LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twist	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 71 matches)

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Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
348.2.a.a	$1$	$2.779$	$\Q$	None	$0$	$-1$	$-2$	$1$	$-$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots$
348.2.a.b	$1$	$2.779$	$\Q$	None	$0$	$-1$	$0$	$-3$	$+$	$q-q^{3}-3q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots$
348.2.a.c	$1$	$2.779$	$\Q$	None	$0$	$1$	$-4$	$-3$	$+$	$q+q^{3}-4q^{5}-3q^{7}+q^{9}-q^{11}-3q^{13}+\cdots$
348.2.a.d	$1$	$2.779$	$\Q$	None	$0$	$1$	$2$	$1$	$-$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots$
348.2.b.a	$8$	$2.779$	8.0.12960000.1	None	$0$	$0$	$0$	$0$		$q+\beta _{3}q^{2}-\beta _{4}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$
348.2.b.b	$12$	$2.779$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$\Q(\sqrt{-29}) $	$0$	$0$	$0$	$0$		$q+\beta _{3}q^{2}-\beta _{11}q^{3}-2q^{4}+\beta _{9}q^{5}+\cdots$
348.2.b.c	$12$	$2.779$	12.0.$\cdots$.3	$\Q(\sqrt{-87}) $	$0$	$0$	$0$	$0$		$q-\beta _{6}q^{2}+\beta _{4}q^{3}+\beta _{5}q^{4}-\beta _{3}q^{6}+\cdots$
348.2.b.d	$24$	$2.779$		None	$0$	$0$	$0$	$0$
348.2.c.a	$16$	$2.779$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$0$	$0$	$0$		$q+\beta _{4}q^{2}+\beta _{1}q^{3}+(\beta _{2}+\beta _{9}+\beta _{11}+\cdots)q^{4}+\cdots$
348.2.c.b	$40$	$2.779$		None	$0$	$0$	$0$	$0$
348.2.h.a	$2$	$2.779$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$-6$		$q+iq^{3}-2q^{5}-3q^{7}-q^{9}-3iq^{11}+\cdots$
348.2.h.b	$2$	$2.779$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$8$		$q+iq^{3}-2q^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots$
348.2.h.c	$2$	$2.779$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$8$	$2$		$q+iq^{3}+4q^{5}+q^{7}-q^{9}-5iq^{11}+\cdots$
348.2.i.a	$60$	$2.779$		None	$4$	$0$	$0$	$0$
348.2.l.a	$20$	$2.779$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{14}q^{3}+\beta _{19}q^{5}-\beta _{8}q^{7}-\beta _{3}q^{9}+\cdots$
348.2.m.a	$12$	$2.779$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$-2$	$-5$	$2$		$q+\beta _{11}q^{3}+(-1+\beta _{2}-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$
348.2.m.b	$12$	$2.779$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$0$	$2$	$9$	$2$		$q+\beta _{8}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
348.2.n.a	$36$	$2.779$		None	$0$	$0$	$0$	$-4$
348.2.s.a	$336$	$2.779$		None	$0$	$0$	$0$	$0$
348.2.t.a	$336$	$2.779$		None	$0$	$0$	$0$	$0$
348.2.u.a	$120$	$2.779$		None	$0$	$0$	$0$	$0$
348.2.x.a	$360$	$2.779$		None	$-4$	$0$	$0$	$0$
348.3.d.a	$4$	$9.482$	$\Q(\sqrt{-5}, \sqrt{-29})$	None	$0$	$8$	$0$	$-22$		$q+(2+\beta _{2})q^{3}-2\beta _{2}q^{5}+(-6+\beta _{3})q^{7}+\cdots$
348.3.d.b	$14$	$9.482$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$0$	$-2$	$0$	$26$		$q-\beta _{1}q^{3}-\beta _{11}q^{5}+(2+\beta _{4})q^{7}+\beta _{2}q^{9}+\cdots$
348.3.e.a	$4$	$9.482$	$\Q(i, \sqrt{29})$	None	$0$	$0$	$0$	$-20$		$q-3\beta _{1}q^{3}-\beta _{2}q^{5}-5q^{7}-9q^{9}-2\beta _{3}q^{11}+\cdots$
348.3.e.b	$16$	$9.482$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$0$	$0$	$12$		$q-\beta _{8}q^{3}-\beta _{5}q^{5}+(1+\beta _{4})q^{7}+(1-\beta _{7}+\cdots)q^{9}+\cdots$
348.3.f.a	$56$	$9.482$		None	$0$	$0$	$0$	$0$
348.3.g.a	$60$	$9.482$		None	$0$	$0$	$-8$	$0$
348.3.j.a	$20$	$9.482$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$0$	$0$	$0$		$q+\beta _{6}q^{3}+(-\beta _{1}+\beta _{6}-\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots$
348.3.k.a	$232$	$9.482$		None	$0$	$0$	$0$	$0$
348.3.o.a	$360$	$9.482$		None	$0$	$0$	$8$	$0$
348.3.p.a	$360$	$9.482$		None	$4$	$0$	$8$	$0$
348.3.q.a	$120$	$9.482$		None	$0$	$0$	$0$	$8$
348.3.r.a	$120$	$9.482$		None	$0$	$0$	$0$	$-8$
