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 245 matches)

Next Download to Pari/GP SageMath Magma

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
360.1.p.a	$1$	$0.180$	$\Q$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	$-1$	$0$	$1$	$0$	$-$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots$
360.1.p.b	$1$	$0.180$	$\Q$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	$1$	$0$	$-1$	$0$	$-$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots$
360.1.u.a	$4$	$0.180$	$\Q(\zeta_{8})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$-4$	$-$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots$
360.2.a.a	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$-1$	$-4$	$+$	$q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots$
360.2.a.b	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$-1$	$0$	$-$	$q-q^{5}+4q^{11}+6q^{13}+6q^{17}-4q^{19}+\cdots$
360.2.a.c	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$-1$	$2$	$-$	$q-q^{5}+2q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots$
360.2.a.d	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$1$	$2$	$-$	$q+q^{5}+2q^{7}-2q^{11}+4q^{13}+2q^{17}+\cdots$
360.2.a.e	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$1$	$4$	$-$	$q+q^{5}+4q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots$
360.2.b.a	$2$	$2.875$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$-2$	$0$	$-$	$q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots$
360.2.b.b	$2$	$2.875$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$2$	$0$	$-$	$q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots$
360.2.b.c	$6$	$2.875$	6.0.2580992.1	None	None	$-2$	$0$	$-6$	$0$	$-$	$q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots$
360.2.b.d	$6$	$2.875$	6.0.2580992.1	None	None	$2$	$0$	$6$	$0$	$-$	$q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots$
360.2.d.a	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-30}) $	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots$
360.2.d.b	$4$	$2.875$	$\Q(\sqrt{2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots$
360.2.d.c	$4$	$2.875$	$\Q(\sqrt{-3}, \sqrt{5})$	$\Q(\sqrt{-15}) $	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
360.2.d.d	$4$	$2.875$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots$
360.2.d.e	$6$	$2.875$	6.0.839056.1	None	None	$-1$	$0$	$0$	$0$	$-$	$q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
360.2.d.f	$6$	$2.875$	6.0.839056.1	None	None	$1$	$0$	$0$	$0$	$-$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots$
360.2.f.a	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-4$	$0$	$-$	$q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots$
360.2.f.b	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-4$	$0$	$-$	$q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots$
360.2.f.c	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$2$	$0$	$-$	$q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots$
360.2.f.d	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$4$	$0$	$-$	$q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots$
360.2.k.a	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$-2$	$0$	$0$	$-8$	$-$	$q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots$
360.2.k.b	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$-2$	$0$	$0$	$4$	$-$	$q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots$
360.2.k.c	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$2$	$0$	$0$	$-8$	$-$	$q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots$
360.2.k.d	$4$	$2.875$	$\Q(i, \sqrt{7})$	None	None	$0$	$0$	$0$	$8$	$-$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots$
360.2.k.e	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$2$	$0$	$0$	$-4$	$-$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots$
360.2.k.f	$6$	$2.875$	6.0.399424.1	None	None	$-2$	$0$	$0$	$4$	$-$	$q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots$
360.2.m.a	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-10}) $	None	$0$	$0$	$0$	$-8$	$-$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots$
360.2.m.b	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-10}) $	None	$0$	$0$	$0$	$8$	$-$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots$
360.2.m.c	$16$	$2.875$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$
360.2.q.a	$2$	$2.875$	$\Q(\sqrt{-3}) $	None	None	$0$	$-3$	$1$	$0$	$-$	$q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots$
360.2.q.b	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$-4$	$-$	$q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots$
360.2.q.c	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$2$	$2$	$-2$	$-$	$q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
360.2.q.d	$6$	$2.875$	6.0.954288.1	None	None	$0$	$-1$	$-3$	$5$	$-$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
360.2.q.e	$8$	$2.875$	8.0.856615824.2	None	None	$0$	$0$	$-4$	$1$	$-$	$q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots$
360.2.s.a	$4$	$2.875$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots$
360.2.s.b	$8$	$2.875$	8.0.40960000.1	None	None	$0$	$0$	$0$	$-8$	$-$	$q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots$
360.2.w.a	$4$	$2.875$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$4$	$-$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
360.2.w.b	$4$	$2.875$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$-4$	$-$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots$
360.2.w.c	$8$	$2.875$	$\Q(\zeta_{20})$	None	None	$2$	$0$	$0$	$0$	$-$	$q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots$
360.2.w.d	$16$	$2.875$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots$
360.2.w.e	$24$	$2.875$		None	None	$0$	$0$	$0$	$0$	$-$
360.2.x.a	$48$	$2.875$		None	None	$0$	$0$	$0$	$0$	$-$
360.2.bd.a	$8$	$2.875$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots$
360.2.bd.b	$128$	$2.875$		None	None	$0$	$0$	$0$	$0$	$-$
360.2.bf.a	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$-2$	$0$	$0$	$8$	$-$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
360.2.bf.b	$92$	$2.875$		None	None	$2$	$0$	$0$	$-8$	$-$
360.2.bi.a	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$0$	$-$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
360.2.bi.b	$32$	$2.875$		None	None	$0$	$0$	$-2$	$0$	$-$

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 245 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.

