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

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 198 matches)

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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
304.1.e.a	$1$	$0.152$	$\Q$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-1$	$1$	$-$	$q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots$
304.2.a.a	$1$	$2.427$	$\Q$	None	None	$0$	$-2$	$-1$	$3$	$+$	$q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots$
304.2.a.b	$1$	$2.427$	$\Q$	None	None	$0$	$-1$	$0$	$-3$	$+$	$q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots$
304.2.a.c	$1$	$2.427$	$\Q$	None	None	$0$	$-1$	$0$	$1$	$-$	$q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots$
304.2.a.d	$1$	$2.427$	$\Q$	None	None	$0$	$1$	$-4$	$-3$	$+$	$q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
304.2.a.e	$1$	$2.427$	$\Q$	None	None	$0$	$2$	$-1$	$3$	$-$	$q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots$
304.2.a.f	$1$	$2.427$	$\Q$	None	None	$0$	$2$	$3$	$1$	$-$	$q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots$
304.2.a.g	$3$	$2.427$	3.3.961.1	None	None	$0$	$-1$	$1$	$-4$	$-$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
304.2.h.a	$2$	$2.427$	$\Q(\sqrt{-19}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-2$	$0$	$-$	$q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots$
304.2.h.b	$4$	$2.427$	$\Q(\sqrt{-3}, \sqrt{7})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots$
304.2.h.c	$4$	$2.427$	$\Q(\sqrt{-3}, \sqrt{-19})$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$2$	$0$	$-$	$q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots$
304.2.i.a	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$1$	$0$	$-$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
304.2.i.b	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-3$	$0$	$-$	$q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
304.2.i.c	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$0$	$8$	$-$	$q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots$
304.2.i.d	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$4$	$0$	$-$	$q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
304.2.i.e	$4$	$2.427$	$\Q(\sqrt{-3}, \sqrt{7})$	None	None	$0$	$0$	$-2$	$-4$	$-$	$q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
304.2.i.f	$6$	$2.427$	6.0.2696112.1	None	None	$0$	$1$	$-1$	$4$	$-$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
304.2.k.a	$4$	$2.427$	$\Q(\zeta_{8})$	None	None	$0$	$-4$	$-8$	$0$	$-$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$
304.2.k.b	$68$	$2.427$		None	None	$0$	$4$	$8$	$0$	$-$
304.2.m.a	$76$	$2.427$		None	None	$0$	$0$	$-4$	$-8$	$-$
304.2.n.a	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-3$	$0$	$-$	$q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots$
304.2.n.b	$2$	$2.427$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-3$	$0$	$-$	$q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$
304.2.n.c	$4$	$2.427$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$0$	$-$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots$
304.2.n.d	$6$	$2.427$	6.0.31726512.1	None	None	$0$	$-1$	$2$	$0$	$-$	$q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$
304.2.n.e	$6$	$2.427$	6.0.31726512.1	None	None	$0$	$1$	$2$	$0$	$-$	$q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots$
304.2.u.a	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$-9$	$-6$	$-6$	$-$	$q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots$
304.2.u.b	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$3$	$-6$	$0$	$-$	$q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots$
304.2.u.c	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$3$	$0$	$6$	$-$	$q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots$
304.2.u.d	$6$	$2.427$	$\Q(\zeta_{18})$	None	None	$0$	$6$	$6$	$-3$	$-$	$q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots$
304.2.u.e	$12$	$2.427$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$3$	$0$	$-3$	$-$	$q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots$
304.2.u.f	$18$	$2.427$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$0$	$0$	$9$	$-$	$q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots$
304.2.v.a	$152$	$2.427$		None	None	$-2$	$-2$	$-2$	$0$	$-$
304.2.x.a	$4$	$2.427$	$\Q(\zeta_{12})$	None	None	$-2$	$2$	$-2$	$-4$	$-$	$q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
304.2.x.b	$4$	$2.427$	$\Q(\zeta_{12})$	None	None	$2$	$4$	$-2$	$-4$	$-$	$q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
304.2.x.c	$144$	$2.427$		None	None	$-6$	$-12$	$2$	$-8$	$-$
304.2.be.a	$12$	$2.427$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$0$	$0$	$-$	$q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots$
304.2.be.b	$12$	$2.427$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$0$	$0$	$0$	$-$	$q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots$
304.2.be.c	$18$	$2.427$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$0$	$0$	$-9$	$-$	$q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots$
304.2.be.d	$18$	$2.427$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$0$	$0$	$9$	$-$	$q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots$
304.2.bg.a	$456$	$2.427$		None	None	$-12$	$-12$	$-12$	$-12$	$-$
304.2.bi.a	$456$	$2.427$		None	None	$-12$	$-12$	$-12$	$0$	$-$
304.3.d.a	$6$	$8.283$	6.0.210056875.1	None	None	$0$	$0$	$14$	$0$	$-$	$q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots$
304.3.d.b	$12$	$8.283$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$0$	$-2$	$0$	$-$	$q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots$
304.3.e.a	$1$	$8.283$	$\Q$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-9$	$5$	$-$	$q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots$
304.3.e.b	$2$	$8.283$	$\Q(\sqrt{-29}) $	None	None	$0$	$0$	$-8$	$2$	$-$	$q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots$
304.3.e.c	$2$	$8.283$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$-2$	$-10$	$-$	$q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots$
304.3.e.d	$2$	$8.283$	$\Q(\sqrt{-13}) $	None	None	$0$	$0$	$8$	$10$	$-$	$q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots$
304.3.e.e	$2$	$8.283$	$\Q(\sqrt{57}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$9$	$-5$	$-$	$q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots$
304.3.e.f	$2$	$8.283$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$14$	$-22$	$-$	$q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots$
304.3.e.g	$8$	$8.283$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	None	$0$	$0$	$-14$	$6$	$-$	$q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots$

