LMFDB - Newform Search Results

Refine search

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
		Only for weight 1:
				Sort order

Results (displaying matches 1-50 of 28440) 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
5.4.a.a	$1$	$0.295$	$\Q$	None	$-4$	$2$	$-5$	$6$	$+$	$q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots$
6.4.a.a	$1$	$0.354$	$\Q$	None	$-2$	$-3$	$6$	$-16$	$+$	$q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots$
7.4.a.a	$1$	$0.413$	$\Q$	None	$-1$	$-2$	$16$	$-7$	$+$	$q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots$
7.4.c.a	$2$	$0.413$	$\Q(\sqrt{-3}) $	None	$-2$	$-7$	$-7$	$28$		$q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots$
8.4.a.a	$1$	$0.472$	$\Q$	None	$0$	$-4$	$-2$	$24$	$+$	$q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots$
8.4.b.a	$2$	$0.472$	$\Q(\sqrt{-7}) $	None	$-2$	$0$	$0$	$-16$		$q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots$
9.4.a.a	$1$	$0.531$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$0$	$0$	$20$	$+$	$q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots$
9.4.c.a	$4$	$0.531$	$\Q(\sqrt{-3}, \sqrt{-11})$	None	$-3$	$-3$	$-15$	$-7$		$q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
10.4.a.a	$1$	$0.590$	$\Q$	None	$2$	$-8$	$5$	$-4$	$+$	$q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots$
10.4.b.a	$2$	$0.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-10$	$0$		$q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots$
11.4.a.a	$2$	$0.649$	$\Q(\sqrt{3}) $	None	$2$	$-2$	$2$	$20$	$+$	$q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots$
11.4.c.a	$8$	$0.649$	8.0.$\cdots$.1	None	$-7$	$-3$	$-7$	$-35$		$q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots$
12.4.a.a	$1$	$0.708$	$\Q$	None	$0$	$3$	$-18$	$8$	$+$	$q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
12.4.b.a	$4$	$0.708$	$\Q(\sqrt{3}, \sqrt{-5})$	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$
13.4.a.a	$1$	$0.767$	$\Q$	None	$-5$	$-7$	$-7$	$-13$	$-$	$q-5q^{2}-7q^{3}+17q^{4}-7q^{5}+35q^{6}+\cdots$
13.4.a.b	$2$	$0.767$	$\Q(\sqrt{17}) $	None	$1$	$5$	$-3$	$-9$	$+$	$q+\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots$
13.4.b.a	$2$	$0.767$	$\Q(\sqrt{-1}) $	None	$0$	$-2$	$0$	$0$		$q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots$
13.4.c.a	$2$	$0.767$	$\Q(\sqrt{-3}) $	None	$-4$	$-2$	$34$	$-20$		$q+(-4+4\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots$
13.4.c.b	$4$	$0.767$	$\Q(\sqrt{-3}, \sqrt{17})$	None	$5$	$-5$	$-30$	$-15$		$q+(2-\beta _{1}-2\beta _{2}-\beta _{3})q^{2}+(-1+3\beta _{1}+\cdots)q^{3}+\cdots$
13.4.e.a	$2$	$0.767$	$\Q(\sqrt{-3}) $	None	$-6$	$7$	$0$	$39$		$q+(-2-2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots$
13.4.e.b	$2$	$0.767$	$\Q(\sqrt{-3}) $	None	$3$	$-2$	$0$	$-24$		$q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots$
14.4.a.a	$1$	$0.826$	$\Q$	None	$-2$	$8$	$-14$	$-7$	$+$	$q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots$
14.4.a.b	$1$	$0.826$	$\Q$	None	$2$	$-2$	$-12$	$7$	$+$	$q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots$
14.4.c.a	$2$	$0.826$	$\Q(\sqrt{-3}) $	None	$-2$	$5$	$9$	$-28$		$q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots$
