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 84 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
3720.1.ba.a	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
3720.1.ba.b	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
3720.1.ba.c	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$-1$	$1$	$-1$	$-1$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
3720.1.ba.d	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$-1$	$1$	$1$	$1$	$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
3720.1.ba.e	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$1$	$-1$	$-1$	$1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
3720.1.ba.f	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$1$	$-1$	$1$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
3720.1.ba.g	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$1$	$1$	$-1$	$1$	$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
3720.1.ba.h	$3720$	$1$	3720.ba	3720.aa	$2$	$1$	$1$	$1.857$	$\Q$	$D_{3}$	$\Q(\sqrt{-930}) $	None	✓	✓			3720.1.ba.a	$2$	$0$	$1$	$1$	$1$	$-1$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
3720.1.ba.i	$3720$	$1$	3720.ba	3720.aa	$2$	$2$	$2$	$1.857$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-186}) $	$\Q(\sqrt{310}) $		✓			3720.1.ba.i	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-i q^{2}-i q^{3}-q^{4}-i q^{5}-q^{6}+\cdots$
3720.1.ba.j	$3720$	$1$	3720.ba	3720.aa	$2$	$2$	$2$	$1.857$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-186}) $	$\Q(\sqrt{310}) $		✓			3720.1.ba.i	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-i q^{2}+i q^{3}-q^{4}-i q^{5}+q^{6}+\cdots$
3720.1.ba.k	$3720$	$1$	3720.ba	3720.aa	$2$	$4$	$4$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-186}) $	None		✓			3720.1.ba.k	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{3}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots$
3720.1.ba.l	$3720$	$1$	3720.ba	3720.aa	$2$	$4$	$4$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-186}) $	None		✓			3720.1.ba.k	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{3}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots$
3720.1.bn.a	$3720$	$1$	3720.bn	3720.an	$4$	$4$	$2$	$1.857$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{186}) $		✓			3720.1.bn.a	$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots$
3720.1.bn.b	$3720$	$1$	3720.bn	3720.an	$4$	$4$	$2$	$1.857$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.bn.b	$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
3720.1.bn.c	$3720$	$1$	3720.bn	3720.an	$4$	$4$	$2$	$1.857$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.bn.b	$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
3720.1.bn.d	$3720$	$1$	3720.bn	3720.an	$4$	$4$	$2$	$1.857$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{186}) $		✓			3720.1.bn.a	$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots$
3720.1.cd.a	$3720$	$1$	3720.cd	3720.bd	$6$	$4$	$2$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.cd.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
3720.1.cd.b	$3720$	$1$	3720.cd	3720.bd	$6$	$4$	$2$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.cd.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
3720.1.co.a	$3720$	$1$	3720.co	3720.bo	$6$	$2$	$1$	$1.857$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.co.a	$4$	$0$	$-2$	$-1$	$1$	$0$	$1$		$q-q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
3720.1.co.b	$3720$	$1$	3720.co	3720.bo	$6$	$2$	$1$	$1.857$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.co.a	$4$	$0$	$-2$	$1$	$-1$	$0$	$1$		$q-q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
3720.1.co.c	$3720$	$1$	3720.co	3720.bo	$6$	$2$	$1$	$1.857$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.co.a	$4$	$0$	$2$	$-1$	$-1$	$0$	$1$		$q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
3720.1.co.d	$3720$	$1$	3720.co	3720.bo	$6$	$2$	$1$	$1.857$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.co.a	$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
3720.1.co.e	$3720$	$1$	3720.co	3720.bo	$6$	$4$	$2$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.co.e	$8$	$0$	$0$	$0$	$0$	$-6$	$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots$
3720.1.co.f	$3720$	$1$	3720.co	3720.bo	$6$	$4$	$2$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.co.e	$8$	$0$	$0$	$0$	$0$	$6$	$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots$
3720.1.co.g	$3720$	$1$	3720.co	3720.bo	$6$	$4$	$2$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.co.g	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}+\cdots$
3720.1.co.h	$3720$	$1$	3720.co	3720.bo	$6$	$4$	$2$	$1.857$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.co.g	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
3720.1.cz.a	$3720$	$1$	3720.cz	465.u	$6$	$8$	$4$	$1.857$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	3720.1.cz.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{3}-\zeta_{24}^{2}q^{5}-\zeta_{24}^{2}q^{9}+\cdots$
3720.1.di.a	$3720$	$1$	3720.di	3720.ci	$10$	$8$	$2$	$1.857$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.di.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{3}q^{3}+\zeta_{20}^{6}q^{4}+\cdots$
