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 61 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
3025.1.f.a	$3025$	$1$	3025.f	5.c	$4$	$2$	$1$	$1.510$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			3025.1.f.a	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q+(-i-1)q^{2}+i q^{4}+(i+1)q^{7}+\cdots$
3025.1.f.b	$3025$	$1$	3025.f	5.c	$4$	$2$	$1$	$1.510$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None					605.1.f.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(i-1)q^{3}-i q^{4}-i q^{9}+(i+1)q^{12}+\cdots$
3025.1.f.c	$3025$	$1$	3025.f	5.c	$4$	$2$	$1$	$1.510$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			3025.1.f.a	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+(i+1)q^{2}+i q^{4}+(-i-1)q^{7}+\cdots$
3025.1.m.a	$3025$	$1$	3025.m	275.m	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.v.a	$4$	$0$	$0$	$3$	$-1$	$0$		$1$		$q+(1-\zeta_{10})q^{3}+q^{4}+\zeta_{10}^{2}q^{5}+(1+\cdots)q^{9}+\cdots$
3025.1.o.a	$3025$	$1$	3025.o	275.o	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.s.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+(-\zeta_{10}-\zeta_{10}^{4})q^{3}-\zeta_{10}^{4}q^{4}-\zeta_{10}^{4}q^{5}+\cdots$
3025.1.p.a	$3025$	$1$	3025.p	275.p	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.s.a	$4$	$0$	$0$	$-5$	$1$	$0$		$1$		$q+(-1-\zeta_{10})q^{3}-\zeta_{10}^{4}q^{4}+\zeta_{10}q^{5}+\cdots$
3025.1.r.a	$3025$	$1$	3025.r	275.r	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.s.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+(-\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}q^{4}+\zeta_{10}^{3}q^{5}+\cdots$
3025.1.u.a	$3025$	$1$	3025.u	275.u	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.v.a	$4$	$0$	$0$	$3$	$-1$	$0$		$1$		$q+(1+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\cdots$
3025.1.w.a	$3025$	$1$	3025.w	275.w	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.v.a	$4$	$0$	$0$	$-2$	$-1$	$0$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{5}+\cdots$
3025.1.x.a	$3025$	$1$	3025.x	11.d	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $			✓	✓	55.1.d.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{10}^{3}q^{4}-\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots$
3025.1.bc.a	$3025$	$1$	3025.bc	275.ac	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.v.a	$4$	$0$	$0$	$-2$	$-1$	$0$		$1$		$q+(-\zeta_{10}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}-\zeta_{10}q^{5}+\cdots$
3025.1.bd.a	$3025$	$1$	3025.bd	275.ad	$10$	$4$	$1$	$1.510$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None			✓	✓	275.1.s.a	$4$	$0$	$0$	$5$	$1$	$0$		$1$		$q+(1-\zeta_{10}^{2})q^{3}-q^{4}-\zeta_{10}^{4}q^{5}+(1+\cdots)q^{9}+\cdots$
3025.1.bf.a	$3025$	$1$	3025.bf	275.ae	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	3025.1.bj.a	$4$	$0$	$0$	$8$	$0$	$0$		$1$		$q+(1+\zeta_{20}^{9})q^{3}+\zeta_{20}^{5}q^{4}+\zeta_{20}^{3}q^{5}+\cdots$
3025.1.bi.a	$3025$	$1$	3025.bi	275.ah	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	3025.1.bj.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{9}q^{4}+\cdots$
3025.1.bj.a	$3025$	$1$	3025.bj	25.f	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	3025.1.bj.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(\zeta_{20}+\zeta_{20}^{8})q^{3}-\zeta_{20}^{7}q^{4}-\zeta_{20}^{5}q^{5}+\cdots$
3025.1.bk.a	$3025$	$1$	3025.bk	275.aj	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	3025.1.bj.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(\zeta_{20}^{3}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{7}q^{5}+\cdots$
3025.1.bl.a	$3025$	$1$	3025.bl	55.k	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			3025.1.f.a	$16$	$0$	$-2$	$0$	$0$	$2$		$1$		$q+(\zeta_{20}-\zeta_{20}^{6})q^{2}-\zeta_{20}^{7}q^{4}+(\zeta_{20}^{2}+\cdots)q^{7}+\cdots$
3025.1.bl.b	$3025$	$1$	3025.bl	55.k	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{4}$	$\Q(\sqrt{-11}) $	None					605.1.f.a	$16$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{8})q^{3}+\zeta_{20}^{7}q^{4}+\cdots$
3025.1.bl.c	$3025$	$1$	3025.bl	55.k	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓			3025.1.f.a	$16$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+(-\zeta_{20}+\zeta_{20}^{6})q^{2}-\zeta_{20}^{7}q^{4}+(-\zeta_{20}^{2}+\cdots)q^{7}+\cdots$
3025.1.bq.a	$3025$	$1$	3025.bq	275.ap	$20$	$8$	$1$	$1.510$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	3025.1.bj.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-\zeta_{20}^{2}-\zeta_{20}^{5})q^{3}+\zeta_{20}^{3}q^{4}+\cdots$
3025.2.a.a	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	$\Q$	$_{}$	None	None	✓				11.2.a.a	$1$	$0$	$-2$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots$
3025.2.a.b	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	$\Q$	$_{}$	None	None	✓				121.2.a.a	$1$	$0$	$-1$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}+2q^{6}+2q^{7}+3q^{8}+\cdots$
3025.2.a.c	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	$\Q$	$_{}$	None	None	✓				605.2.a.a	$1$	$0$	$-1$	$3$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-q^{4}-3q^{6}-3q^{7}+3q^{8}+\cdots$