348.3.v.a	$1392$	$9.482$		None	$0$	$0$	$0$	$0$
348.3.w.a	$120$	$9.482$		None	$0$	$0$	$0$	$0$
348.4.a.a	$1$	$20.533$	$\Q$	None	$0$	$3$	$-9$	$21$	$-$	$q+3q^{3}-9q^{5}+21q^{7}+9q^{9}-66q^{11}+\cdots$
348.4.a.b	$2$	$20.533$	$\Q(\sqrt{13}) $	None	$0$	$6$	$-2$	$-40$	$-$	$q+3q^{3}+(-1-\beta )q^{5}+(-20+3\beta )q^{7}+\cdots$
348.4.a.c	$3$	$20.533$	3.3.189021.1	None	$0$	$9$	$19$	$9$	$+$	$q+3q^{3}+(6-\beta _{2})q^{5}+(3+\beta _{1}-\beta _{2})q^{7}+\cdots$
348.4.a.d	$4$	$20.533$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$0$	$-12$	$-1$	$17$	$+$	$q-3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots$
348.4.a.e	$4$	$20.533$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$0$	$-12$	$9$	$-11$	$-$	$q-3q^{3}+(2-\beta _{2})q^{5}+(-3+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
348.4.h.a	$14$	$20.533$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	$0$	$0$	$24$	$-12$		$q+\beta _{8}q^{3}+(2+\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots$
348.4.l.a	$60$	$20.533$		None	$0$	$0$	$0$	$0$
348.4.m.a	$48$	$20.533$		None	$0$	$-24$	$-21$	$-6$
348.4.m.b	$48$	$20.533$		None	$0$	$24$	$41$	$-6$
348.4.n.a	$84$	$20.533$		None	$0$	$0$	$-24$	$12$
348.5.d.a	$38$	$35.973$		None	$0$	$-18$	$0$	$108$
348.5.e.a	$40$	$35.973$		None	$0$	$0$	$0$	$80$
348.5.j.a	$40$	$35.973$		None	$0$	$0$	$0$	$0$
348.6.a.a	$6$	$55.814$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$0$	$-54$	$-36$	$117$	$-$	$q-9q^{3}+(-6-\beta _{2})q^{5}+(20-\beta _{5})q^{7}+\cdots$

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Abelian varieties over $\F_{q}$

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
348.2.a.a	\(1\)	\(2.779\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(1\)	\(-\)	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots\)
348.2.a.b	\(1\)	\(2.779\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-3\)	\(+\)	\(q-q^{3}-3q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
348.2.a.c	\(1\)	\(2.779\)	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(-3\)	\(+\)	\(q+q^{3}-4q^{5}-3q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
348.2.a.d	\(1\)	\(2.779\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(1\)	\(-\)	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
348.2.b.a	\(8\)	\(2.779\)	8.0.12960000.1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
348.2.b.b	\(12\)	\(2.779\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	\(\Q(\sqrt{-29}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}-\beta _{11}q^{3}-2q^{4}+\beta _{9}q^{5}+\cdots\)
348.2.b.c	\(12\)	\(2.779\)	12.0.\(\cdots\).3	\(\Q(\sqrt{-87}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{6}q^{2}+\beta _{4}q^{3}+\beta _{5}q^{4}-\beta _{3}q^{6}+\cdots\)
348.2.b.d	\(24\)	\(2.779\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.2.c.a	\(16\)	\(2.779\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(\beta _{2}+\beta _{9}+\beta _{11}+\cdots)q^{4}+\cdots\)
348.2.c.b	\(40\)	\(2.779\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.2.h.a	\(2\)	\(2.779\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(-6\)		\(q+iq^{3}-2q^{5}-3q^{7}-q^{9}-3iq^{11}+\cdots\)
348.2.h.b	\(2\)	\(2.779\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(8\)		\(q+iq^{3}-2q^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots\)
348.2.h.c	\(2\)	\(2.779\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(8\)	\(2\)		\(q+iq^{3}+4q^{5}+q^{7}-q^{9}-5iq^{11}+\cdots\)
348.2.i.a	\(60\)	\(2.779\)		None	\(4\)	\(0\)	\(0\)	\(0\)
348.2.l.a	\(20\)	\(2.779\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{14}q^{3}+\beta _{19}q^{5}-\beta _{8}q^{7}-\beta _{3}q^{9}+\cdots\)
348.2.m.a	\(12\)	\(2.779\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(-2\)	\(-5\)	\(2\)		\(q+\beta _{11}q^{3}+(-1+\beta _{2}-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
