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 (1-50 of 87 matches)

Next Download to Pari/GP SageMath Magma

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
289.2.a.a	$1$	$2.308$	$\Q$	None	$-1$	$0$	$2$	$-4$	$+$	$q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots$
289.2.a.b	$2$	$2.308$	$\Q(\sqrt{13}) $	None	$-1$	$-1$	$-1$	$-3$	$+$	$q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots$
289.2.a.c	$2$	$2.308$	$\Q(\sqrt{13}) $	None	$-1$	$1$	$1$	$3$	$-$	$q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots$
289.2.a.d	$3$	$2.308$	$\Q(\zeta_{18})^+$	None	$0$	$-3$	$-6$	$0$	$+$	$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots$
289.2.a.e	$3$	$2.308$	$\Q(\zeta_{18})^+$	None	$0$	$3$	$6$	$0$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
289.2.a.f	$4$	$2.308$	$\Q(\zeta_{16})^+$	None	$4$	$0$	$0$	$0$	$-$	$q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots$
289.2.b.a	$2$	$2.308$	$\Q(\sqrt{-1}) $	None	$2$	$0$	$0$	$0$		$q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots$
289.2.b.b	$4$	$2.308$	4.0.2048.2	None	$-4$	$0$	$0$	$0$		$q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots$
289.2.b.c	$4$	$2.308$	$\Q(i, \sqrt{13})$	None	$2$	$0$	$0$	$0$		$q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
289.2.b.d	$6$	$2.308$	6.0.419904.1	None	$0$	$0$	$0$	$0$		$q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots$
289.2.c.a	$4$	$2.308$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots$
289.2.c.b	$8$	$2.308$	8.0.1871773696.1	None	$0$	$0$	$0$	$0$		$q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
289.2.c.c	$8$	$2.308$	$\Q(\zeta_{16})$	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots$
289.2.c.d	$12$	$2.308$	12.0.$\cdots$.1	None	$0$	$0$	$0$	$0$		$q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots$
289.2.d.a	$4$	$2.308$	$\Q(\zeta_{8})$	None	$-4$	$4$	$0$	$4$		$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
289.2.d.b	$4$	$2.308$	$\Q(\zeta_{8})$	None	$4$	$-4$	$-4$	$-4$		$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
289.2.d.c	$4$	$2.308$	$\Q(\zeta_{8})$	None	$4$	$4$	$4$	$4$		$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
289.2.d.d	$8$	$2.308$	$\Q(\zeta_{16})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots$
289.2.d.e	$16$	$2.308$	16.0.$\cdots$.1	None	$0$	$0$	$0$	$0$		$q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots$
289.2.d.f	$24$	$2.308$		None	$0$	$0$	$0$	$0$
289.2.f.a	$384$	$2.308$		None	$-13$	$-13$	$-43$	$-13$
289.2.g.a	$384$	$2.308$		None	$-17$	$-17$	$17$	$-17$
289.2.h.a	$768$	$2.308$		None	$-34$	$-34$	$-34$	$-34$
289.2.i.a	$1600$	$2.308$		None	$-64$	$-64$	$-68$	$-64$
289.3.e.a	$8$	$7.875$	$\Q(\zeta_{16})$	None	$-8$	$-16$	$-8$	$-16$		$q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-2-2\zeta_{16}+\cdots)q^{3}+\cdots$
289.3.e.b	$8$	$7.875$	$\Q(\zeta_{16})$	None	$-8$	$-8$	$0$	$-8$		$q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