3025.2.a.d	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	$\Q$	$_{}$	$\Q(\sqrt{-11}) $	None	✓				121.2.a.b	$2$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+q^{3}-2q^{4}-2q^{9}-2q^{12}+4q^{16}+\cdots$
3025.2.a.e	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	$\Q$	$_{}$	None	None	✓				121.2.a.a	$1$	$0$	$1$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}-2q^{6}-2q^{7}-3q^{8}+\cdots$
3025.2.a.f	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	$\Q$	$_{}$	None	None	✓				55.2.a.a	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}-3q^{9}+2q^{13}+\cdots$
3025.2.a.g	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	$\Q$	$_{}$	None	None	✓				605.2.a.a	$1$	$0$	$1$	$3$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-q^{4}+3q^{6}+3q^{7}-3q^{8}+\cdots$
3025.2.a.h	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				275.2.a.e	$1$	$1$	$-1$	$1$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+3q^{6}+\cdots$
3025.2.a.i	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				275.2.a.d	$1$	$0$	$-1$	$3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
3025.2.a.j	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				605.2.a.f	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-2q^{3}+q^{4}-2\beta q^{6}+2\beta q^{7}+\cdots$
3025.2.a.k	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{11}) $	$_{}$	$\Q(\sqrt{-11}) $	None	✓				605.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-\beta q^{3}-2q^{4}+8q^{9}+2\beta q^{12}+4q^{16}+\cdots$
3025.2.a.l	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				605.2.a.e	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{7}-\beta q^{8}+\cdots$
3025.2.a.m	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				275.2.a.d	$1$	$1$	$1$	$-3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
3025.2.a.n	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				275.2.a.e	$1$	$0$	$1$	$-1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}+3q^{6}+\cdots$
3025.2.a.o	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				55.2.a.b	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+2\beta q^{3}+(1+2\beta )q^{4}+(4+\cdots)q^{6}+\cdots$
3025.2.a.p	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.404.1	$_{}$	None	None	✓				605.2.a.g	$1$	$0$	$-1$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots$
3025.2.a.q	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	$_{}$	None	None	✓	✓			3025.2.a.q	$1$	$1$	$0$	$-3$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
3025.2.a.r	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	$_{}$	None	None	✓	✓			3025.2.a.q	$1$	$1$	$0$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
3025.2.a.s	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	$_{}$	None	None	✓	✓			3025.2.a.q	$1$	$0$	$0$	$3$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
3025.2.a.t	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	$_{}$	None	None	✓	✓			3025.2.a.q	$1$	$0$	$0$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
3025.2.a.u	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.404.1	$_{}$	None	None	✓				605.2.a.g	$1$	$0$	$1$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots$
3025.2.a.v	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.2525.1	$_{}$	None	None	✓				55.2.g.a	$1$	$1$	$-3$	$2$	$0$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
3025.2.a.w	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.725.1	$_{}$	None	None	✓				55.2.g.b	$1$	$0$	$-1$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
3025.2.a.x	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.105840.1	$_{}$	None	None	✓	✓			3025.2.a.x	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(3+\beta _{2})q^{4}+\cdots$
3025.2.a.y	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓				605.2.b.d	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
3025.2.a.z	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓				605.2.b.d	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
3025.2.a.ba	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	$\Q(\sqrt{3}, \sqrt{11})$	$_{}$	None	None	✓				55.2.b.a	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{3})q^{4}+\cdots$
3025.2.a.bb	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.4400.1	$_{}$	$\Q(\sqrt{-55}) $	None	✓				605.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$N(\mathrm{U}(1))$	$q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}+\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots$
3025.2.a.bc	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.105840.1	$_{}$	None	None	✓	✓			3025.2.a.x	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(3+\beta _{2})q^{4}+\cdots$
3025.2.a.bd	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.725.1	$_{}$	None	None	✓				55.2.g.b	$1$	$1$	$1$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$

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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.