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 57 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
3712.1.b.a	$3712$	$1$	3712.b	232.b	$2$	$1$	$1$	$1.853$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-58}) $	$\Q(\sqrt{58}) $	✓	✓			3712.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+q^{25}-q^{29}+2q^{37}+q^{49}+\cdots$
3712.1.b.b	$3712$	$1$	3712.b	232.b	$2$	$1$	$1$	$1.853$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-58}) $	$\Q(\sqrt{58}) $	✓	✓			3712.1.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+q^{25}+q^{29}-2q^{37}+q^{49}+\cdots$
3712.1.b.c	$3712$	$1$	3712.b	232.b	$2$	$4$	$4$	$1.853$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-29}) $	None		✓			3712.1.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{9}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
3712.1.b.d	$3712$	$1$	3712.b	232.b	$2$	$8$	$8$	$1.853$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-29}) $	None		✓	✓		3712.1.b.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q+(-\zeta_{24}-\zeta_{24}^{11})q^{3}+(-\zeta_{24}^{4}-\zeta_{24}^{8}+\cdots)q^{5}+\cdots$
3712.1.r.a	$3712$	$1$	3712.r	232.l	$4$	$2$	$1$	$1.853$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.r.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-2 q^{5}+i q^{9}+(-i-1)q^{17}+3 q^{25}+\cdots$
3712.1.r.b	$3712$	$1$	3712.r	232.l	$4$	$2$	$1$	$1.853$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.r.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q+2 q^{5}+i q^{9}+(-i-1)q^{17}+3 q^{25}+\cdots$
3712.1.r.c	$3712$	$1$	3712.r	232.l	$4$	$4$	$2$	$1.853$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3712.1.r.c	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{8}q^{3}-q^{5}-\zeta_{8}q^{11}+q^{13}+\zeta_{8}q^{15}+\cdots$
3712.1.r.d	$3712$	$1$	3712.r	232.l	$4$	$4$	$2$	$1.853$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			3712.1.r.c	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}q^{3}+q^{5}-\zeta_{8}q^{11}-q^{13}-\zeta_{8}q^{15}+\cdots$
3712.1.bf.a	$3712$	$1$	3712.bf	232.p	$14$	$6$	$1$	$1.853$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.bf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{14}+\zeta_{14}^{3})q^{5}-\zeta_{14}^{6}q^{9}+(\zeta_{14}^{4}+\cdots)q^{13}+\cdots$
3712.1.bf.b	$3712$	$1$	3712.bf	232.p	$14$	$6$	$1$	$1.853$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.bf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{14}-\zeta_{14}^{3})q^{5}-\zeta_{14}^{6}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots$
3712.1.bj.a	$3712$	$1$	3712.bj	232.t	$14$	$6$	$1$	$1.853$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.bj.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{14}-\zeta_{14}^{3})q^{5}+\zeta_{14}^{6}q^{9}+(\zeta_{14}^{4}+\cdots)q^{13}+\cdots$
3712.1.bj.b	$3712$	$1$	3712.bj	232.t	$14$	$6$	$1$	$1.853$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.bj.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{14}+\zeta_{14}^{3})q^{5}+\zeta_{14}^{6}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots$
3712.1.bu.a	$3712$	$1$	3712.bu	232.u	$28$	$12$	$1$	$1.853$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.bu.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+(\zeta_{28}^{8}-\zeta_{28}^{10})q^{5}+\zeta_{28}^{13}q^{9}+\cdots$
3712.1.bu.b	$3712$	$1$	3712.bu	232.u	$28$	$12$	$1$	$1.853$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		✓			3712.1.bu.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q+(-\zeta_{28}^{8}+\zeta_{28}^{10})q^{5}+\zeta_{28}^{13}q^{9}+\cdots$
3712.2.a.a	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.a	$1$	$2$	$0$	$-3$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-2q^{7}+6q^{9}-5q^{11}+\cdots$
3712.2.a.b	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.a	$1$	$1$	$0$	$-3$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+2q^{7}+6q^{9}-5q^{11}+\cdots$
3712.2.a.c	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.c	$1$	$1$	$0$	$-2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots$
3712.2.a.d	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.c	$1$	$0$	$0$	$-2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots$
3712.2.a.e	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.e	$1$	$2$	$0$	$-1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}-2q^{9}-3q^{11}+\cdots$
3712.2.a.f	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.f	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}-2q^{9}+q^{11}+5q^{13}+\cdots$
3712.2.a.g	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.f	$1$	$0$	$0$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}-2q^{9}+q^{11}-5q^{13}+\cdots$
3712.2.a.h	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.e	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}-2q^{9}-3q^{11}+\cdots$
3712.2.a.i	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.f	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}-2q^{9}-q^{11}+5q^{13}+\cdots$
3712.2.a.j	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.e	$1$	$0$	$0$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}-2q^{9}+3q^{11}+\cdots$
3712.2.a.k	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.e	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}-2q^{9}+3q^{11}+\cdots$
