LMFDB - Newform search results

Refine search

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
		Only for weight 1:

				Sort order

Results (displaying matches 1-50 of 189) Next

Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
672.1.ba.a	$2$	$0.335$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-6}) $	None	$0$	$-1$	$-1$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
672.1.ba.b	$2$	$0.335$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-6}) $	None	$0$	$1$	$1$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
672.2.a.a	$1$	$5.366$	$\Q$	None	None	$0$	$-1$	$-4$	$-1$	$-$	$q-q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
672.2.a.b	$1$	$5.366$	$\Q$	None	None	$0$	$-1$	$-2$	$1$	$+$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
672.2.a.c	$1$	$5.366$	$\Q$	None	None	$0$	$-1$	$0$	$-1$	$+$	$q-q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
672.2.a.d	$1$	$5.366$	$\Q$	None	None	$0$	$-1$	$2$	$-1$	$-$	$q-q^{3}+2q^{5}-q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots$
672.2.a.e	$1$	$5.366$	$\Q$	None	None	$0$	$1$	$-4$	$1$	$+$	$q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
672.2.a.f	$1$	$5.366$	$\Q$	None	None	$0$	$1$	$-2$	$-1$	$+$	$q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
672.2.a.g	$1$	$5.366$	$\Q$	None	None	$0$	$1$	$0$	$1$	$-$	$q+q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
672.2.a.h	$1$	$5.366$	$\Q$	None	None	$0$	$1$	$2$	$1$	$-$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots$
672.2.a.i	$2$	$5.366$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$0$	$2$	$-$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
672.2.a.j	$2$	$5.366$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$0$	$-2$	$-$	$q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
672.2.b.a	$8$	$5.366$	8.0.836829184.2	None	None	$0$	$-8$	$0$	$-4$		$q-q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
672.2.b.b	$8$	$5.366$	8.0.836829184.2	None	None	$0$	$8$	$0$	$4$		$q+q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
672.2.c.a	$4$	$5.366$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$4$		$q-\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+q^{7}+\cdots$
672.2.c.b	$8$	$5.366$	8.0.386672896.3	None	None	$0$	$0$	$0$	$-8$		$q+\beta _{2}q^{3}+\beta _{1}q^{5}-q^{7}-q^{9}+(-2\beta _{2}+\cdots)q^{11}+\cdots$
672.2.h.a	$4$	$5.366$	$\Q(\zeta_{8})$	None	None	$0$	$-4$	$0$	$0$		$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
672.2.h.b	$4$	$5.366$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$0$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots$
672.2.h.c	$4$	$5.366$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$0$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots$
672.2.h.d	$4$	$5.366$	$\Q(\zeta_{8})$	None	None	$0$	$4$	$0$	$0$		$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
672.2.h.e	$8$	$5.366$	8.0.40960000.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots$
672.2.i.a	$4$	$5.366$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$-4$	$0$	$8$		$q+(-1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots$
672.2.i.b	$4$	$5.366$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$-4$		$q+\beta _{2}q^{3}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots$
672.2.i.c	$4$	$5.366$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$4$	$0$	$8$		$q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots$
672.2.i.d	$8$	$5.366$	8.0.3317760000.1	None	None	$0$	$0$	$0$	$-8$		$q+(-\beta _{2}-\beta _{3})q^{3}-\beta _{3}q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots$
672.2.i.e	$8$	$5.366$	8.0.$\cdots$.11	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}+(\beta _{6}-\beta _{7})q^{5}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots$
672.2.j.a	$4$	$5.366$	$\Q(\zeta_{8})$	None	None	$0$	$-4$	$0$	$0$		$q+(-1-\zeta_{8}^{2})q^{3}-2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+\cdots$
672.2.j.b	$4$	$5.366$	$\Q(i, \sqrt{5})$	None	None	$0$	$2$	$-4$	$0$		$q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots$
672.2.j.c	$4$	$5.366$	$\Q(i, \sqrt{5})$	None	None	$0$	$2$	$4$	$0$		$q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
672.2.j.d	$12$	$5.366$	12.0.$\cdots$.2	None	None	$0$	$0$	$0$	$0$		$q+\beta _{3}q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\beta _{1}q^{7}+\cdots$
672.2.k.a	$8$	$5.366$	8.0.342102016.5	None	None	$0$	$0$	$0$	$-4$		$q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots$
672.2.k.b	$8$	$5.366$	8.0.49787136.1	$\Q(\sqrt{-21}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-3q^{9}+\beta _{3}q^{11}+\cdots$
672.2.k.c	$8$	$5.366$	8.0.40960000.1	None	None	$0$	$0$	$0$	$0$		$q+(-\beta _{4}+\beta _{5})q^{3}+\beta _{7}q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
672.2.k.d	$8$	$5.366$	8.0.342102016.5	None	None	$0$	$0$	$0$	$4$		$q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
672.2.p.a	$16$	$5.366$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{7}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots$
672.2.q.a	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-3$	$1$		$q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
672.2.q.b	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-1$	$-5$		$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$
672.2.q.c	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$0$	$1$		$q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
672.2.q.d	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$0$	$5$		$q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
672.2.q.e	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$4$	$5$		$q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$
672.2.q.f	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-3$	$-1$		$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
672.2.q.g	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-1$	$5$		$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots$
672.2.q.h	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$0$	$-5$		$q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
672.2.q.i	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$0$	$-1$		$q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots$
672.2.q.j	$2$	$5.366$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$4$	$-5$		$q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$
672.2.q.k	$6$	$5.366$	6.0.1156923.1	None	None	$0$	$-3$	$0$	$-3$		$q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
672.2.q.l	$6$	$5.366$	6.0.1156923.1	None	None	$0$	$3$	$0$	$3$		$q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
672.2.bb.a	$32$	$5.366$		None	None	$0$	$0$	$0$	$0$
672.2.bc.a	$4$	$5.366$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$-2$	$0$		$q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
672.2.bc.b	$4$	$5.366$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$0$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}+(2\zeta_{12}+\cdots)q^{7}+\cdots$

