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

Coefficient ring index	Coefficient ring gens.	Only for weight 1:	Projective image	Projective image type
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Results (displaying matches 1-50 of 63) Next

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
354.2.a.a	$1$	$2.827$	$\Q$	None	$-1$	$-1$	$0$	$-1$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
354.2.a.b	$1$	$2.827$	$\Q$	None	$-1$	$-1$	$2$	$0$	$-$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots$
354.2.a.c	$1$	$2.827$	$\Q$	None	$-1$	$1$	$0$	$-1$	$-$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
354.2.a.d	$1$	$2.827$	$\Q$	None	$1$	$-1$	$-4$	$-1$	$+$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots$
354.2.a.e	$1$	$2.827$	$\Q$	None	$1$	$-1$	$0$	$0$	$-$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
354.2.a.f	$1$	$2.827$	$\Q$	None	$1$	$-1$	$4$	$0$	$-$	$q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots$
354.2.a.g	$2$	$2.827$	$\Q(\sqrt{11}) $	None	$-2$	$2$	$2$	$8$	$-$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
354.2.a.h	$3$	$2.827$	3.3.316.1	None	$3$	$3$	$2$	$-1$	$-$	$q+q^{2}+q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
354.2.c.a	$10$	$2.827$	10.0.$\cdots$.1	None	$-10$	$-1$	$0$	$-2$		$q-q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots$
354.2.c.b	$10$	$2.827$	10.0.$\cdots$.1	None	$10$	$-1$	$0$	$-2$		$q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{6}q^{6}+\cdots$
354.2.e.a	$56$	$2.827$		None	$-2$	$-2$	$4$	$9$
354.2.e.b	$56$	$2.827$		None	$2$	$2$	$-2$	$1$
354.2.e.c	$84$	$2.827$		None	$-3$	$3$	$0$	$1$
354.2.e.d	$84$	$2.827$		None	$3$	$-3$	$-2$	$-7$
354.2.g.a	$280$	$2.827$		None	$-10$	$1$	$0$	$2$
354.2.g.b	$280$	$2.827$		None	$10$	$1$	$0$	$2$
354.3.b.a	$40$	$9.646$		None	$0$	$0$	$0$	$8$
354.3.d.a	$20$	$9.646$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$0$	$0$	$8$		$q+\beta _{4}q^{2}-\beta _{7}q^{3}-2q^{4}+\beta _{5}q^{5}+\beta _{6}q^{6}+\cdots$
354.3.f.a	$560$	$9.646$		None	$0$	$0$	$0$	$-8$
354.3.h.a	$1120$	$9.646$		None	$0$	$0$	$0$	$-8$
354.4.a.a	$2$	$20.887$	$\Q(\sqrt{21}) $	None	$-4$	$6$	$-12$	$-23$	$-$	$q-2q^{2}+3q^{3}+4q^{4}+(-5-2\beta )q^{5}+\cdots$
354.4.a.b	$2$	$20.887$	$\Q(\sqrt{51}) $	None	$-4$	$6$	$26$	$0$	$+$	$q-2q^{2}+3q^{3}+4q^{4}+(13+\beta )q^{5}+\cdots$
354.4.a.c	$2$	$20.887$	$\Q(\sqrt{13}) $	None	$4$	$6$	$-20$	$-23$	$-$	$q+2q^{2}+3q^{3}+4q^{4}+(-9-2\beta )q^{5}+\cdots$
354.4.a.d	$3$	$20.887$	3.3.30645.1	None	$-6$	$-9$	$-6$	$6$	$-$	$q-2q^{2}-3q^{3}+4q^{4}+(-2-\beta _{1}-2\beta _{2})q^{5}+\cdots$
354.4.a.e	$3$	$20.887$	3.3.45581.1	None	$-6$	$-9$	$4$	$13$	$+$	$q-2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots$
354.4.a.f	$3$	$20.887$	3.3.18989.1	None	$-6$	$9$	$-28$	$26$	$+$	$q-2q^{2}+3q^{3}+4q^{4}+(-9+\beta _{1}+\beta _{2})q^{5}+\cdots$
354.4.a.g	$3$	$20.887$	3.3.47277.1	None	$6$	$-9$	$-18$	$6$	$-$	$q+2q^{2}-3q^{3}+4q^{4}+(-6+\beta _{1}+\beta _{2})q^{5}+\cdots$
354.4.a.h	$4$	$20.887$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$8$	$-12$	$22$	$13$	$+$	$q+2q^{2}-3q^{3}+4q^{4}+(5+\beta _{1}-\beta _{3})q^{5}+\cdots$