3712.2.a.l	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.f	$1$	$1$	$0$	$1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{11}-5q^{13}+\cdots$
3712.2.a.m	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.c	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots$
3712.2.a.n	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.c	$1$	$0$	$0$	$2$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots$
3712.2.a.o	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.a	$1$	$0$	$0$	$3$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+2q^{7}+6q^{9}+5q^{11}+\cdots$
3712.2.a.p	$3712$	$2$	3712.a	1.a	$1$	$1$	$1$	$29.640$	$\Q$	$_{}$	None	None	✓	✓			3712.2.a.a	$1$	$0$	$0$	$3$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-2q^{7}+6q^{9}+5q^{11}+\cdots$
3712.2.a.q	$3712$	$2$	3712.a	1.a	$1$	$2$	$2$	$29.640$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			3712.2.a.q	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+(4+\cdots)q^{11}+\cdots$
3712.2.a.r	$3712$	$2$	3712.a	1.a	$1$	$2$	$2$	$29.640$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			3712.2.a.q	$1$	$0$	$0$	$-1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}+(4+\beta )q^{11}+\cdots$
3712.2.a.s	$3712$	$2$	3712.a	1.a	$1$	$2$	$2$	$29.640$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			3712.2.a.q	$1$	$1$	$0$	$1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots$
3712.2.a.t	$3712$	$2$	3712.a	1.a	$1$	$2$	$2$	$29.640$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			3712.2.a.q	$1$	$1$	$0$	$1$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots$
3712.2.a.u	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.126032.1	$_{}$	None	None	✓	✓			3712.2.a.u	$1$	$1$	$0$	$-3$	$-5$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$
3712.2.a.v	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.1172304.1	$_{}$	None	None	✓	✓			3712.2.a.v	$1$	$1$	$0$	$-3$	$-3$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{4})q^{3}+(-1+\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots$
3712.2.a.w	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.153424.1	$_{}$	None	None	✓	✓			3712.2.a.w	$1$	$1$	$0$	$-3$	$-1$	$6$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{3}+\beta _{3}q^{5}+(1-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
3712.2.a.x	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.153424.1	$_{}$	None	None	✓	✓			3712.2.a.w	$1$	$1$	$0$	$-3$	$1$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{3}-\beta _{3}q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots$
3712.2.a.y	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.1172304.1	$_{}$	None	None	✓	✓			3712.2.a.v	$1$	$0$	$0$	$-3$	$3$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{4})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
3712.2.a.z	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.126032.1	$_{}$	None	None	✓	✓			3712.2.a.u	$1$	$1$	$0$	$-3$	$5$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots$
3712.2.a.ba	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.126032.1	$_{}$	None	None	✓	✓			3712.2.a.u	$1$	$1$	$0$	$3$	$-5$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$
3712.2.a.bb	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.1172304.1	$_{}$	None	None	✓	✓			3712.2.a.v	$1$	$0$	$0$	$3$	$-3$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{3}+(-1+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
3712.2.a.bc	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.153424.1	$_{}$	None	None	✓	✓			3712.2.a.w	$1$	$1$	$0$	$3$	$-1$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{4})q^{3}+\beta _{3}q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
3712.2.a.bd	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.153424.1	$_{}$	None	None	✓	✓			3712.2.a.w	$1$	$0$	$0$	$3$	$1$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{4})q^{3}-\beta _{3}q^{5}+(1-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
3712.2.a.be	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.1172304.1	$_{}$	None	None	✓	✓			3712.2.a.v	$1$	$0$	$0$	$3$	$3$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{3}+(1-\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
3712.2.a.bf	$3712$	$2$	3712.a	1.a	$1$	$5$	$5$	$29.640$	5.5.126032.1	$_{}$	None	None	✓	✓			3712.2.a.u	$1$	$0$	$0$	$3$	$5$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
3712.2.a.bg	$3712$	$2$	3712.a	1.a	$1$	$7$	$7$	$29.640$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		3712.2.a.bg	$1$	$1$	$0$	$-1$	$-7$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(-1-\beta _{3}+\cdots)q^{7}+\cdots$
3712.2.a.bh	$3712$	$2$	3712.a	1.a	$1$	$7$	$7$	$29.640$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			3712.2.a.bg	$1$	$0$	$0$	$-1$	$7$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{4})q^{5}+(1+\beta _{3})q^{7}+\cdots$
3712.2.a.bi	$3712$	$2$	3712.a	1.a	$1$	$7$	$7$	$29.640$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		3712.2.a.bg	$1$	$0$	$0$	$1$	$-7$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(1+\beta _{3})q^{7}+\cdots$
3712.2.a.bj	$3712$	$2$	3712.a	1.a	$1$	$7$	$7$	$29.640$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓			3712.2.a.bg	$1$	$0$	$0$	$1$	$7$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+(-1-\beta _{3})q^{7}+\cdots$

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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.