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 106 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
69.2.a.a	$1$	$0.551$	$\Q$	None	$1$	$1$	$0$	$-2$	$-$	$q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots$
69.2.a.b	$2$	$0.551$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$-2$	$2$	$-$	$q-\beta q^{2}-q^{3}+3q^{4}+(-1+\beta )q^{5}+\cdots$
69.2.c.a	$6$	$0.551$	6.0.8869743.1	$\Q(\sqrt{-23}) $	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
69.2.e.a	$10$	$0.551$	$\Q(\zeta_{22})$	None	$-4$	$1$	$5$	$-8$		$q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
69.2.e.b	$10$	$0.551$	$\Q(\zeta_{22})$	None	$4$	$1$	$-3$	$6$		$q+(-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}+\cdots$
69.2.e.c	$20$	$0.551$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$-4$	$-2$	$-6$	$-6$		$q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots$
69.2.g.a	$60$	$0.551$		None	$0$	$-11$	$0$	$-22$
69.3.b.a	$14$	$1.880$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	$0$	$-4$	$0$	$-4$		$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
69.3.d.a	$8$	$1.880$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$-4$	$0$	$0$	$0$		$q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
69.3.f.a	$80$	$1.880$		None	$4$	$0$	$0$	$0$
69.3.h.a	$140$	$1.880$		None	$0$	$-7$	$0$	$-18$
69.4.a.a	$2$	$4.071$	$\Q(\sqrt{5}) $	None	$-4$	$6$	$-26$	$-10$	$-$	$q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots$
69.4.a.b	$2$	$4.071$	$\Q(\sqrt{2}) $	None	$-2$	$-6$	$8$	$-28$	$-$	$q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots$
69.4.a.c	$4$	$4.071$	4.4.1140200.1	None	$-2$	$-12$	$-2$	$32$	$+$	$q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots$
69.4.a.d	$4$	$4.071$	4.4.2009704.1	None	$4$	$12$	$4$	$-14$	$+$	$q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
69.4.c.a	$2$	$4.071$	$\Q(\sqrt{-23}) $	$\Q(\sqrt{-23}) $	$0$	$4$	$0$	$0$		$q-\beta q^{2}+(2-\beta )q^{3}-15q^{4}+(-23+\cdots)q^{6}+\cdots$
69.4.c.b	$4$	$4.071$	$\Q(\sqrt{-3}, \sqrt{-23})$	$\Q(\sqrt{-23}) $	$0$	$-4$	$0$	$0$		$q+(-1-\beta _{2}-\beta _{3})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots$
69.4.c.c	$16$	$4.071$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$-6$	$0$	$0$		$q-\beta _{11}q^{2}-\beta _{10}q^{3}+(-2+\beta _{1})q^{4}+\cdots$
69.4.e.a	$60$	$4.071$		None	$0$	$-18$	$22$	$24$
69.4.e.b	$60$	$4.071$		None	$4$	$18$	$-6$	$-4$
69.4.g.a	$220$	$4.071$		None	$0$	$-5$	$0$	$-22$
69.5.b.a	$30$	$7.133$		None	$0$	$8$	$0$	$-4$
69.5.d.a	$16$	$7.133$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$12$	$0$	$0$	$0$		$q+(1+\beta _{2})q^{2}+\beta _{3}q^{3}+(9+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
69.5.f.a	$160$	$7.133$		None	$-12$	$0$	$0$	$0$
69.5.h.a	$300$	$7.133$		None	$0$	$-19$	$0$	$-18$
69.6.a.a	$2$	$11.066$	$\Q(\sqrt{29}) $	None	$0$	$-18$	$94$	$-118$	$-$	$q-2\beta q^{2}-9q^{3}+84q^{4}+(47-\beta )q^{5}+\cdots$