3720.1.di.b	$3720$	$1$	3720.di	3720.ci	$10$	$8$	$2$	$1.857$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.di.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{3}q^{3}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{5}q^{5}+\cdots$
3720.1.dt.a	$3720$	$1$	3720.dt	3720.ct	$10$	$4$	$1$	$1.857$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.dt.a	$4$	$0$	$-1$	$-1$	$4$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
3720.1.dt.b	$3720$	$1$	3720.dt	3720.ct	$10$	$4$	$1$	$1.857$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.dt.a	$4$	$0$	$-1$	$1$	$-4$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
3720.1.dt.c	$3720$	$1$	3720.dt	3720.ct	$10$	$4$	$1$	$1.857$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.dt.a	$4$	$0$	$1$	$-1$	$-4$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
3720.1.dt.d	$3720$	$1$	3720.dt	3720.ct	$10$	$4$	$1$	$1.857$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.dt.a	$4$	$0$	$1$	$1$	$4$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
3720.1.dt.e	$3720$	$1$	3720.dt	3720.ct	$10$	$8$	$2$	$1.857$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.dt.e	$8$	$0$	$0$	$0$	$0$	$-10$	$1$		$q-\zeta_{20}^{9}q^{2}-\zeta_{20}q^{3}-\zeta_{20}^{8}q^{4}-\zeta_{20}^{7}q^{5}+\cdots$
3720.1.dt.f	$3720$	$1$	3720.dt	3720.ct	$10$	$8$	$2$	$1.857$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.dt.e	$8$	$0$	$0$	$0$	$0$	$10$	$1$		$q-\zeta_{20}^{9}q^{2}-\zeta_{20}q^{3}-\zeta_{20}^{8}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
3720.1.dt.g	$3720$	$1$	3720.dt	3720.ct	$10$	$8$	$2$	$1.857$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.dt.g	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}q^{2}-\zeta_{20}q^{3}+\zeta_{20}^{2}q^{4}+\zeta_{20}^{5}q^{5}+\cdots$
3720.1.dt.h	$3720$	$1$	3720.dt	3720.ct	$10$	$8$	$2$	$1.857$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.dt.g	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{7}q^{2}+\zeta_{20}q^{3}-\zeta_{20}^{4}q^{4}-\zeta_{20}^{5}q^{5}+\cdots$
3720.1.et.a	$3720$	$1$	3720.et	3720.dt	$12$	$8$	$2$	$1.857$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.et.a	$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{24}^{3}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{6}q^{4}+\cdots$
3720.1.et.b	$3720$	$1$	3720.et	3720.dt	$12$	$8$	$2$	$1.857$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.et.a	$8$	$0$	$0$	$0$	$0$	$8$	$1$		$q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{6}q^{4}+\cdots$
3720.1.fi.a	$3720$	$1$	3720.fi	3720.ei	$20$	$16$	$2$	$1.857$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.fi.a	$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{19}q^{3}-\zeta_{40}^{2}q^{4}+\cdots$
3720.1.fi.b	$3720$	$1$	3720.fi	3720.ei	$20$	$16$	$2$	$1.857$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.fi.a	$8$	$0$	$0$	$0$	$0$	$16$	$1$		$q-\zeta_{40}^{11}q^{2}+\zeta_{40}^{19}q^{3}-\zeta_{40}^{2}q^{4}+\cdots$
3720.1.gd.a	$3720$	$1$	3720.gd	3720.fd	$30$	$8$	$1$	$1.857$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.gd.a	$4$	$0$	$-2$	$-1$	$4$	$0$	$1$		$q-\zeta_{30}^{3}q^{2}+\zeta_{30}^{7}q^{3}+\zeta_{30}^{6}q^{4}+\cdots$
3720.1.gd.b	$3720$	$1$	3720.gd	3720.fd	$30$	$8$	$1$	$1.857$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.gd.a	$4$	$0$	$-2$	$1$	$-4$	$0$	$1$		$q-\zeta_{30}^{3}q^{2}-\zeta_{30}^{7}q^{3}+\zeta_{30}^{6}q^{4}+\cdots$
3720.1.gd.c	$3720$	$1$	3720.gd	3720.fd	$30$	$8$	$1$	$1.857$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.gd.a	$4$	$0$	$2$	$-1$	$-4$	$0$	$1$		$q+\zeta_{30}^{3}q^{2}+\zeta_{30}^{7}q^{3}+\zeta_{30}^{6}q^{4}+\cdots$
3720.1.gd.d	$3720$	$1$	3720.gd	3720.fd	$30$	$8$	$1$	$1.857$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-30}) $	None		✓			3720.1.gd.a	$4$	$0$	$2$	$1$	$4$	$0$	$1$		$q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{7}q^{3}+\zeta_{30}^{6}q^{4}+\cdots$
3720.1.gd.e	$3720$	$1$	3720.gd	3720.fd	$30$	$16$	$2$	$1.857$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.gd.e	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{60}^{29}q^{2}+\zeta_{60}^{17}q^{3}-\zeta_{60}^{28}q^{4}+\cdots$
3720.1.gd.f	$3720$	$1$	3720.gd	3720.fd	$30$	$16$	$2$	$1.857$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.gd.e	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{60}^{7}q^{2}+\zeta_{60}^{17}q^{3}+\zeta_{60}^{14}q^{4}+\cdots$
3720.1.gd.g	$3720$	$1$	3720.gd	3720.fd	$30$	$16$	$2$	$1.857$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.gd.g	$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+\zeta_{60}^{3}q^{2}-\zeta_{60}^{17}q^{3}+\zeta_{60}^{6}q^{4}+\cdots$
3720.1.gd.h	$3720$	$1$	3720.gd	3720.fd	$30$	$16$	$2$	$1.857$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-6}) $	None		✓			3720.1.gd.g	$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{60}^{3}q^{2}+\zeta_{60}^{17}q^{3}+\zeta_{60}^{6}q^{4}+\cdots$
3720.1.go.a	$3720$	$1$	3720.go	3720.fo	$30$	$16$	$2$	$1.857$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		✓			3720.1.go.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{60}^{23}q^{2}+\zeta_{60}^{13}q^{3}-\zeta_{60}^{16}q^{4}+\cdots$

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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.