289.3.e.c	$8$	$7.875$	$\Q(\zeta_{16})$	None	$-8$	$8$	$-16$	$-8$		$q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
289.3.e.d	$8$	$7.875$	$\Q(\zeta_{16})$	None	$-8$	$8$	$0$	$8$		$q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
289.3.e.e	$8$	$7.875$	$\Q(\zeta_{16})$	None	$-8$	$16$	$8$	$16$		$q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(2+2\zeta_{16}+\cdots)q^{3}+\cdots$
289.3.e.f	$8$	$7.875$	$\Q(\zeta_{16})$	None	$0$	$-8$	$-8$	$8$		$q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots$
289.3.e.g	$8$	$7.875$	$\Q(\zeta_{16})$	None	$0$	$0$	$24$	$16$		$q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots$
289.3.e.h	$8$	$7.875$	$\Q(\zeta_{16})$	None	$0$	$8$	$8$	$-8$		$q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots$
289.3.e.i	$8$	$7.875$	$\Q(\zeta_{16})$	None	$8$	$-8$	$-16$	$8$		$q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
289.3.e.j	$8$	$7.875$	$\Q(\zeta_{16})$	None	$8$	$-8$	$16$	$-8$		$q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots$
289.3.e.k	$8$	$7.875$	$\Q(\zeta_{16})$	None	$8$	$0$	$-16$	$40$		$q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
289.3.e.l	$8$	$7.875$	$\Q(\zeta_{16})$	None	$8$	$0$	$16$	$-40$		$q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
289.3.e.m	$8$	$7.875$	$\Q(\zeta_{16})$	None	$8$	$8$	$16$	$-8$		$q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
289.3.e.n	$8$	$7.875$	$\Q(\zeta_{16})$	None	$8$	$8$	$-16$	$8$		$q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots$
289.3.e.o	$16$	$7.875$	16.0.$\cdots$.1	None	$0$	$0$	$0$	$0$		$q-\beta _{6}q^{2}+\beta _{11}q^{3}+3\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots$
289.3.e.p	$32$	$7.875$		None	$0$	$0$	$0$	$0$
289.3.e.q	$48$	$7.875$		None	$0$	$0$	$0$	$0$
289.3.e.r	$96$	$7.875$		None	$0$	$0$	$0$	$0$
289.3.j.a	$6400$	$7.875$		None	$-128$	$-128$	$-128$	$-128$
289.4.a.a	$1$	$17.052$	$\Q$	None	$-3$	$8$	$-6$	$28$	$+$	$q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots$
289.4.a.b	$3$	$17.052$	3.3.2636.1	None	$1$	$-4$	$8$	$-22$	$+$	$q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots$
289.4.a.c	$4$	$17.052$	4.4.2555057.1	None	$1$	$-2$	$14$	$36$	$+$	$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots$
289.4.a.d	$4$	$17.052$	4.4.2555057.1	None	$1$	$2$	$-14$	$-36$	$-$	$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots$
289.4.a.e	$4$	$17.052$	4.4.4669632.2	None	$2$	$0$	$0$	$0$	$+$	$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\cdots$
289.4.a.f	$8$	$17.052$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$8$	$0$	$0$	$0$	$+$	$q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(5-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots$
289.4.a.g	$12$	$17.052$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$-8$	$0$	$0$	$0$	$-$	$q+(-1+\beta _{5})q^{2}+\beta _{7}q^{3}+(2+2\beta _{1}+\cdots)q^{4}+\cdots$