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
360.1.p.a	$1$	$0.180$	\(\Q\)	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	\(-1\)	\(0\)	\(1\)	\(0\)	$-$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
360.1.p.b	$1$	$0.180$	\(\Q\)	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	\(1\)	\(0\)	\(-1\)	\(0\)	$-$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)
360.1.u.a	$4$	$0.180$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
360.2.a.a	$1$	$2.875$	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(-4\)	$+$	\(q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
360.2.a.b	$1$	$2.875$	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(0\)	$-$	\(q-q^{5}+4q^{11}+6q^{13}+6q^{17}-4q^{19}+\cdots\)
360.2.a.c	$1$	$2.875$	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(2\)	$-$	\(q-q^{5}+2q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
360.2.a.d	$1$	$2.875$	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(2\)	$-$	\(q+q^{5}+2q^{7}-2q^{11}+4q^{13}+2q^{17}+\cdots\)
360.2.a.e	$1$	$2.875$	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(4\)	$-$	\(q+q^{5}+4q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
360.2.b.a	$2$	$2.875$	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.b	$2$	$2.875$	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.c	$6$	$2.875$	6.0.2580992.1	None	None	\(-2\)	\(0\)	\(-6\)	\(0\)	$-$	\(q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.b.d	$6$	$2.875$	6.0.2580992.1	None	None	\(2\)	\(0\)	\(6\)	\(0\)	$-$	\(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.d.a	$4$	$2.875$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-30}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
360.2.d.b	$4$	$2.875$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
360.2.d.c	$4$	$2.875$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
360.2.d.d	$4$	$2.875$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots\)
360.2.d.e	$6$	$2.875$	6.0.839056.1	None	None	\(-1\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
360.2.d.f	$6$	$2.875$	6.0.839056.1	None	None	\(1\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
360.2.f.a	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots\)
360.2.f.b	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots\)
360.2.f.c	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots\)
360.2.f.d	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots\)
360.2.k.a	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(-8\)	$-$	\(q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.b	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(4\)	$-$	\(q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots\)
360.2.k.c	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None	None	\(2\)	\(0\)	\(0\)	\(-8\)	$-$	\(q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.d	$4$	$2.875$	\(\Q(i, \sqrt{7})\)	None	None	\(0\)	\(0\)	\(0\)	\(8\)	$-$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots\)
360.2.k.e	$4$	$2.875$	\(\Q(\zeta_{12})\)	None	None	\(2\)	\(0\)	\(0\)	\(-4\)	$-$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
360.2.k.f	$6$	$2.875$	6.0.399424.1	None	None	\(-2\)	\(0\)	\(0\)	\(4\)	$-$	\(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots\)
360.2.m.a	$4$	$2.875$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)	None	\(0\)	\(0\)	\(0\)	\(-8\)	$-$	\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
360.2.m.b	$4$	$2.875$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)	None	\(0\)	\(0\)	\(0\)	\(8\)	$-$	\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots\)
360.2.m.c	$16$	$2.875$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
360.2.q.a	$2$	$2.875$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-3\)	\(1\)	\(0\)	$-$	\(q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots\)
360.2.q.b	$4$	$2.875$	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(-4\)	$-$	\(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots\)
360.2.q.c	$4$	$2.875$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(2\)	\(2\)	\(-2\)	$-$	\(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
360.2.q.d	$6$	$2.875$	6.0.954288.1	None	None	\(0\)	\(-1\)	\(-3\)	\(5\)	$-$	\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
360.2.q.e	$8$	$2.875$	8.0.856615824.2	None	None	\(0\)	\(0\)	\(-4\)	\(1\)	$-$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots\)
360.2.s.a	$4$	$2.875$	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots\)
360.2.s.b	$8$	$2.875$	8.0.40960000.1	None	None	\(0\)	\(0\)	\(0\)	\(-8\)	$-$	\(q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
360.2.w.a	$4$	$2.875$	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	$-$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
360.2.w.b	$4$	$2.875$	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
360.2.w.c	$8$	$2.875$	\(\Q(\zeta_{20})\)	None	None	\(2\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots\)
360.2.w.d	$16$	$2.875$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots\)
360.2.w.e	$24$	$2.875$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
360.2.x.a	$48$	$2.875$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
360.2.bd.a	$8$	$2.875$	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
360.2.bd.b	$128$	$2.875$		None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$
360.2.bf.a	$4$	$2.875$	\(\Q(\zeta_{12})\)	None	None	\(-2\)	\(0\)	\(0\)	\(8\)	$-$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
360.2.bf.b	$92$	$2.875$		None	None	\(2\)	\(0\)	\(0\)	\(-8\)	$-$
360.2.bi.a	$4$	$2.875$	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
360.2.bi.b	$32$	$2.875$		None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$