69.6.a.b	$3$	$11.066$	3.3.5333.1	None	$-8$	$27$	$-56$	$-114$	$+$	$q+(-3+\beta _{2})q^{2}+9q^{3}+(9-4\beta _{1}-9\beta _{2})q^{4}+\cdots$
69.6.a.c	$4$	$11.066$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$4$	$-36$	$-122$	$62$	$-$	$q+(1+\beta _{1})q^{2}-9q^{3}+(-12+4\beta _{1}+\cdots)q^{4}+\cdots$
69.6.a.d	$4$	$11.066$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$4$	$-36$	$22$	$-62$	$+$	$q+(1-\beta _{1})q^{2}-9q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots$
69.6.a.e	$5$	$11.066$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$8$	$45$	$94$	$272$	$-$	$q+(2-\beta _{2})q^{2}+9q^{3}+(24-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
69.6.c.a	$6$	$11.066$	6.0.8869743.1	$\Q(\sqrt{-23}) $	$0$	$0$	$0$	$0$		$q+(-\beta _{1}-3\beta _{2}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+\cdots$
69.6.c.b	$32$	$11.066$		None	$0$	$0$	$0$	$0$
69.6.e.a	$100$	$11.066$		None	$-8$	$90$	$6$	$118$
69.6.e.b	$100$	$11.066$		None	$12$	$-90$	$-50$	$-78$
69.6.g.a	$380$	$11.066$		None	$0$	$-11$	$0$	$-22$
69.7.b.a	$44$	$15.874$		None	$0$	$20$	$0$	$568$
69.7.d.a	$24$	$15.874$		None	$-20$	$0$	$0$	$0$
69.7.f.a	$240$	$15.874$		None	$20$	$0$	$0$	$0$
69.7.h.a	$460$	$15.874$		None	$0$	$23$	$0$	$-18$
69.8.a.a	$5$	$21.555$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$0$	$-135$	$-266$	$-496$	$-$	$q+\beta _{1}q^{2}-3^{3}q^{3}+(54+2\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
69.8.a.b	$6$	$21.555$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-8$	$162$	$-372$	$-1104$	$-$	$q+(-1-\beta _{1})q^{2}+3^{3}q^{3}+(29+3\beta _{1}+\cdots)q^{4}+\cdots$
69.8.a.c	$7$	$21.555$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$0$	$-189$	$-516$	$1018$	$+$	$q+\beta _{1}q^{2}-3^{3}q^{3}+(93+\beta _{1}+\beta _{2})q^{4}+\cdots$
69.8.a.d	$8$	$21.555$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$24$	$216$	$378$	$126$	$+$	$q+(3-\beta _{1})q^{2}+3^{3}q^{3}+(70-4\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
69.8.c.a	$6$	$21.555$	6.0.8869743.1	$\Q(\sqrt{-23}) $	$0$	$0$	$0$	$0$		$q+(-2\beta _{1}-6\beta _{2}+3\beta _{3}+2\beta _{4}+2\beta _{5})q^{2}+\cdots$
69.8.c.b	$48$	$21.555$		None	$0$	$24$	$0$	$0$
69.8.e.a	$140$	$21.555$		None	$-16$	$-378$	$-6$	$978$
69.8.e.b	$140$	$21.555$		None	$-12$	$378$	$2$	$-394$
69.8.g.a	$540$	$21.555$		None	$0$	$-35$	$0$	$-22$
69.9.b.a	$58$	$28.109$		None	$0$	$-112$	$0$	$6996$
69.9.d.a	$32$	$28.109$		None	$12$	$0$	$0$	$0$

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$\zeta$ zeros

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Higher genus families
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
69.2.a.a	\(1\)	\(0.551\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(-2\)	\(-\)	\(q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots\)
