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 108 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
2325.1.m.a	$2325$	$1$	2325.m	465.m	$4$	$4$	$2$	$1.160$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{93}) $		✓			2325.1.m.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{9}+\zeta_{8}q^{12}+\cdots$
2325.1.m.b	$2325$	$1$	2325.m	465.m	$4$	$4$	$2$	$1.160$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{465}) $		✓			2325.1.m.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{9}-\zeta_{8}^{3}q^{12}+\cdots$
2325.1.u.a	$2325$	$1$	2325.u	93.h	$6$	$2$	$1$	$1.160$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.u.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{12}+\cdots$
2325.1.u.b	$2325$	$1$	2325.u	93.h	$6$	$2$	$1$	$1.160$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.u.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{12}+\cdots$
2325.1.u.c	$2325$	$1$	2325.u	93.h	$6$	$4$	$2$	$1.160$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓			2325.1.u.c	$4$	$0$	$0$	$-2$	$0$	$2$		$1$		$q-\beta _{3}q^{2}-\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{6}+\cdots$
2325.1.u.d	$2325$	$1$	2325.u	93.h	$6$	$4$	$2$	$1.160$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-15}) $	None					465.1.u.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{4}q^{6}-\zeta_{12}^{3}q^{8}+\cdots$
2325.1.u.e	$2325$	$1$	2325.u	93.h	$6$	$4$	$2$	$1.160$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓			2325.1.u.c	$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q-\beta _{3}q^{2}+\beta _{2}q^{3}-q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots$
2325.1.z.a	$2325$	$1$	2325.z	465.u	$6$	$4$	$2$	$1.160$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.u.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-q^{4}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{4}q^{9}+\cdots$
2325.1.z.b	$2325$	$1$	2325.z	465.u	$6$	$8$	$4$	$1.160$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓		2325.1.u.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{24}^{3}+\zeta_{24}^{9})q^{2}-\zeta_{24}^{10}q^{3}+\cdots$
2325.1.bq.a	$2325$	$1$	2325.bq	465.x	$10$	$8$	$2$	$1.160$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-3}) $	None			✓	✓	93.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{6}q^{4}+(\zeta_{20}^{3}-\zeta_{20}^{9}+\cdots)q^{7}+\cdots$
2325.1.bv.a	$2325$	$1$	2325.bv	2325.av	$10$	$8$	$2$	$1.160$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓	✓	✓	2325.1.bv.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{20}^{5}q^{3}-\zeta_{20}^{6}q^{4}+\zeta_{20}q^{5}-\zeta_{20}^{4}q^{7}+\cdots$
2325.1.bz.a	$2325$	$1$	2325.bz	2325.az	$10$	$8$	$2$	$1.160$	$\Q(\zeta_{20})$	$A_{5}$	None	None		✓	✓	✓	2325.1.bv.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{20}^{3}q^{3}-\zeta_{20}^{6}q^{4}-\zeta_{20}^{7}q^{5}+\cdots$
2325.1.ca.a	$2325$	$1$	2325.ca	93.l	$10$	$4$	$1$	$1.160$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None					93.1.l.a	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q-\zeta_{10}^{2}q^{3}-\zeta_{10}q^{4}+(\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
2325.1.ca.b	$2325$	$1$	2325.ca	93.l	$10$	$8$	$2$	$1.160$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-15}) $	None			✓		465.1.x.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+\zeta_{20}^{9}q^{3}+(\zeta_{20}^{2}+\cdots)q^{4}+\cdots$
2325.1.cq.a	$2325$	$1$	2325.cq	465.ac	$12$	$8$	$2$	$1.160$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.cq.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{3}+\zeta_{24}^{6}q^{4}+(\zeta_{24}-\zeta_{24}^{9}+\cdots)q^{7}+\cdots$
2325.1.cq.b	$2325$	$1$	2325.cq	465.ac	$12$	$8$	$2$	$1.160$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			2325.1.cq.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{11})q^{2}-\zeta_{24}^{5}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
2325.1.dj.a	$2325$	$1$	2325.dj	465.ah	$20$	$16$	$2$	$1.160$	$\Q(\zeta_{40})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.dj.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{3}q^{3}+\zeta_{40}^{14}q^{4}+(\zeta_{40}-\zeta_{40}^{17}+\cdots)q^{7}+\cdots$
2325.1.dj.b	$2325$	$1$	2325.dj	465.ah	$20$	$16$	$2$	$1.160$	$\Q(\zeta_{40})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			2325.1.dj.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{40}^{3}-\zeta_{40}^{11})q^{2}+\zeta_{40}^{13}q^{3}+\cdots$
2325.1.ee.a	$2325$	$1$	2325.ee	465.al	$30$	$16$	$2$	$1.160$	$\Q(\zeta_{60})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	2325.1.fd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{60}^{13}q^{3}-\zeta_{60}^{24}q^{4}+(\zeta_{60}^{11}+\cdots)q^{7}+\cdots$
2325.1.fd.a	$2325$	$1$	2325.fd	93.o	$30$	$8$	$1$	$1.160$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.fd.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q+\zeta_{30}^{13}q^{3}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{11}-\zeta_{30}^{12}+\cdots)q^{7}+\cdots$
2325.1.fd.b	$2325$	$1$	2325.fd	93.o	$30$	$8$	$1$	$1.160$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.fd.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q-\zeta_{30}^{13}q^{3}-\zeta_{30}^{9}q^{4}+(-\zeta_{30}^{11}+\cdots)q^{7}+\cdots$
