600.1.e.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
3600.1.e.d	$3600$	$1$	3600.e	4.b	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3600.1.e.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
3600.1.j.a	$3600$	$1$	3600.j	20.d	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $					144.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-2 i q^{13}-2 i q^{37}-q^{49}+2 q^{61}+\cdots$
3600.1.j.b	$3600$	$1$	3600.j	20.d	$2$	$4$	$4$	$1.797$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓		3600.1.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{12}+\zeta_{12}^{5})q^{7}-\zeta_{12}^{3}q^{13}+\cdots$
3600.1.l.a	$3600$	$1$	3600.l	3.b	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None					1800.1.l.a	$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}+\beta q^{11}-q^{13}-\beta q^{17}-q^{19}+\cdots$
3600.1.l.b	$3600$	$1$	3600.l	3.b	$2$	$2$	$2$	$1.797$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None					1800.1.l.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q+q^{7}-\beta q^{11}+q^{13}-\beta q^{17}-q^{19}+\cdots$
3600.1.bb.a	$3600$	$1$	3600.bb	80.i	$4$	$2$	$1$	$1.797$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3600.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}+q^{16}+(i-1)q^{17}+\cdots$
3600.1.bb.b	$3600$	$1$	3600.bb	80.i	$4$	$2$	$1$	$1.797$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3600.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-q^{4}-i q^{8}+q^{16}+(-i+1)q^{17}+\cdots$
3600.1.bf.a	$3600$	$1$	3600.bf	80.t	$4$	$2$	$1$	$1.797$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3600.1.bb.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{16}+(-i+1)q^{17}+\cdots$
3600.1.bf.b	$3600$	$1$	3600.bf	80.t	$4$	$2$	$1$	$1.797$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3600.1.bb.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+(i-1)q^{17}+\cdots$
3600.1.bh.a	$3600$	$1$	3600.bh	5.c	$4$	$2$	$1$	$1.797$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{5}) $					225.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-2 i q^{19}+2 q^{31}-i q^{49}+2 q^{61}+\cdots$
3600.1.bh.b	$3600$	$1$	3600.bh	5.c	$4$	$4$	$2$	$1.797$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓		900.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{7}+\beta _{3}q^{13}+\beta _{2}q^{19}-q^{31}+\cdots$
3600.1.bk.a	$3600$	$1$	3600.bk	60.l	$4$	$4$	$2$	$1.797$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	720.1.bk.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-1-\zeta_{8}^{2})q^{13}-\zeta_{8}q^{17}+(-\zeta_{8}+\cdots)q^{29}+\cdots$
3600.1.bo.a	$3600$	$1$	3600.bo	16.f	$4$	$4$	$2$	$1.797$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None			✓	✓	720.1.r.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}-q^{16}+\cdots$
3600.1.cc.a	$3600$	$1$	3600.cc	36.f	$6$	$2$	$1$	$1.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None					720.1.bu.a	$4$	$0$	$0$	$-1$	$0$	$-3$		$1$		$q-\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
3600.1.cc.b	$3600$	$1$	3600.cc	36.f	$6$	$2$	$1$	$1.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None					720.1.bu.a	$4$	$0$	$0$	$1$	$0$	$3$		$1$		$q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\cdots)q^{21}+\cdots$
3600.1.cj.a	$3600$	$1$	3600.cj	100.j	$10$	$8$	$2$	$1.797$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	3600.1.cj.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{9}q^{5}+(\zeta_{20}^{6}-\zeta_{20}^{8})q^{13}+(-\zeta_{20}+\cdots)q^{17}+\cdots$
3600.1.ct.a	$3600$	$1$	3600.ct	100.h	$10$	$4$	$1$	$1.797$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None			✓	✓	400.1.x.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+\zeta_{10}^{4}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{13}+\cdots$
3600.1.da.a	$3600$	$1$	3600.da	180.v	$12$	$8$	$2$	$1.797$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	3600.1.da.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{7}-\zeta_{24}^{2}q^{9}+\cdots$
3600.1.dx.a	$3600$	$1$	3600.dx	300.u	$20$	$16$	$2$	$1.797$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	3600.1.dx.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{7}q^{5}+(-\zeta_{40}^{4}+\zeta_{40}^{18})q^{13}+\cdots$
3600.2.a.a	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				600.2.a.e	$1$	$0$	$0$	$0$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{7}-6q^{11}+3q^{13}-2q^{17}-q^{19}+\cdots$
