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 157 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
3900.1.f.a	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.f.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+q^{9}+\zeta_{6}q^{13}+\cdots$
3900.1.f.b	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓			3900.1.f.b	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{23}+\cdots$
3900.1.f.c	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None					780.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}-i q^{7}-q^{9}-q^{11}-i q^{13}+\cdots$
3900.1.f.d	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-195}) $	None					780.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{3}-i q^{7}-q^{9}+q^{11}-i q^{13}+\cdots$
3900.1.f.e	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓			3900.1.f.b	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{23}+\cdots$
3900.1.f.f	$3900$	$1$	3900.f	39.d	$2$	$2$	$2$	$1.946$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.f.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
3900.1.o.a	$3900$	$1$	3900.o	195.e	$2$	$4$	$4$	$1.946$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}+\zeta_{12}^{5})q^{7}-q^{9}+\cdots$
3900.1.o.b	$3900$	$1$	3900.o	195.e	$2$	$4$	$4$	$1.946$	$\Q(\zeta_{12})$	$D_{6}$	None	$\Q(\sqrt{13}) $		✓			3900.1.f.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{3}q^{13}+\cdots$
3900.1.t.a	$3900$	$1$	3900.t	195.j	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$S_{4}$	None	None					780.1.t.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}+\cdots$
3900.1.t.b	$3900$	$1$	3900.t	195.j	$4$	$8$	$4$	$1.946$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓		3900.1.t.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{9}q^{3}+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{7}+\cdots$
3900.1.w.a	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		✓			3900.1.w.a	$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}-q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{6}-\zeta_{8}^{3}q^{8}+\cdots$
3900.1.w.b	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		✓			3900.1.w.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{6}+\cdots$
3900.1.w.c	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		✓			3900.1.w.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
3900.1.w.d	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		✓			3900.1.w.a	$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{6}-\zeta_{8}^{3}q^{8}+\cdots$
3900.1.w.e	$3900$	$1$	3900.w	780.w	$4$	$8$	$4$	$1.946$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None					780.1.w.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{2}q^{4}-\zeta_{16}^{3}q^{6}+\cdots$
3900.1.w.f	$3900$	$1$	3900.w	780.w	$4$	$8$	$4$	$1.946$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None					780.1.w.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
3900.1.bo.a	$3900$	$1$	3900.bo	195.u	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$S_{4}$	None	None					780.1.t.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}q^{3}-q^{7}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}+\cdots$
3900.1.bo.b	$3900$	$1$	3900.bo	195.u	$4$	$8$	$4$	$1.946$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓		3900.1.t.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}+\zeta_{24}^{11})q^{7}+\cdots$
3900.1.br.a	$3900$	$1$	3900.br	195.y	$6$	$4$	$2$	$1.946$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.ca.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{5}q^{13}+\cdots$
3900.1.br.b	$3900$	$1$	3900.br	195.y	$6$	$4$	$2$	$1.946$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None					156.1.s.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{7}+\cdots$
3900.1.bu.a	$3900$	$1$	3900.bu	39.i	$6$	$2$	$1$	$1.946$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.bu.a	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
3900.1.bu.b	$3900$	$1$	3900.bu	39.i	$6$	$2$	$1$	$1.946$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					156.1.o.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\zeta_{6}q^{13}+\cdots$
3900.1.bu.c	$3900$	$1$	3900.bu	39.i	$6$	$2$	$1$	$1.946$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.bu.a	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
3900.1.ca.a	$3900$	$1$	3900.ca	39.h	$6$	$2$	$1$	$1.946$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.ca.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
3900.1.ca.b	$3900$	$1$	3900.ca	39.h	$6$	$2$	$1$	$1.946$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					156.1.s.a	$4$	$0$	$0$	$-1$	$0$	$3$		$1$		$q+\zeta_{6}^{2}q^{3}+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots$