354.4.a.i	$6$	$20.887$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$12$	$18$	$20$	$26$	$+$	$q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots$
354.4.c.a	$30$	$20.887$		None	$-60$	$5$	$0$	$6$
354.4.c.b	$30$	$20.887$		None	$60$	$5$	$0$	$6$
354.5.b.a	$76$	$36.593$		None	$0$	$0$	$0$	$-184$
354.5.d.a	$40$	$36.593$		None	$0$	$0$	$0$	$-80$
354.6.a.a	$1$	$56.776$	$\Q$	None	$4$	$-9$	$10$	$144$	$-$	$q+4q^{2}-9q^{3}+2^{4}q^{4}+10q^{5}-6^{2}q^{6}+\cdots$
354.6.a.b	$4$	$56.776$	4.4.32832.1	None	$16$	$36$	$-104$	$-162$	$+$	$q+4q^{2}+9q^{3}+2^{4}q^{4}+(-5^{2}+2\beta _{1}+\cdots)q^{5}+\cdots$
354.6.a.c	$5$	$56.776$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-20$	$45$	$-10$	$-162$	$+$	$q-4q^{2}+9q^{3}+2^{4}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
354.6.a.d	$5$	$56.776$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$20$	$-45$	$-24$	$-103$	$+$	$q+4q^{2}-9q^{3}+2^{4}q^{4}+(-5+\beta _{3}+\cdots)q^{5}+\cdots$
354.6.a.e	$5$	$56.776$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$20$	$-45$	$166$	$-198$	$-$	$q+4q^{2}-9q^{3}+2^{4}q^{4}+(33-\beta _{2})q^{5}+\cdots$
354.6.a.f	$6$	$56.776$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-24$	$-54$	$-46$	$-103$	$+$	$q-4q^{2}-9q^{3}+2^{4}q^{4}+(-8+\beta _{5})q^{5}+\cdots$
354.6.a.g	$6$	$56.776$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-24$	$-54$	$4$	$-54$	$-$	$q-4q^{2}-9q^{3}+2^{4}q^{4}+(1-\beta _{5})q^{5}+\cdots$
354.6.a.h	$8$	$56.776$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-32$	$72$	$40$	$181$	$-$	$q-4q^{2}+9q^{3}+2^{4}q^{4}+(5+\beta _{1})q^{5}+\cdots$
354.6.a.i	$8$	$56.776$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$32$	$72$	$96$	$181$	$-$	$q+4q^{2}+9q^{3}+2^{4}q^{4}+(12-\beta _{1})q^{5}+\cdots$
354.6.c.a	$50$	$56.776$		None	$-200$	$-13$	$0$	$38$
354.6.c.b	$50$	$56.776$		None	$200$	$-13$	$0$	$38$
354.7.d.a	$60$	$81.439$		None	$0$	$0$	$0$	$408$
354.8.a.a	$1$	$110.584$	$\Q$	None	$8$	$27$	$-320$	$-505$	$-$	$q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-320q^{5}+\cdots$
354.8.a.b	$5$	$110.584$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$40$	$135$	$164$	$-76$	$-$	$q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(33+\beta _{1}+\cdots)q^{5}+\cdots$
354.8.a.c	$7$	$110.584$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$-56$	$189$	$-158$	$-581$	$-$	$q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-23-\beta _{2}+\cdots)q^{5}+\cdots$
354.8.a.d	$8$	$110.584$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$64$	$-216$	$-592$	$-340$	$-$	$q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-74+\beta _{3}+\cdots)q^{5}+\cdots$
354.8.a.e	$9$	$110.584$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$-72$	$-243$	$-230$	$-340$	$-$	$q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-26+\beta _{3}+\cdots)q^{5}+\cdots$

Introduction	Features
Universe	News

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
354.2.a.a	\(1\)	\(2.827\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(-1\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.b	\(1\)	\(2.827\)	\(\Q\)	None	\(-1\)	\(-1\)	\(2\)	\(0\)	\(-\)	\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
