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 99 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
2320.1.h.a	$2320$	$1$	2320.h	580.e	$2$	$1$	$1$	$1.158$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-145}) $	$\Q(\sqrt{29}) $	✓	✓			2320.1.h.a	$4$	$0$	$0$	$0$	$-1$	$-2$		$1$		$q-q^{5}-2q^{7}+q^{9}+2q^{23}+q^{25}+\cdots$
2320.1.h.b	$2320$	$1$	2320.h	580.e	$2$	$1$	$1$	$1.158$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-145}) $	$\Q(\sqrt{29}) $	✓	✓			2320.1.h.a	$4$	$0$	$0$	$0$	$-1$	$2$		$1$		$q-q^{5}+2q^{7}+q^{9}-2q^{23}+q^{25}+\cdots$
2320.1.h.c	$2320$	$1$	2320.h	580.e	$2$	$1$	$1$	$1.158$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-145}) $	$\Q(\sqrt{5}) $	✓	✓			2320.1.h.c	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}-2q^{11}+2q^{19}+q^{25}+\cdots$
2320.1.h.d	$2320$	$1$	2320.h	580.e	$2$	$1$	$1$	$1.158$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-145}) $	$\Q(\sqrt{5}) $	✓	✓			2320.1.h.c	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}+2q^{11}-2q^{19}+q^{25}+\cdots$
2320.1.h.e	$2320$	$1$	2320.h	580.e	$2$	$2$	$2$	$1.158$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None		✓			2320.1.h.e	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+\zeta_{6}^{2}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
2320.1.h.f	$2320$	$1$	2320.h	580.e	$2$	$2$	$2$	$1.158$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-29}) $	None		✓			2320.1.h.e	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
2320.1.v.a	$2320$	$1$	2320.v	580.i	$4$	$2$	$1$	$1.158$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2320.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{5}+q^{9}+(i+1)q^{13}-2 i q^{17}+\cdots$
2320.1.bj.a	$2320$	$1$	2320.bj	145.f	$4$	$2$	$1$	$1.158$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $			✓	✓	145.1.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}+i q^{9}+(i+1)q^{11}+(i+1)q^{19}+\cdots$
2320.1.bm.a	$2320$	$1$	2320.bm	145.h	$4$	$2$	$1$	$1.158$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{29}) $			✓	✓	145.1.h.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+i q^{5}+(i+1)q^{7}-i q^{9}+(-i+1)q^{13}+\cdots$
2320.1.co.a	$2320$	$1$	2320.co	580.t	$4$	$2$	$1$	$1.158$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2320.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}-q^{9}+(-i-1)q^{13}-2 q^{17}+\cdots$
2320.1.cx.a	$2320$	$1$	2320.cx	580.v	$14$	$6$	$1$	$1.158$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		✓			2320.1.cx.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{14}^{3}q^{5}-\zeta_{14}^{6}q^{9}+(-\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{13}+\cdots$
2320.1.cx.b	$2320$	$1$	2320.cx	580.v	$14$	$6$	$1$	$1.158$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		✓			2320.1.cx.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{14}q^{5}-\zeta_{14}^{6}q^{9}+(\zeta_{14}^{4}+\zeta_{14}^{5}+\cdots)q^{13}+\cdots$
2320.1.cx.c	$2320$	$1$	2320.cx	580.v	$14$	$12$	$2$	$1.158$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-5}) $	None		✓	✓		2320.1.cx.c	$8$	$0$	$0$	$0$	$2$	$0$		$7$		$q+(\zeta_{28}^{3}+\zeta_{28}^{9})q^{3}-\zeta_{28}^{4}q^{5}+(\zeta_{28}^{5}+\cdots)q^{7}+\cdots$
2320.1.dd.a	$2320$	$1$	2320.dd	580.y	$14$	$6$	$1$	$1.158$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-5}) $	None		✓			2320.1.dd.a	$4$	$0$	$0$	$0$	$1$	$-5$		$1$		$q+(\zeta_{14}-\zeta_{14}^{5})q^{3}-\zeta_{14}^{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
2320.1.dd.b	$2320$	$1$	2320.dd	580.y	$14$	$6$	$1$	$1.158$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-5}) $	None		✓			2320.1.dd.a	$4$	$0$	$0$	$0$	$1$	$5$		$1$		$q+(-\zeta_{14}+\zeta_{14}^{5})q^{3}-\zeta_{14}^{2}q^{5}+(1+\cdots)q^{7}+\cdots$
2320.1.dr.a	$2320$	$1$	2320.dr	580.ad	$28$	$12$	$1$	$1.158$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2320.1.dr.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{28}^{13}q^{5}-\zeta_{28}^{12}q^{9}+(\zeta_{28}^{3}-\zeta_{28}^{8}+\cdots)q^{13}+\cdots$
2320.1.fg.a	$2320$	$1$	2320.fg	580.am	$28$	$12$	$1$	$1.158$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2320.1.dr.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{9}q^{5}+\zeta_{28}^{12}q^{9}+(\zeta_{28}-\zeta_{28}^{10}+\cdots)q^{13}+\cdots$
2320.2.a.a	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				1160.2.a.d	$1$	$1$	$0$	$-2$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-4q^{7}+q^{9}+6q^{13}+\cdots$
2320.2.a.b	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				1160.2.a.c	$1$	$1$	$0$	$-2$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots$
2320.2.a.c	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				580.2.a.a	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+2q^{11}-2q^{13}+2q^{19}+\cdots$
2320.2.a.d	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				290.2.a.a	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}-2q^{11}-6q^{13}+\cdots$
2320.2.a.e	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				145.2.a.a	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots$
2320.2.a.f	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				1160.2.a.b	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-2q^{13}-6q^{17}+8q^{19}+\cdots$
2320.2.a.g	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				580.2.a.b	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}+4q^{11}-6q^{13}+\cdots$