3900.1.ca.c	$3900$	$1$	3900.ca	39.h	$6$	$2$	$1$	$1.946$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.ca.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
3900.1.cb.a	$3900$	$1$	3900.cb	195.x	$6$	$4$	$2$	$1.946$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.bu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots$
3900.1.cb.b	$3900$	$1$	3900.cb	195.x	$6$	$4$	$2$	$1.946$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None					156.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots$
3900.1.cu.a	$3900$	$1$	3900.cu	195.ac	$12$	$8$	$2$	$1.946$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.cu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{7}q^{3}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{7}-\zeta_{24}^{2}q^{9}+\cdots$
3900.1.cu.b	$3900$	$1$	3900.cu	195.ac	$12$	$8$	$2$	$1.946$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.cu.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{3}+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{7}-\zeta_{24}^{2}q^{9}+\cdots$
3900.1.cz.a	$3900$	$1$	3900.cz	780.bj	$12$	$8$	$2$	$1.946$	$\Q(\zeta_{24})$	$D_{6}$	None	$\Q(\sqrt{3}) $		✓			3900.1.cz.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{8}q^{6}+\cdots$
3900.1.cz.b	$3900$	$1$	3900.cz	780.bj	$12$	$8$	$2$	$1.946$	$\Q(\zeta_{24})$	$D_{6}$	None	$\Q(\sqrt{3}) $		✓			3900.1.cz.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{8}q^{6}+\cdots$
3900.1.dp.a	$3900$	$1$	3900.dp	195.an	$12$	$8$	$2$	$1.946$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.cu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{5}q^{3}+(\zeta_{24}^{3}-\zeta_{24}^{5})q^{7}+\zeta_{24}^{10}q^{9}+\cdots$
3900.1.dp.b	$3900$	$1$	3900.dp	195.an	$12$	$8$	$2$	$1.946$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			3900.1.cu.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{5}q^{3}+(\zeta_{24}-\zeta_{24}^{7})q^{7}+\zeta_{24}^{10}q^{9}+\cdots$
3900.1.el.a	$3900$	$1$	3900.el	3900.dl	$20$	$32$	$4$	$1.946$	$\Q(\zeta_{80})$	$D_{40}$	$\Q(\sqrt{-39}) $	None		✓			3900.1.el.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{80}^{31}q^{2}+\zeta_{80}^{6}q^{3}-\zeta_{80}^{22}q^{4}+\cdots$
3900.1.el.b	$3900$	$1$	3900.el	3900.dl	$20$	$32$	$4$	$1.946$	$\Q(\zeta_{80})$	$D_{40}$	$\Q(\sqrt{-39}) $	None		✓			3900.1.el.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{80}^{35}q^{2}+\zeta_{80}^{2}q^{3}-\zeta_{80}^{30}q^{4}+\cdots$
3900.2.a.a	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				156.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-q^{13}+6q^{17}+\cdots$
3900.2.a.b	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓	✓			3900.2.a.b	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}-3q^{17}+\cdots$
3900.2.a.c	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.h.a	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}+7q^{17}+\cdots$
3900.2.a.d	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.a.d	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+3q^{11}-q^{13}-3q^{17}+\cdots$
3900.2.a.e	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.a.c	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-6q^{11}+q^{13}+\cdots$
3900.2.a.f	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓	✓			3900.2.a.f	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}+q^{11}+q^{13}+3q^{17}+\cdots$
3900.2.a.g	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.h.b	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}+3q^{11}+q^{13}+\cdots$
3900.2.a.h	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓	✓			3900.2.a.f	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+q^{11}-q^{13}-3q^{17}+\cdots$
3900.2.a.i	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.a.b	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+q^{11}-q^{13}+3q^{17}+\cdots$
3900.2.a.j	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.h.b	$1$	$0$	$0$	$1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$
3900.2.a.k	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.h.a	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}-7q^{17}+\cdots$
3900.2.a.l	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓	✓			3900.2.a.b	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}+3q^{17}+\cdots$
3900.2.a.m	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				156.2.a.a	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}-4q^{11}-q^{13}+\cdots$
3900.2.a.n	$3900$	$2$	3900.a	1.a	$1$	$1$	$1$	$31.142$	$\Q$	$_{}$	None	None	✓				780.2.a.a	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}-2q^{11}+q^{13}+\cdots$

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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.