354.2.a.c	\(1\)	\(2.827\)	\(\Q\)	None	\(-1\)	\(1\)	\(0\)	\(-1\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.d	\(1\)	\(2.827\)	\(\Q\)	None	\(1\)	\(-1\)	\(-4\)	\(-1\)	\(+\)	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
354.2.a.e	\(1\)	\(2.827\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
354.2.a.f	\(1\)	\(2.827\)	\(\Q\)	None	\(1\)	\(-1\)	\(4\)	\(0\)	\(-\)	\(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
354.2.a.g	\(2\)	\(2.827\)	\(\Q(\sqrt{11}) \)	None	\(-2\)	\(2\)	\(2\)	\(8\)	\(-\)	\(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
354.2.a.h	\(3\)	\(2.827\)	3.3.316.1	None	\(3\)	\(3\)	\(2\)	\(-1\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.2.c.a	\(10\)	\(2.827\)	10.0.\(\cdots\).1	None	\(-10\)	\(-1\)	\(0\)	\(-2\)		\(q-q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{6}q^{6}+\cdots\)
354.2.c.b	\(10\)	\(2.827\)	10.0.\(\cdots\).1	None	\(10\)	\(-1\)	\(0\)	\(-2\)		\(q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{6}q^{6}+\cdots\)
354.2.e.a	\(56\)	\(2.827\)		None	\(-2\)	\(-2\)	\(4\)	\(9\)
354.2.e.b	\(56\)	\(2.827\)		None	\(2\)	\(2\)	\(-2\)	\(1\)
354.2.e.c	\(84\)	\(2.827\)		None	\(-3\)	\(3\)	\(0\)	\(1\)
354.2.e.d	\(84\)	\(2.827\)		None	\(3\)	\(-3\)	\(-2\)	\(-7\)
354.2.g.a	\(280\)	\(2.827\)		None	\(-10\)	\(1\)	\(0\)	\(2\)
354.2.g.b	\(280\)	\(2.827\)		None	\(10\)	\(1\)	\(0\)	\(2\)
354.3.b.a	\(40\)	\(9.646\)		None	\(0\)	\(0\)	\(0\)	\(8\)
354.3.d.a	\(20\)	\(9.646\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(8\)		\(q+\beta _{4}q^{2}-\beta _{7}q^{3}-2q^{4}+\beta _{5}q^{5}+\beta _{6}q^{6}+\cdots\)
354.3.f.a	\(560\)	\(9.646\)		None	\(0\)	\(0\)	\(0\)	\(-8\)
354.3.h.a	\(1120\)	\(9.646\)		None	\(0\)	\(0\)	\(0\)	\(-8\)
354.4.a.a	\(2\)	\(20.887\)	\(\Q(\sqrt{21}) \)	None	\(-4\)	\(6\)	\(-12\)	\(-23\)	\(-\)	\(q-2q^{2}+3q^{3}+4q^{4}+(-5-2\beta )q^{5}+\cdots\)
354.4.a.b	\(2\)	\(20.887\)	\(\Q(\sqrt{51}) \)	None	\(-4\)	\(6\)	\(26\)	\(0\)	\(+\)	\(q-2q^{2}+3q^{3}+4q^{4}+(13+\beta )q^{5}+\cdots\)
354.4.a.c	\(2\)	\(20.887\)	\(\Q(\sqrt{13}) \)	None	\(4\)	\(6\)	\(-20\)	\(-23\)	\(-\)	\(q+2q^{2}+3q^{3}+4q^{4}+(-9-2\beta )q^{5}+\cdots\)
354.4.a.d	\(3\)	\(20.887\)	3.3.30645.1	None	\(-6\)	\(-9\)	\(-6\)	\(6\)	\(-\)	\(q-2q^{2}-3q^{3}+4q^{4}+(-2-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
354.4.a.e	\(3\)	\(20.887\)	3.3.45581.1	None	\(-6\)	\(-9\)	\(4\)	\(13\)	\(+\)	\(q-2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.f	\(3\)	\(20.887\)	3.3.18989.1	None	\(-6\)	\(9\)	\(-28\)	\(26\)	\(+\)	\(q-2q^{2}+3q^{3}+4q^{4}+(-9+\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.g	\(3\)	\(20.887\)	3.3.47277.1	None	\(6\)	\(-9\)	\(-18\)	\(6\)	\(-\)	\(q+2q^{2}-3q^{3}+4q^{4}+(-6+\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.h	\(4\)	\(20.887\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(8\)	\(-12\)	\(22\)	\(13\)	\(+\)	\(q+2q^{2}-3q^{3}+4q^{4}+(5+\beta _{1}-\beta _{3})q^{5}+\cdots\)
354.4.a.i	\(6\)	\(20.887\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(12\)	\(18\)	\(20\)	\(26\)	\(+\)	\(q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)
354.4.c.a	\(30\)	\(20.887\)		None	\(-60\)	\(5\)	\(0\)	\(6\)