69.2.a.b	\(2\)	\(0.551\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(-2\)	\(2\)	\(-\)	\(q-\beta q^{2}-q^{3}+3q^{4}+(-1+\beta )q^{5}+\cdots\)
69.2.c.a	\(6\)	\(0.551\)	6.0.8869743.1	\(\Q(\sqrt{-23}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
69.2.e.a	\(10\)	\(0.551\)	\(\Q(\zeta_{22})\)	None	\(-4\)	\(1\)	\(5\)	\(-8\)		\(q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
69.2.e.b	\(10\)	\(0.551\)	\(\Q(\zeta_{22})\)	None	\(4\)	\(1\)	\(-3\)	\(6\)		\(q+(-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}+\cdots\)
69.2.e.c	\(20\)	\(0.551\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(-4\)	\(-2\)	\(-6\)	\(-6\)		\(q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots\)
69.2.g.a	\(60\)	\(0.551\)		None	\(0\)	\(-11\)	\(0\)	\(-22\)
69.3.b.a	\(14\)	\(1.880\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	\(0\)	\(-4\)	\(0\)	\(-4\)		\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
69.3.d.a	\(8\)	\(1.880\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
69.3.f.a	\(80\)	\(1.880\)		None	\(4\)	\(0\)	\(0\)	\(0\)
69.3.h.a	\(140\)	\(1.880\)		None	\(0\)	\(-7\)	\(0\)	\(-18\)
69.4.a.a	\(2\)	\(4.071\)	\(\Q(\sqrt{5}) \)	None	\(-4\)	\(6\)	\(-26\)	\(-10\)	\(-\)	\(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
69.4.a.b	\(2\)	\(4.071\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(-6\)	\(8\)	\(-28\)	\(-\)	\(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
69.4.a.c	\(4\)	\(4.071\)	4.4.1140200.1	None	\(-2\)	\(-12\)	\(-2\)	\(32\)	\(+\)	\(q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots\)
69.4.a.d	\(4\)	\(4.071\)	4.4.2009704.1	None	\(4\)	\(12\)	\(4\)	\(-14\)	\(+\)	\(q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
69.4.c.a	\(2\)	\(4.071\)	\(\Q(\sqrt{-23}) \)	\(\Q(\sqrt{-23}) \)	\(0\)	\(4\)	\(0\)	\(0\)		\(q-\beta q^{2}+(2-\beta )q^{3}-15q^{4}+(-23+\cdots)q^{6}+\cdots\)
69.4.c.b	\(4\)	\(4.071\)	\(\Q(\sqrt{-3}, \sqrt{-23})\)	\(\Q(\sqrt{-23}) \)	\(0\)	\(-4\)	\(0\)	\(0\)		\(q+(-1-\beta _{2}-\beta _{3})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots\)
69.4.c.c	\(16\)	\(4.071\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(-6\)	\(0\)	\(0\)		\(q-\beta _{11}q^{2}-\beta _{10}q^{3}+(-2+\beta _{1})q^{4}+\cdots\)
69.4.e.a	\(60\)	\(4.071\)		None	\(0\)	\(-18\)	\(22\)	\(24\)
69.4.e.b	\(60\)	\(4.071\)		None	\(4\)	\(18\)	\(-6\)	\(-4\)
69.4.g.a	\(220\)	\(4.071\)		None	\(0\)	\(-5\)	\(0\)	\(-22\)
69.5.b.a	\(30\)	\(7.133\)		None	\(0\)	\(8\)	\(0\)	\(-4\)
69.5.d.a	\(16\)	\(7.133\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(12\)	\(0\)	\(0\)	\(0\)		\(q+(1+\beta _{2})q^{2}+\beta _{3}q^{3}+(9+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
69.5.f.a	\(160\)	\(7.133\)		None	\(-12\)	\(0\)	\(0\)	\(0\)
69.5.h.a	\(300\)	\(7.133\)		None	\(0\)	\(-19\)	\(0\)	\(-18\)
69.6.a.a	\(2\)	\(11.066\)	\(\Q(\sqrt{29}) \)	None	\(0\)	\(-18\)	\(94\)	\(-118\)	\(-\)	\(q-2\beta q^{2}-9q^{3}+84q^{4}+(47-\beta )q^{5}+\cdots\)