14.4.c.b	$2$	$0.826$	$\Q(\sqrt{-3}) $	None	$2$	$1$	$-7$	$-20$		$q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots$
15.4.a.a	$1$	$0.885$	$\Q$	None	$1$	$3$	$5$	$-24$	$+$	$q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots$
15.4.a.b	$1$	$0.885$	$\Q$	None	$3$	$-3$	$-5$	$20$	$+$	$q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots$
15.4.b.a	$4$	$0.885$	$\Q(i, \sqrt{41})$	None	$0$	$0$	$6$	$0$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$
15.4.e.a	$8$	$0.885$	8.0.$\cdots$.8	None	$0$	$-6$	$0$	$-16$		$q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
16.4.a.a	$1$	$0.944$	$\Q$	None	$0$	$4$	$-2$	$-24$	$+$	$q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots$
16.4.e.a	$10$	$0.944$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-2$	$-2$	$-2$	$0$		$q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
17.4.a.a	$1$	$1.003$	$\Q$	None	$-3$	$-8$	$6$	$-28$	$-$	$q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots$
17.4.a.b	$3$	$1.003$	3.3.2636.1	None	$1$	$4$	$-8$	$22$	$+$	$q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots$
17.4.b.a	$4$	$1.003$	4.0.4669632.2	None	$-2$	$0$	$0$	$0$		$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots$
17.4.c.a	$8$	$1.003$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$0$	$0$	$14$	$2$		$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots$
17.4.d.a	$12$	$1.003$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$-4$	$-4$	$-20$	$-4$		$q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
18.4.a.a	$1$	$1.062$	$\Q$	None	$2$	$0$	$-6$	$-16$	$+$	$q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots$
18.4.c.a	$2$	$1.062$	$\Q(\sqrt{-3}) $	None	$-2$	$0$	$9$	$31$		$q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
18.4.c.b	$4$	$1.062$	$\Q(\sqrt{-3}, \sqrt{-35})$	None	$4$	$3$	$9$	$-19$		$q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots$
19.4.a.a	$1$	$1.121$	$\Q$	None	$-3$	$-5$	$-12$	$11$	$-$	$q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots$
19.4.a.b	$3$	$1.121$	3.3.3144.1	None	$3$	$1$	$14$	$-35$	$+$	$q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots$
19.4.c.a	$4$	$1.121$	$\Q(\sqrt{-3}, \sqrt{55})$	None	$-2$	$0$	$14$	$-28$		$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots$
19.4.c.b	$4$	$1.121$	$\Q(\sqrt{-3}, \sqrt{73})$	None	$-1$	$-2$	$-19$	$40$		$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots$
19.4.e.a	$24$	$1.121$		None	$-6$	$-3$	$-6$	$3$
20.4.a.a	$1$	$1.180$	$\Q$	None	$0$	$4$	$5$	$-16$	$+$	$q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots$
20.4.c.a	$2$	$1.180$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$14$	$0$		$q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots$
20.4.e.a	$2$	$1.180$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	$4$	$0$	$-4$	$0$		$q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots$
20.4.e.b	$12$	$1.180$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$-6$	$0$	$0$	$0$		$q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
21.4.a.a	$1$	$1.239$	$\Q$	None	$-3$	$-3$	$-18$	$7$	$-$	$q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots$
21.4.a.b	$1$	$1.239$	$\Q$	None	$4$	$-3$	$-4$	$-7$	$+$	$q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots$

