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 73 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
3888.1.e.a	$3888$	$1$	3888.e	3.b	$2$	$1$	$1$	$1.940$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				972.1.c.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-2q^{7}-q^{13}+q^{19}+q^{25}+q^{31}+\cdots$
3888.1.e.b	$3888$	$1$	3888.e	3.b	$2$	$1$	$1$	$1.940$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				243.1.b.a	$2$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}-q^{13}+q^{19}+q^{25}+q^{31}+\cdots$
3888.1.e.c	$3888$	$1$	3888.e	3.b	$2$	$1$	$1$	$1.940$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓				972.1.c.a	$2$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}+2q^{13}-2q^{19}+q^{25}+q^{31}+\cdots$
3888.1.e.d	$3888$	$1$	3888.e	3.b	$2$	$2$	$2$	$1.940$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None			✓		1944.1.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{5}-\beta q^{11}+q^{13}-\beta q^{17}+q^{19}+\cdots$
3888.1.g.a	$3888$	$1$	3888.g	4.b	$2$	$2$	$2$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}-q^{25}+(\zeta_{6}+\cdots)q^{31}+\cdots$
3888.1.g.b	$3888$	$1$	3888.g	4.b	$2$	$2$	$2$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
3888.1.g.c	$3888$	$1$	3888.g	4.b	$2$	$2$	$2$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}-q^{25}+(\zeta_{6}+\cdots)q^{31}+\cdots$
3888.1.o.a	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.b	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+(-1+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(-\zeta_{6}+\cdots)q^{19}+\cdots$
3888.1.o.b	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+(-1+\zeta_{6}^{2})q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+\cdots$
3888.1.o.c	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}+\zeta_{6}q^{25}+\cdots$
3888.1.o.d	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{13}+(-\zeta_{6}-\zeta_{6}^{2})q^{19}+\zeta_{6}q^{25}+\cdots$
3888.1.o.e	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.b	$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
3888.1.o.f	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3888.1.g.a	$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+\cdots$
3888.1.q.a	$3888$	$1$	3888.q	9.d	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					972.1.c.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
3888.1.q.b	$3888$	$1$	3888.q	9.d	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					243.1.b.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
3888.1.q.c	$3888$	$1$	3888.q	9.d	$6$	$2$	$1$	$1.940$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					972.1.c.b	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
3888.1.q.d	$3888$	$1$	3888.q	9.d	$6$	$4$	$2$	$1.940$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None			✓		1944.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots$
3888.2.a.a	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.a	$1$	$2$	$0$	$0$	$-4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-3q^{7}-2q^{11}-5q^{13}-2q^{17}+\cdots$
3888.2.a.b	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				486.2.a.a	$1$	$1$	$0$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-2q^{7}-4q^{13}+6q^{17}+7q^{19}+\cdots$
3888.2.a.c	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				486.2.a.c	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}+6q^{11}+2q^{13}+q^{19}+\cdots$
3888.2.a.d	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.d	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{7}+2q^{11}+q^{13}-4q^{17}+\cdots$
3888.2.a.e	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.c	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{11}+q^{13}+2q^{17}-5q^{19}+\cdots$
3888.2.a.f	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.b	$1$	$0$	$0$	$0$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+3q^{7}+2q^{11}+q^{13}+8q^{17}+\cdots$
3888.2.a.g	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.e	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}-2q^{13}+4q^{17}+q^{19}+\cdots$
3888.2.a.h	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				243.2.a.b	$2$	$0$	$0$	$0$	$0$	$-5$	$-$	$1$	$N(\mathrm{U}(1))$	$q-5q^{7}+2q^{13}-8q^{19}-5q^{25}+7q^{31}+\cdots$
3888.2.a.i	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				972.2.a.d	$2$	$1$	$0$	$0$	$0$	$-5$	$+$	$1$	$N(\mathrm{U}(1))$	$q-5q^{7}+5q^{13}+7q^{19}-5q^{25}-11q^{31}+\cdots$
3888.2.a.j	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				486.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-6q^{11}-q^{13}+6q^{17}-5q^{19}+\cdots$
3888.2.a.k	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				972.2.a.b	$2$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$N(\mathrm{U}(1))$	$q+q^{7}-7q^{13}+q^{19}-5q^{25}+7q^{31}+\cdots$