2325.1.fd.c	$2325$	$1$	2325.fd	93.o	$30$	$16$	$2$	$1.160$	$\Q(\zeta_{60})$	$D_{15}$	$\Q(\sqrt{-15}) $	None			✓		465.1.bl.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{60}^{11}+\zeta_{60}^{13})q^{2}+\zeta_{60}^{23}q^{3}+\cdots$
2325.1.gg.a	$2325$	$1$	2325.gg	465.av	$60$	$32$	$2$	$1.160$	$\Q(\zeta_{120})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			2325.1.gg.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{120}^{23}-\zeta_{120}^{31})q^{2}-\zeta_{120}^{13}q^{3}+\cdots$
2325.1.gg.b	$2325$	$1$	2325.gg	465.av	$60$	$32$	$2$	$1.160$	$\Q(\zeta_{120})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		✓			2325.1.gg.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{120}^{43}q^{3}+\zeta_{120}^{54}q^{4}+(-\zeta_{120}^{41}+\cdots)q^{7}+\cdots$
2325.2.a.a	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.a	$1$	$1$	$-2$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+4q^{7}+\cdots$
2325.2.a.b	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.b	$1$	$1$	$-2$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-4q^{7}+\cdots$
2325.2.a.c	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.c	$1$	$1$	$-1$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}-2q^{7}+3q^{8}+\cdots$
2325.2.a.d	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓				465.2.a.b	$1$	$1$	$-1$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots$
2325.2.a.e	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.e	$1$	$1$	$-1$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots$
2325.2.a.f	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.f	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{9}-3q^{11}+2q^{12}+\cdots$
2325.2.a.g	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.f	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{9}-3q^{11}-2q^{12}+\cdots$
2325.2.a.h	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.e	$1$	$1$	$1$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-2q^{7}-3q^{8}+\cdots$
2325.2.a.i	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓				465.2.a.a	$1$	$1$	$1$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+4q^{7}-3q^{8}+\cdots$
2325.2.a.j	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.c	$1$	$1$	$1$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+2q^{7}-3q^{8}+\cdots$
2325.2.a.k	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.b	$1$	$1$	$2$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+4q^{7}+\cdots$
2325.2.a.l	$2325$	$2$	2325.a	1.a	$1$	$1$	$1$	$18.565$	$\Q$	$_{}$	None	None	✓	✓			2325.2.a.a	$1$	$1$	$2$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}-4q^{7}+\cdots$
2325.2.a.m	$2325$	$2$	2325.a	1.a	$1$	$2$	$2$	$18.565$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				465.2.a.d	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}+(3-\beta )q^{7}+\cdots$
2325.2.a.n	$2325$	$2$	2325.a	1.a	$1$	$2$	$2$	$18.565$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				465.2.a.c	$1$	$0$	$2$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
2325.2.a.o	$2325$	$2$	2325.a	1.a	$1$	$2$	$2$	$18.565$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				93.2.a.a	$1$	$0$	$3$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots$
2325.2.a.p	$2325$	$2$	2325.a	1.a	$1$	$3$	$3$	$18.565$	3.3.148.1	$_{}$	None	None	✓				465.2.a.g	$1$	$1$	$-3$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2325.2.a.q	$2325$	$2$	2325.a	1.a	$1$	$3$	$3$	$18.565$	3.3.148.1	$_{}$	None	None	✓				465.2.a.f	$1$	$0$	$-1$	$-3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2325.2.a.r	$2325$	$2$	2325.a	1.a	$1$	$3$	$3$	$18.565$	3.3.564.1	$_{}$	None	None	✓		✓		465.2.a.e	$1$	$1$	$-1$	$3$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
2325.2.a.s	$2325$	$2$	2325.a	1.a	$1$	$3$	$3$	$18.565$	3.3.229.1	$_{}$	None	None	✓				93.2.a.b	$1$	$1$	$0$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
2325.2.a.t	$2325$	$2$	2325.a	1.a	$1$	$3$	$3$	$18.565$	3.3.148.1	$_{}$	None	None	✓	✓			2325.2.a.t	$1$	$1$	$0$	$-3$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$
2325.2.a.u	$2325$	$2$	2325.a	1.a	$1$	$3$	$3$	$18.565$	3.3.148.1	$_{}$	None	None	✓	✓			2325.2.a.t	$1$	$1$	$0$	$3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots$
2325.2.a.v	$2325$	$2$	2325.a	1.a	$1$	$4$	$4$	$18.565$	4.4.8468.1	$_{}$	None	None	✓				465.2.a.h	$1$	$0$	$-2$	$4$	$0$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+q^{3}+(2-\beta _{1})q^{4}+\beta _{2}q^{6}+\cdots$
2325.2.a.w	$2325$	$2$	2325.a	1.a	$1$	$5$	$5$	$18.565$	5.5.126032.1	$_{}$	None	None	✓		✓		465.2.c.a	$1$	$1$	$-3$	$5$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}+q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
2325.2.a.x	$2325$	$2$	2325.a	1.a	$1$	$5$	$5$	$18.565$	5.5.126032.1	$_{}$	None	None	✓				465.2.c.a	$1$	$0$	$3$	$-5$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}-q^{3}+(1-\beta _{1}+\beta _{3})q^{4}+\cdots$
2325.2.a.y	$2325$	$2$	2325.a	1.a	$1$	$6$	$6$	$18.565$	6.6.75968016.1	$_{}$	None	None	✓	✓	✓		2325.2.a.y	$1$	$0$	$-1$	$-6$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\beta _{1}q^{6}+\cdots$
2325.2.a.z	$2325$	$2$	2325.a	1.a	$1$	$6$	$6$	$18.565$	6.6.136751504.1	$_{}$	None	None	✓	✓			2325.2.a.z	$1$	$0$	$-1$	$6$	$0$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$

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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.