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
5.4.a.a	\(1\)	\(0.295\)	\(\Q\)	None	\(-4\)	\(2\)	\(-5\)	\(6\)	\(+\)	\(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
6.4.a.a	\(1\)	\(0.354\)	\(\Q\)	None	\(-2\)	\(-3\)	\(6\)	\(-16\)	\(+\)	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
7.4.a.a	\(1\)	\(0.413\)	\(\Q\)	None	\(-1\)	\(-2\)	\(16\)	\(-7\)	\(+\)	\(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
7.4.c.a	\(2\)	\(0.413\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(-7\)	\(-7\)	\(28\)		\(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)
8.4.a.a	\(1\)	\(0.472\)	\(\Q\)	None	\(0\)	\(-4\)	\(-2\)	\(24\)	\(+\)	\(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
8.4.b.a	\(2\)	\(0.472\)	\(\Q(\sqrt{-7}) \)	None	\(-2\)	\(0\)	\(0\)	\(-16\)		\(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
9.4.a.a	\(1\)	\(0.531\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(0\)	\(0\)	\(20\)	\(+\)	\(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a	\(4\)	\(0.531\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None	\(-3\)	\(-3\)	\(-15\)	\(-7\)		\(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.4.a.a	\(1\)	\(0.590\)	\(\Q\)	None	\(2\)	\(-8\)	\(5\)	\(-4\)	\(+\)	\(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)
10.4.b.a	\(2\)	\(0.590\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-10\)	\(0\)		\(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)
11.4.a.a	\(2\)	\(0.649\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(-2\)	\(2\)	\(20\)	\(+\)	\(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)
11.4.c.a	\(8\)	\(0.649\)	8.0.\(\cdots\).1	None	\(-7\)	\(-3\)	\(-7\)	\(-35\)		\(q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
12.4.a.a	\(1\)	\(0.708\)	\(\Q\)	None	\(0\)	\(3\)	\(-18\)	\(8\)	\(+\)	\(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
12.4.b.a	\(4\)	\(0.708\)	\(\Q(\sqrt{3}, \sqrt{-5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
13.4.a.a	\(1\)	\(0.767\)	\(\Q\)	None	\(-5\)	\(-7\)	\(-7\)	\(-13\)	\(-\)	\(q-5q^{2}-7q^{3}+17q^{4}-7q^{5}+35q^{6}+\cdots\)
13.4.a.b	\(2\)	\(0.767\)	\(\Q(\sqrt{17}) \)	None	\(1\)	\(5\)	\(-3\)	\(-9\)	\(+\)	\(q+\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
13.4.b.a	\(2\)	\(0.767\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)		\(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
13.4.c.a	\(2\)	\(0.767\)	\(\Q(\sqrt{-3}) \)	None	\(-4\)	\(-2\)	\(34\)	\(-20\)		\(q+(-4+4\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots\)
13.4.c.b	\(4\)	\(0.767\)	\(\Q(\sqrt{-3}, \sqrt{17})\)	None	\(5\)	\(-5\)	\(-30\)	\(-15\)		\(q+(2-\beta _{1}-2\beta _{2}-\beta _{3})q^{2}+(-1+3\beta _{1}+\cdots)q^{3}+\cdots\)
13.4.e.a	\(2\)	\(0.767\)	\(\Q(\sqrt{-3}) \)	None	\(-6\)	\(7\)	\(0\)	\(39\)		\(q+(-2-2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots\)
13.4.e.b	\(2\)	\(0.767\)	\(\Q(\sqrt{-3}) \)	None	\(3\)	\(-2\)	\(0\)	\(-24\)		\(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots\)
14.4.a.a	\(1\)	\(0.826\)	\(\Q\)	None	\(-2\)	\(8\)	\(-14\)	\(-7\)	\(+\)	\(q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots\)
14.4.a.b	\(1\)	\(0.826\)	\(\Q\)	None	\(2\)	\(-2\)	\(-12\)	\(7\)	\(+\)	\(q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots\)
14.4.c.a	\(2\)	\(0.826\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(5\)	\(9\)	\(-28\)		\(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b	\(2\)	\(0.826\)	\(\Q(\sqrt{-3}) \)	None	\(2\)	\(1\)	\(-7\)	\(-20\)		\(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)