69.6.a.b	\(3\)	\(11.066\)	3.3.5333.1	None	\(-8\)	\(27\)	\(-56\)	\(-114\)	\(+\)	\(q+(-3+\beta _{2})q^{2}+9q^{3}+(9-4\beta _{1}-9\beta _{2})q^{4}+\cdots\)
69.6.a.c	\(4\)	\(11.066\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(4\)	\(-36\)	\(-122\)	\(62\)	\(-\)	\(q+(1+\beta _{1})q^{2}-9q^{3}+(-12+4\beta _{1}+\cdots)q^{4}+\cdots\)
69.6.a.d	\(4\)	\(11.066\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(4\)	\(-36\)	\(22\)	\(-62\)	\(+\)	\(q+(1-\beta _{1})q^{2}-9q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
69.6.a.e	\(5\)	\(11.066\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(8\)	\(45\)	\(94\)	\(272\)	\(-\)	\(q+(2-\beta _{2})q^{2}+9q^{3}+(24-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
69.6.c.a	\(6\)	\(11.066\)	6.0.8869743.1	\(\Q(\sqrt{-23}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}-3\beta _{2}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+\cdots\)
69.6.c.b	\(32\)	\(11.066\)		None	\(0\)	\(0\)	\(0\)	\(0\)
69.6.e.a	\(100\)	\(11.066\)		None	\(-8\)	\(90\)	\(6\)	\(118\)
69.6.e.b	\(100\)	\(11.066\)		None	\(12\)	\(-90\)	\(-50\)	\(-78\)
69.6.g.a	\(380\)	\(11.066\)		None	\(0\)	\(-11\)	\(0\)	\(-22\)
69.7.b.a	\(44\)	\(15.874\)		None	\(0\)	\(20\)	\(0\)	\(568\)
69.7.d.a	\(24\)	\(15.874\)		None	\(-20\)	\(0\)	\(0\)	\(0\)
69.7.f.a	\(240\)	\(15.874\)		None	\(20\)	\(0\)	\(0\)	\(0\)
69.7.h.a	\(460\)	\(15.874\)		None	\(0\)	\(23\)	\(0\)	\(-18\)
69.8.a.a	\(5\)	\(21.555\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(0\)	\(-135\)	\(-266\)	\(-496\)	\(-\)	\(q+\beta _{1}q^{2}-3^{3}q^{3}+(54+2\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
69.8.a.b	\(6\)	\(21.555\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-8\)	\(162\)	\(-372\)	\(-1104\)	\(-\)	\(q+(-1-\beta _{1})q^{2}+3^{3}q^{3}+(29+3\beta _{1}+\cdots)q^{4}+\cdots\)
69.8.a.c	\(7\)	\(21.555\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(0\)	\(-189\)	\(-516\)	\(1018\)	\(+\)	\(q+\beta _{1}q^{2}-3^{3}q^{3}+(93+\beta _{1}+\beta _{2})q^{4}+\cdots\)
69.8.a.d	\(8\)	\(21.555\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(24\)	\(216\)	\(378\)	\(126\)	\(+\)	\(q+(3-\beta _{1})q^{2}+3^{3}q^{3}+(70-4\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
69.8.c.a	\(6\)	\(21.555\)	6.0.8869743.1	\(\Q(\sqrt{-23}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-2\beta _{1}-6\beta _{2}+3\beta _{3}+2\beta _{4}+2\beta _{5})q^{2}+\cdots\)
69.8.c.b	\(48\)	\(21.555\)		None	\(0\)	\(24\)	\(0\)	\(0\)
69.8.e.a	\(140\)	\(21.555\)		None	\(-16\)	\(-378\)	\(-6\)	\(978\)
69.8.e.b	\(140\)	\(21.555\)		None	\(-12\)	\(378\)	\(2\)	\(-394\)
69.8.g.a	\(540\)	\(21.555\)		None	\(0\)	\(-35\)	\(0\)	\(-22\)
69.9.b.a	\(58\)	\(28.109\)		None	\(0\)	\(-112\)	\(0\)	\(6996\)
69.9.d.a	\(32\)	\(28.109\)		None	\(12\)	\(0\)	\(0\)	\(0\)

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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.