Introduction	Features
Universe	News

Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
672.1.ba.a	\(2\)	\(0.335\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(-1\)	\(-1\)	\(1\)		\(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
672.1.ba.b	\(2\)	\(0.335\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(1\)	\(1\)	\(1\)		\(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
672.2.a.a	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-4\)	\(-1\)	\(-\)	\(q-q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
672.2.a.b	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(1\)	\(+\)	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
672.2.a.c	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(-1\)	\(+\)	\(q-q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
672.2.a.d	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(2\)	\(-1\)	\(-\)	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
672.2.a.e	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-4\)	\(1\)	\(+\)	\(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
672.2.a.f	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-2\)	\(-1\)	\(+\)	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
672.2.a.g	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(1\)	\(0\)	\(1\)	\(-\)	\(q+q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
672.2.a.h	\(1\)	\(5.366\)	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(1\)	\(-\)	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
672.2.a.i	\(2\)	\(5.366\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(-\)	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
672.2.a.j	\(2\)	\(5.366\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
672.2.b.a	\(8\)	\(5.366\)	8.0.836829184.2	None	None	\(0\)	\(-8\)	\(0\)	\(-4\)		\(q-q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.b.b	\(8\)	\(5.366\)	8.0.836829184.2	None	None	\(0\)	\(8\)	\(0\)	\(4\)		\(q+q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.c.a	\(4\)	\(5.366\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q-\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+q^{7}+\cdots\)
672.2.c.b	\(8\)	\(5.366\)	8.0.386672896.3	None	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\beta _{2}q^{3}+\beta _{1}q^{5}-q^{7}-q^{9}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.h.a	\(4\)	\(5.366\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(-4\)	\(0\)	\(0\)		\(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.b	\(4\)	\(5.366\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.c	\(4\)	\(5.366\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.d	\(4\)	\(5.366\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(4\)	\(0\)	\(0\)		\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.e	\(8\)	\(5.366\)	8.0.40960000.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots\)
672.2.i.a	\(4\)	\(5.366\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(-4\)	\(0\)	\(8\)		\(q+(-1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.b	\(4\)	\(5.366\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta _{2}q^{3}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
672.2.i.c	\(4\)	\(5.366\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(4\)	\(0\)	\(8\)		\(q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.d	\(8\)	\(5.366\)	8.0.3317760000.1	None	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+(-\beta _{2}-\beta _{3})q^{3}-\beta _{3}q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
672.2.i.e	\(8\)	\(5.366\)	8.0.\(\cdots\).11	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{7})q^{5}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
672.2.j.a	\(4\)	\(5.366\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(-4\)	\(0\)	\(0\)		\(q+(-1-\zeta_{8}^{2})q^{3}-2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.j.b	\(4\)	\(5.366\)	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(2\)	\(-4\)	\(0\)		\(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
672.2.j.c	\(4\)	\(5.366\)	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(2\)	\(4\)	\(0\)		\(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
672.2.j.d	\(12\)	\(5.366\)	12.0.\(\cdots\).2	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\beta _{1}q^{7}+\cdots\)
672.2.k.a	\(8\)	\(5.366\)	8.0.342102016.5	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
672.2.k.b	\(8\)	\(5.366\)	8.0.49787136.1	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-3q^{9}+\beta _{3}q^{11}+\cdots\)
672.2.k.c	\(8\)	\(5.366\)	8.0.40960000.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{4}+\beta _{5})q^{3}+\beta _{7}q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
672.2.k.d	\(8\)	\(5.366\)	8.0.342102016.5	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
672.2.p.a	\(16\)	\(5.366\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{7}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
672.2.q.a	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-3\)	\(1\)		\(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
672.2.q.b	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-1\)	\(-5\)		\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
672.2.q.c	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(0\)	\(1\)		\(q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.d	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(0\)	\(5\)		\(q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.e	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(4\)	\(5\)		\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
672.2.q.f	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-3\)	\(-1\)		\(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
672.2.q.g	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-1\)	\(5\)		\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
672.2.q.h	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(0\)	\(-5\)		\(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.i	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(0\)	\(-1\)		\(q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.j	\(2\)	\(5.366\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(4\)	\(-5\)		\(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
672.2.q.k	\(6\)	\(5.366\)	6.0.1156923.1	None	None	\(0\)	\(-3\)	\(0\)	\(-3\)		\(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.q.l	\(6\)	\(5.366\)	6.0.1156923.1	None	None	\(0\)	\(3\)	\(0\)	\(3\)		\(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.bb.a	\(32\)	\(5.366\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
672.2.bc.a	\(4\)	\(5.366\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
672.2.bc.b	\(4\)	\(5.366\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}+(2\zeta_{12}+\cdots)q^{7}+\cdots\)

Introduction and more

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Knowledge

Learn more about

Refine search

Results (displaying matches 1-50 of 189) 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.