3600.2.a.b	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				225.2.a.c	$2$	$1$	$0$	$0$	$0$	$-5$	$+$	$1$	$N(\mathrm{U}(1))$	$q-5q^{7}+5q^{13}+q^{19}+7q^{31}-10q^{37}+\cdots$
3600.2.a.c	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				360.2.f.b	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-4q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots$
3600.2.a.d	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				60.2.d.a	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-4q^{11}-4q^{17}+4q^{23}+6q^{29}+\cdots$
3600.2.a.e	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				36.2.a.a	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$N(\mathrm{U}(1))$	$q-4q^{7}-2q^{13}-8q^{19}+4q^{31}+10q^{37}+\cdots$
3600.2.a.f	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				30.2.a.a	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-2q^{13}+6q^{17}+4q^{19}+6q^{29}+\cdots$
3600.2.a.g	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				360.2.f.b	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}+4q^{11}-4q^{13}-6q^{17}+4q^{19}+\cdots$
3600.2.a.h	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				40.2.a.a	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots$
3600.2.a.i	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				600.2.a.b	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+2q^{11}-3q^{13}-6q^{17}+7q^{19}+\cdots$
3600.2.a.j	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				75.2.a.a	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+2q^{11}-q^{13}+2q^{17}+5q^{19}+\cdots$
3600.2.a.k	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				40.2.c.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-4q^{11}+4q^{13}+4q^{19}-2q^{23}+\cdots$
3600.2.a.l	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				50.2.a.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{11}-4q^{13}+3q^{17}-5q^{19}+\cdots$
3600.2.a.m	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				200.2.a.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}+4q^{13}-5q^{17}-q^{19}+\cdots$
3600.2.a.n	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				120.2.f.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{11}-2q^{13}+6q^{17}-8q^{19}+\cdots$
3600.2.a.o	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				30.2.c.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{11}+6q^{13}-2q^{17}-4q^{23}+\cdots$
3600.2.a.p	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				1800.2.a.k	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{11}-q^{13}+4q^{17}-q^{19}+\cdots$
3600.2.a.q	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				900.2.a.d	$2$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$N(\mathrm{U}(1))$	$q-q^{7}+7q^{13}+7q^{19}-11q^{31}+10q^{37}+\cdots$
3600.2.a.r	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				1800.2.a.k	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{11}-q^{13}-4q^{17}-q^{19}+\cdots$
3600.2.a.s	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				300.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+6q^{11}-5q^{13}-6q^{17}-5q^{19}+\cdots$
3600.2.a.t	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				120.2.a.b	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{11}-6q^{13}-6q^{17}+4q^{19}+\cdots$
3600.2.a.u	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots$
3600.2.a.v	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				24.2.a.a	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots$
3600.2.a.w	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				1800.2.a.k	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-4q^{11}+q^{13}-4q^{17}-q^{19}+\cdots$
3600.2.a.x	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				900.2.a.d	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$N(\mathrm{U}(1))$	$q+q^{7}-7q^{13}+7q^{19}-11q^{31}-10q^{37}+\cdots$
3600.2.a.y	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				1800.2.a.k	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{11}+q^{13}+4q^{17}-q^{19}+\cdots$
3600.2.a.z	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				300.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+6q^{11}+5q^{13}+6q^{17}-5q^{19}+\cdots$
3600.2.a.ba	$3600$	$2$	3600.a	1.a	$1$	$1$	$1$	$28.746$	$\Q$	$_{}$	None	None	✓				90.2.a.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-6q^{11}+4q^{13}+6q^{17}+4q^{19}+\cdots$

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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.