3888.2.a.l	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				972.2.a.c	$2$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$N(\mathrm{U}(1))$	$q+q^{7}+2q^{13}-8q^{19}-5q^{25}-11q^{31}+\cdots$
3888.2.a.m	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				486.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+6q^{11}-q^{13}-6q^{17}-5q^{19}+\cdots$
3888.2.a.n	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				243.2.a.a	$2$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$N(\mathrm{U}(1))$	$q+4q^{7}-7q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots$
3888.2.a.o	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓				972.2.a.a	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{7}+5q^{13}+7q^{19}-5q^{25}+7q^{31}+\cdots$
3888.2.a.p	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.e	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}-2q^{13}-4q^{17}+q^{19}+\cdots$
3888.2.a.q	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.d	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{7}-2q^{11}+q^{13}+4q^{17}+\cdots$
3888.2.a.r	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.c	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{11}+q^{13}-2q^{17}-5q^{19}+\cdots$
3888.2.a.s	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.b	$1$	$0$	$0$	$0$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+3q^{7}-2q^{11}+q^{13}-8q^{17}+\cdots$
3888.2.a.t	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				486.2.a.a	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{7}-4q^{13}-6q^{17}+7q^{19}+\cdots$
3888.2.a.u	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				486.2.a.c	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-6q^{11}+2q^{13}+q^{19}+\cdots$
3888.2.a.v	$3888$	$2$	3888.a	1.a	$1$	$1$	$1$	$31.046$	$\Q$	$_{}$	None	None	✓				1944.2.a.a	$1$	$0$	$0$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-3q^{7}+2q^{11}-5q^{13}+2q^{17}+\cdots$
3888.2.a.w	$3888$	$2$	3888.a	1.a	$1$	$2$	$2$	$31.046$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				1944.2.a.k	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}-2\beta q^{7}+(1+3\beta )q^{11}+\cdots$
3888.2.a.x	$3888$	$2$	3888.a	1.a	$1$	$2$	$2$	$31.046$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓				1944.2.a.l	$1$	$0$	$0$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(1+\beta )q^{7}-4q^{11}+(2-2\beta )q^{13}+\cdots$
3888.2.a.y	$3888$	$2$	3888.a	1.a	$1$	$2$	$2$	$31.046$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				972.2.a.e	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$3$	$\mathrm{SU}(2)$	$q+\beta q^{5}-2q^{7}-\beta q^{11}-q^{13}-\beta q^{17}+\cdots$
3888.2.a.z	$3888$	$2$	3888.a	1.a	$1$	$2$	$2$	$31.046$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓				243.2.a.d	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-2q^{7}+\beta q^{11}-q^{13}+3\beta q^{17}+\cdots$
3888.2.a.ba	$3888$	$2$	3888.a	1.a	$1$	$2$	$2$	$31.046$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				243.2.a.c	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}+\beta q^{11}+5q^{13}+q^{19}+\cdots$
3888.2.a.bb	$3888$	$2$	3888.a	1.a	$1$	$2$	$2$	$31.046$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓				1944.2.a.l	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1+\beta )q^{7}+4q^{11}+(2-2\beta )q^{13}+\cdots$
3888.2.a.bc	$3888$	$2$	3888.a	1.a	$1$	$2$	$2$	$31.046$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				1944.2.a.k	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+2\beta q^{7}+(-1+3\beta )q^{11}+\cdots$
3888.2.a.bd	$3888$	$2$	3888.a	1.a	$1$	$3$	$3$	$31.046$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				243.2.a.e	$1$	$1$	$0$	$0$	$-6$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{5}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots$
3888.2.a.be	$3888$	$2$	3888.a	1.a	$1$	$3$	$3$	$31.046$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				486.2.a.g	$1$	$1$	$0$	$0$	$0$	$-6$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-2-\beta _{2})q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\cdots$
3888.2.a.bf	$3888$	$2$	3888.a	1.a	$1$	$3$	$3$	$31.046$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				486.2.a.g	$1$	$0$	$0$	$0$	$0$	$-6$	$-$	$3$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{11}+\cdots$
3888.2.a.bg	$3888$	$2$	3888.a	1.a	$1$	$3$	$3$	$31.046$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓				972.2.a.f	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+(-3-\beta _{1}+\beta _{2})q^{11}+\cdots$

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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.