2320.2.a.h	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	$\Q$	$_{}$	None	None	✓				1160.2.a.a	$1$	$1$	$0$	$2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
2320.2.a.i	$2320$	$2$	2320.a	1.a	$1$	$2$	$2$	$18.525$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				290.2.a.b	$1$	$1$	$0$	$-1$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(-3+\beta )q^{7}+\beta q^{9}+\cdots$
2320.2.a.j	$2320$	$2$	2320.a	1.a	$1$	$2$	$2$	$18.525$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				290.2.a.c	$1$	$1$	$0$	$-1$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots$
2320.2.a.k	$2320$	$2$	2320.a	1.a	$1$	$2$	$2$	$18.525$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				145.2.a.b	$1$	$0$	$0$	$4$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+(2-\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
2320.2.a.l	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.621.1	$_{}$	None	None	✓				290.2.a.e	$1$	$0$	$0$	$-3$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots$
2320.2.a.m	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.564.1	$_{}$	None	None	✓				580.2.a.c	$1$	$0$	$0$	$-2$	$-3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots$
2320.2.a.n	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	$_{}$	None	None	✓		✓		145.2.a.c	$1$	$1$	$0$	$-2$	$3$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots$
2320.2.a.o	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	$_{}$	None	None	✓				580.2.a.d	$1$	$0$	$0$	$-2$	$3$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots$
2320.2.a.p	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.229.1	$_{}$	None	None	✓		✓		1160.2.a.g	$1$	$1$	$0$	$-1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+(1-\beta _{1})q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots$
2320.2.a.q	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.469.1	$_{}$	None	None	✓				290.2.a.d	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots$
2320.2.a.r	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	$_{}$	None	None	✓				1160.2.a.e	$1$	$0$	$0$	$2$	$-3$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots$
2320.2.a.s	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	$_{}$	None	None	✓		✓		145.2.a.d	$1$	$1$	$0$	$2$	$-3$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots$
2320.2.a.t	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	$_{}$	None	None	✓				1160.2.a.f	$1$	$0$	$0$	$2$	$3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots$
2320.2.a.u	$2320$	$2$	2320.a	1.a	$1$	$5$	$5$	$18.525$	5.5.580484.1	$_{}$	None	None	✓		✓		1160.2.a.j	$1$	$1$	$0$	$-3$	$5$	$-7$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{3}+q^{5}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
2320.2.a.v	$2320$	$2$	2320.a	1.a	$1$	$5$	$5$	$18.525$	5.5.3145252.1	$_{}$	None	None	✓		✓		1160.2.a.h	$1$	$0$	$0$	$1$	$-5$	$-7$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-q^{5}+(-1+\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots$
2320.2.a.w	$2320$	$2$	2320.a	1.a	$1$	$5$	$5$	$18.525$	5.5.6083172.1	$_{}$	None	None	✓		✓		1160.2.a.i	$1$	$0$	$0$	$1$	$5$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(\beta _{2}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
2320.2.d.a	$2320$	$2$	2320.d	5.b	$2$	$2$	$2$	$18.525$	$\Q(\sqrt{-1}) $	$_{}$	None	None					1160.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(\beta-1)q^{5}+\beta q^{7}-q^{9}+\cdots$
2320.2.d.b	$2320$	$2$	2320.d	5.b	$2$	$2$	$2$	$18.525$	$\Q(\sqrt{-1}) $	$_{}$	None	None					1160.2.d.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta+1)q^{5}+\beta q^{7}+3 q^{9}+3\beta q^{17}+\cdots$
2320.2.d.c	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					145.2.b.a	$2$	$0$	$0$	$0$	$-3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
2320.2.d.d	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	$\Q(i, \sqrt{5})$	$_{}$	None	None					290.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$
2320.2.d.e	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					580.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots$
2320.2.d.f	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					145.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}+q^{9}+\cdots$
2320.2.d.g	$2320$	$2$	2320.d	5.b	$2$	$6$	$6$	$18.525$	6.0.84345856.2	$_{}$	None	None					145.2.b.c	$2$	$0$	$0$	$0$	$3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{1}q^{5}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
2320.2.d.h	$2320$	$2$	2320.d	5.b	$2$	$10$	$10$	$18.525$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None					290.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}+\beta _{5}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
2320.2.d.i	$2320$	$2$	2320.d	5.b	$2$	$10$	$10$	$18.525$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None					580.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{8}q^{5}+(-\beta _{1}+\beta _{8}+\beta _{9})q^{7}+\cdots$
2320.2.d.j	$2320$	$2$	2320.d	5.b	$2$	$16$	$16$	$18.525$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					1160.2.d.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{13}q^{7}+(-1+\beta _{9}+\cdots)q^{9}+\cdots$

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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.