Next Download to Pari/GP SageMath Magma

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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
289.2.a.a	\(1\)	\(2.308\)	\(\Q\)	None	\(-1\)	\(0\)	\(2\)	\(-4\)	\(+\)	\(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots\)
289.2.a.b	\(2\)	\(2.308\)	\(\Q(\sqrt{13}) \)	None	\(-1\)	\(-1\)	\(-1\)	\(-3\)	\(+\)	\(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\)
289.2.a.c	\(2\)	\(2.308\)	\(\Q(\sqrt{13}) \)	None	\(-1\)	\(1\)	\(1\)	\(3\)	\(-\)	\(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\)
289.2.a.d	\(3\)	\(2.308\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(-3\)	\(-6\)	\(0\)	\(+\)	\(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
289.2.a.e	\(3\)	\(2.308\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(3\)	\(6\)	\(0\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.a.f	\(4\)	\(2.308\)	\(\Q(\zeta_{16})^+\)	None	\(4\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.a	\(2\)	\(2.308\)	\(\Q(\sqrt{-1}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots\)
289.2.b.b	\(4\)	\(2.308\)	4.0.2048.2	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.c	\(4\)	\(2.308\)	\(\Q(i, \sqrt{13})\)	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.b.d	\(6\)	\(2.308\)	6.0.419904.1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots\)
289.2.c.a	\(4\)	\(2.308\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots\)
289.2.c.b	\(8\)	\(2.308\)	8.0.1871773696.1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.c.c	\(8\)	\(2.308\)	\(\Q(\zeta_{16})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots\)
289.2.c.d	\(12\)	\(2.308\)	12.0.\(\cdots\).1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
289.2.d.a	\(4\)	\(2.308\)	\(\Q(\zeta_{8})\)	None	\(-4\)	\(4\)	\(0\)	\(4\)		\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.b	\(4\)	\(2.308\)	\(\Q(\zeta_{8})\)	None	\(4\)	\(-4\)	\(-4\)	\(-4\)		\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.c	\(4\)	\(2.308\)	\(\Q(\zeta_{8})\)	None	\(4\)	\(4\)	\(4\)	\(4\)		\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.d	\(8\)	\(2.308\)	\(\Q(\zeta_{16})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots\)
289.2.d.e	\(16\)	\(2.308\)	16.0.\(\cdots\).1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots\)
289.2.d.f	\(24\)	\(2.308\)		None	\(0\)	\(0\)	\(0\)	\(0\)
289.2.f.a	\(384\)	\(2.308\)		None	\(-13\)	\(-13\)	\(-43\)	\(-13\)
289.2.g.a	\(384\)	\(2.308\)		None	\(-17\)	\(-17\)	\(17\)	\(-17\)
289.2.h.a	\(768\)	\(2.308\)		None	\(-34\)	\(-34\)	\(-34\)	\(-34\)
289.2.i.a	\(1600\)	\(2.308\)		None	\(-64\)	\(-64\)	\(-68\)	\(-64\)
289.3.e.a	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(-8\)	\(-16\)	\(-8\)	\(-16\)		\(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-2-2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.b	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(-8\)	\(-8\)	\(0\)	\(-8\)		\(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.c	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(-8\)	\(8\)	\(-16\)	\(-8\)		\(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.d	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(-8\)	\(8\)	\(0\)	\(8\)		\(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.e	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(-8\)	\(16\)	\(8\)	\(16\)		\(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(2+2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.f	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(0\)	\(-8\)	\(-8\)	\(8\)		\(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
289.3.e.g	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(0\)	\(0\)	\(24\)	\(16\)		\(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
289.3.e.h	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(0\)	\(8\)	\(8\)	\(-8\)		\(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.i	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(8\)	\(-8\)	\(-16\)	\(8\)		\(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.j	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(8\)	\(-8\)	\(16\)	\(-8\)		\(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.k	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(8\)	\(0\)	\(-16\)	\(40\)		\(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.l	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(8\)	\(0\)	\(16\)	\(-40\)		\(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.m	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(8\)	\(8\)	\(16\)	\(-8\)		\(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.n	\(8\)	\(7.875\)	\(\Q(\zeta_{16})\)	None	\(8\)	\(8\)	\(-16\)	\(8\)		\(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.o	\(16\)	\(7.875\)	16.0.\(\cdots\).1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{6}q^{2}+\beta _{11}q^{3}+3\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots\)
289.3.e.p	\(32\)	\(7.875\)		None	\(0\)	\(0\)	\(0\)	\(0\)
289.3.e.q	\(48\)	\(7.875\)		None	\(0\)	\(0\)	\(0\)	\(0\)
289.3.e.r	\(96\)	\(7.875\)		None	\(0\)	\(0\)	\(0\)	\(0\)
289.3.j.a	\(6400\)	\(7.875\)		None	\(-128\)	\(-128\)	\(-128\)	\(-128\)
289.4.a.a	\(1\)	\(17.052\)	\(\Q\)	None	\(-3\)	\(8\)	\(-6\)	\(28\)	\(+\)	\(q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots\)
289.4.a.b	\(3\)	\(17.052\)	3.3.2636.1	None	\(1\)	\(-4\)	\(8\)	\(-22\)	\(+\)	\(q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
289.4.a.c	\(4\)	\(17.052\)	4.4.2555057.1	None	\(1\)	\(-2\)	\(14\)	\(36\)	\(+\)	\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.d	\(4\)	\(17.052\)	4.4.2555057.1	None	\(1\)	\(2\)	\(-14\)	\(-36\)	\(-\)	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.e	\(4\)	\(17.052\)	4.4.4669632.2	None	\(2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\cdots\)
289.4.a.f	\(8\)	\(17.052\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(8\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(5-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots\)
289.4.a.g	\(12\)	\(17.052\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(-8\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+(-1+\beta _{5})q^{2}+\beta _{7}q^{3}+(2+2\beta _{1}+\cdots)q^{4}+\cdots\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Learn more about

Refine search

Results (1-50 of 87 matches)

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