15.4.a.a	\(1\)	\(0.885\)	\(\Q\)	None	\(1\)	\(3\)	\(5\)	\(-24\)	\(+\)	\(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
15.4.a.b	\(1\)	\(0.885\)	\(\Q\)	None	\(3\)	\(-3\)	\(-5\)	\(20\)	\(+\)	\(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)
15.4.b.a	\(4\)	\(0.885\)	\(\Q(i, \sqrt{41})\)	None	\(0\)	\(0\)	\(6\)	\(0\)		\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
15.4.e.a	\(8\)	\(0.885\)	8.0.\(\cdots\).8	None	\(0\)	\(-6\)	\(0\)	\(-16\)		\(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
16.4.a.a	\(1\)	\(0.944\)	\(\Q\)	None	\(0\)	\(4\)	\(-2\)	\(-24\)	\(+\)	\(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)
16.4.e.a	\(10\)	\(0.944\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-2\)	\(-2\)	\(-2\)	\(0\)		\(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
17.4.a.a	\(1\)	\(1.003\)	\(\Q\)	None	\(-3\)	\(-8\)	\(6\)	\(-28\)	\(-\)	\(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b	\(3\)	\(1.003\)	3.3.2636.1	None	\(1\)	\(4\)	\(-8\)	\(22\)	\(+\)	\(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
17.4.b.a	\(4\)	\(1.003\)	4.0.4669632.2	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
17.4.c.a	\(8\)	\(1.003\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(0\)	\(0\)	\(14\)	\(2\)		\(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots\)
17.4.d.a	\(12\)	\(1.003\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(-4\)	\(-4\)	\(-20\)	\(-4\)		\(q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
18.4.a.a	\(1\)	\(1.062\)	\(\Q\)	None	\(2\)	\(0\)	\(-6\)	\(-16\)	\(+\)	\(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)
18.4.c.a	\(2\)	\(1.062\)	\(\Q(\sqrt{-3}) \)	None	\(-2\)	\(0\)	\(9\)	\(31\)		\(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b	\(4\)	\(1.062\)	\(\Q(\sqrt{-3}, \sqrt{-35})\)	None	\(4\)	\(3\)	\(9\)	\(-19\)		\(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)
19.4.a.a	\(1\)	\(1.121\)	\(\Q\)	None	\(-3\)	\(-5\)	\(-12\)	\(11\)	\(-\)	\(q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots\)
19.4.a.b	\(3\)	\(1.121\)	3.3.3144.1	None	\(3\)	\(1\)	\(14\)	\(-35\)	\(+\)	\(q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
19.4.c.a	\(4\)	\(1.121\)	\(\Q(\sqrt{-3}, \sqrt{55})\)	None	\(-2\)	\(0\)	\(14\)	\(-28\)		\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots\)
19.4.c.b	\(4\)	\(1.121\)	\(\Q(\sqrt{-3}, \sqrt{73})\)	None	\(-1\)	\(-2\)	\(-19\)	\(40\)		\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)
19.4.e.a	\(24\)	\(1.121\)		None	\(-6\)	\(-3\)	\(-6\)	\(3\)
20.4.a.a	\(1\)	\(1.180\)	\(\Q\)	None	\(0\)	\(4\)	\(5\)	\(-16\)	\(+\)	\(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
20.4.c.a	\(2\)	\(1.180\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(14\)	\(0\)		\(q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)
20.4.e.a	\(2\)	\(1.180\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	\(4\)	\(0\)	\(-4\)	\(0\)		\(q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots\)
20.4.e.b	\(12\)	\(1.180\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(-6\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
21.4.a.a	\(1\)	\(1.239\)	\(\Q\)	None	\(-3\)	\(-3\)	\(-18\)	\(7\)	\(-\)	\(q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots\)
21.4.a.b	\(1\)	\(1.239\)	\(\Q\)	None	\(4\)	\(-3\)	\(-4\)	\(-7\)	\(+\)	\(q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Learn more about

Refine search

Results (displaying matches 1-50 of 28440) Next

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.