348.2.m.b	\(12\)	\(2.779\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(0\)	\(2\)	\(9\)	\(2\)		\(q+\beta _{8}q^{3}+(1+\beta _{3}-\beta _{5}+\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
348.2.n.a	\(36\)	\(2.779\)		None	\(0\)	\(0\)	\(0\)	\(-4\)
348.2.s.a	\(336\)	\(2.779\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.2.t.a	\(336\)	\(2.779\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.2.u.a	\(120\)	\(2.779\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.2.x.a	\(360\)	\(2.779\)		None	\(-4\)	\(0\)	\(0\)	\(0\)
348.3.d.a	\(4\)	\(9.482\)	\(\Q(\sqrt{-5}, \sqrt{-29})\)	None	\(0\)	\(8\)	\(0\)	\(-22\)		\(q+(2+\beta _{2})q^{3}-2\beta _{2}q^{5}+(-6+\beta _{3})q^{7}+\cdots\)
348.3.d.b	\(14\)	\(9.482\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(0\)	\(-2\)	\(0\)	\(26\)		\(q-\beta _{1}q^{3}-\beta _{11}q^{5}+(2+\beta _{4})q^{7}+\beta _{2}q^{9}+\cdots\)
348.3.e.a	\(4\)	\(9.482\)	\(\Q(i, \sqrt{29})\)	None	\(0\)	\(0\)	\(0\)	\(-20\)		\(q-3\beta _{1}q^{3}-\beta _{2}q^{5}-5q^{7}-9q^{9}-2\beta _{3}q^{11}+\cdots\)
348.3.e.b	\(16\)	\(9.482\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(12\)		\(q-\beta _{8}q^{3}-\beta _{5}q^{5}+(1+\beta _{4})q^{7}+(1-\beta _{7}+\cdots)q^{9}+\cdots\)
348.3.f.a	\(56\)	\(9.482\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.3.g.a	\(60\)	\(9.482\)		None	\(0\)	\(0\)	\(-8\)	\(0\)
348.3.j.a	\(20\)	\(9.482\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{6}q^{3}+(-\beta _{1}+\beta _{6}-\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots\)
348.3.k.a	\(232\)	\(9.482\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.3.o.a	\(360\)	\(9.482\)		None	\(0\)	\(0\)	\(8\)	\(0\)
348.3.p.a	\(360\)	\(9.482\)		None	\(4\)	\(0\)	\(8\)	\(0\)
348.3.q.a	\(120\)	\(9.482\)		None	\(0\)	\(0\)	\(0\)	\(8\)
348.3.r.a	\(120\)	\(9.482\)		None	\(0\)	\(0\)	\(0\)	\(-8\)
348.3.v.a	\(1392\)	\(9.482\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.3.w.a	\(120\)	\(9.482\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.4.a.a	\(1\)	\(20.533\)	\(\Q\)	None	\(0\)	\(3\)	\(-9\)	\(21\)	\(-\)	\(q+3q^{3}-9q^{5}+21q^{7}+9q^{9}-66q^{11}+\cdots\)
348.4.a.b	\(2\)	\(20.533\)	\(\Q(\sqrt{13}) \)	None	\(0\)	\(6\)	\(-2\)	\(-40\)	\(-\)	\(q+3q^{3}+(-1-\beta )q^{5}+(-20+3\beta )q^{7}+\cdots\)
348.4.a.c	\(3\)	\(20.533\)	3.3.189021.1	None	\(0\)	\(9\)	\(19\)	\(9\)	\(+\)	\(q+3q^{3}+(6-\beta _{2})q^{5}+(3+\beta _{1}-\beta _{2})q^{7}+\cdots\)
348.4.a.d	\(4\)	\(20.533\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(0\)	\(-12\)	\(-1\)	\(17\)	\(+\)	\(q-3q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(4+\beta _{1}+\cdots)q^{7}+\cdots\)
348.4.a.e	\(4\)	\(20.533\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(0\)	\(-12\)	\(9\)	\(-11\)	\(-\)	\(q-3q^{3}+(2-\beta _{2})q^{5}+(-3+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
348.4.h.a	\(14\)	\(20.533\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	\(0\)	\(0\)	\(24\)	\(-12\)		\(q+\beta _{8}q^{3}+(2+\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
348.4.l.a	\(60\)	\(20.533\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.4.m.a	\(48\)	\(20.533\)		None	\(0\)	\(-24\)	\(-21\)	\(-6\)
348.4.m.b	\(48\)	\(20.533\)		None	\(0\)	\(24\)	\(41\)	\(-6\)
348.4.n.a	\(84\)	\(20.533\)		None	\(0\)	\(0\)	\(-24\)	\(12\)
348.5.d.a	\(38\)	\(35.973\)		None	\(0\)	\(-18\)	\(0\)	\(108\)
348.5.e.a	\(40\)	\(35.973\)		None	\(0\)	\(0\)	\(0\)	\(80\)
348.5.j.a	\(40\)	\(35.973\)		None	\(0\)	\(0\)	\(0\)	\(0\)
348.6.a.a	\(6\)	\(55.814\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(0\)	\(-54\)	\(-36\)	\(117\)	\(-\)	\(q-9q^{3}+(-6-\beta _{2})q^{5}+(20-\beta _{5})q^{7}+\cdots\)

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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.