354.4.c.b	\(30\)	\(20.887\)		None	\(60\)	\(5\)	\(0\)	\(6\)
354.5.b.a	\(76\)	\(36.593\)		None	\(0\)	\(0\)	\(0\)	\(-184\)
354.5.d.a	\(40\)	\(36.593\)		None	\(0\)	\(0\)	\(0\)	\(-80\)
354.6.a.a	\(1\)	\(56.776\)	\(\Q\)	None	\(4\)	\(-9\)	\(10\)	\(144\)	\(-\)	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+10q^{5}-6^{2}q^{6}+\cdots\)
354.6.a.b	\(4\)	\(56.776\)	4.4.32832.1	None	\(16\)	\(36\)	\(-104\)	\(-162\)	\(+\)	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-5^{2}+2\beta _{1}+\cdots)q^{5}+\cdots\)
354.6.a.c	\(5\)	\(56.776\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-20\)	\(45\)	\(-10\)	\(-162\)	\(+\)	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
354.6.a.d	\(5\)	\(56.776\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(20\)	\(-45\)	\(-24\)	\(-103\)	\(+\)	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-5+\beta _{3}+\cdots)q^{5}+\cdots\)
354.6.a.e	\(5\)	\(56.776\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(20\)	\(-45\)	\(166\)	\(-198\)	\(-\)	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+(33-\beta _{2})q^{5}+\cdots\)
354.6.a.f	\(6\)	\(56.776\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-24\)	\(-54\)	\(-46\)	\(-103\)	\(+\)	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-8+\beta _{5})q^{5}+\cdots\)
354.6.a.g	\(6\)	\(56.776\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-24\)	\(-54\)	\(4\)	\(-54\)	\(-\)	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(1-\beta _{5})q^{5}+\cdots\)
354.6.a.h	\(8\)	\(56.776\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-32\)	\(72\)	\(40\)	\(181\)	\(-\)	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+(5+\beta _{1})q^{5}+\cdots\)
354.6.a.i	\(8\)	\(56.776\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(32\)	\(72\)	\(96\)	\(181\)	\(-\)	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+(12-\beta _{1})q^{5}+\cdots\)
354.6.c.a	\(50\)	\(56.776\)		None	\(-200\)	\(-13\)	\(0\)	\(38\)
354.6.c.b	\(50\)	\(56.776\)		None	\(200\)	\(-13\)	\(0\)	\(38\)
354.7.d.a	\(60\)	\(81.439\)		None	\(0\)	\(0\)	\(0\)	\(408\)
354.8.a.a	\(1\)	\(110.584\)	\(\Q\)	None	\(8\)	\(27\)	\(-320\)	\(-505\)	\(-\)	\(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-320q^{5}+\cdots\)
354.8.a.b	\(5\)	\(110.584\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(40\)	\(135\)	\(164\)	\(-76\)	\(-\)	\(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(33+\beta _{1}+\cdots)q^{5}+\cdots\)
354.8.a.c	\(7\)	\(110.584\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(-56\)	\(189\)	\(-158\)	\(-581\)	\(-\)	\(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-23-\beta _{2}+\cdots)q^{5}+\cdots\)
354.8.a.d	\(8\)	\(110.584\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(64\)	\(-216\)	\(-592\)	\(-340\)	\(-\)	\(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-74+\beta _{3}+\cdots)q^{5}+\cdots\)
354.8.a.e	\(9\)	\(110.584\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(-72\)	\(-243\)	\(-230\)	\(-340\)	\(-\)	\(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-26+\beta _{3}+\cdots)q^{5}+\cdots\)

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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.