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Results (1-50 of 198 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
304.1.e.a	$1$	$0.152$	\(\Q\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-1\)	\(1\)	$-$	\(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
304.2.a.a	$1$	$2.427$	\(\Q\)	None	None	\(0\)	\(-2\)	\(-1\)	\(3\)	$+$	\(q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
304.2.a.b	$1$	$2.427$	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(-3\)	$+$	\(q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
304.2.a.c	$1$	$2.427$	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(1\)	$-$	\(q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots\)
304.2.a.d	$1$	$2.427$	\(\Q\)	None	None	\(0\)	\(1\)	\(-4\)	\(-3\)	$+$	\(q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
304.2.a.e	$1$	$2.427$	\(\Q\)	None	None	\(0\)	\(2\)	\(-1\)	\(3\)	$-$	\(q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
304.2.a.f	$1$	$2.427$	\(\Q\)	None	None	\(0\)	\(2\)	\(3\)	\(1\)	$-$	\(q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
304.2.a.g	$3$	$2.427$	3.3.961.1	None	None	\(0\)	\(-1\)	\(1\)	\(-4\)	$-$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
304.2.h.a	$2$	$2.427$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b	$4$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c	$4$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
304.2.i.a	$2$	$2.427$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(1\)	\(0\)	$-$	\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.b	$2$	$2.427$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-3\)	\(0\)	$-$	\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.c	$2$	$2.427$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(0\)	\(8\)	$-$	\(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
304.2.i.d	$2$	$2.427$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(4\)	\(0\)	$-$	\(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.e	$4$	$2.427$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None	None	\(0\)	\(0\)	\(-2\)	\(-4\)	$-$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
304.2.i.f	$6$	$2.427$	6.0.2696112.1	None	None	\(0\)	\(1\)	\(-1\)	\(4\)	$-$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
304.2.k.a	$4$	$2.427$	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(-4\)	\(-8\)	\(0\)	$-$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
304.2.k.b	$68$	$2.427$		None	None	\(0\)	\(4\)	\(8\)	\(0\)	$-$
304.2.m.a	$76$	$2.427$		None	None	\(0\)	\(0\)	\(-4\)	\(-8\)	$-$
304.2.n.a	$2$	$2.427$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-3\)	\(0\)	$-$	\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
304.2.n.b	$2$	$2.427$	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-3\)	\(0\)	$-$	\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
304.2.n.c	$4$	$2.427$	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
304.2.n.d	$6$	$2.427$	6.0.31726512.1	None	None	\(0\)	\(-1\)	\(2\)	\(0\)	$-$	\(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
304.2.n.e	$6$	$2.427$	6.0.31726512.1	None	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	\(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
304.2.u.a	$6$	$2.427$	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(-9\)	\(-6\)	\(-6\)	$-$	\(q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
304.2.u.b	$6$	$2.427$	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(3\)	\(-6\)	\(0\)	$-$	\(q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots\)
304.2.u.c	$6$	$2.427$	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(3\)	\(0\)	\(6\)	$-$	\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots\)
304.2.u.d	$6$	$2.427$	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(6\)	\(6\)	\(-3\)	$-$	\(q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots\)
304.2.u.e	$12$	$2.427$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(3\)	\(0\)	\(-3\)	$-$	\(q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
304.2.u.f	$18$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(9\)	$-$	\(q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
304.2.v.a	$152$	$2.427$		None	None	\(-2\)	\(-2\)	\(-2\)	\(0\)	$-$
304.2.x.a	$4$	$2.427$	\(\Q(\zeta_{12})\)	None	None	\(-2\)	\(2\)	\(-2\)	\(-4\)	$-$	\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.b	$4$	$2.427$	\(\Q(\zeta_{12})\)	None	None	\(2\)	\(4\)	\(-2\)	\(-4\)	$-$	\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.c	$144$	$2.427$		None	None	\(-6\)	\(-12\)	\(2\)	\(-8\)	$-$
304.2.be.a	$12$	$2.427$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.b	$12$	$2.427$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
304.2.be.c	$18$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(-9\)	$-$	\(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.d	$18$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(9\)	$-$	\(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.bg.a	$456$	$2.427$		None	None	\(-12\)	\(-12\)	\(-12\)	\(-12\)	$-$
304.2.bi.a	$456$	$2.427$		None	None	\(-12\)	\(-12\)	\(-12\)	\(0\)	$-$
304.3.d.a	$6$	$8.283$	6.0.210056875.1	None	None	\(0\)	\(0\)	\(14\)	\(0\)	$-$	\(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)
304.3.d.b	$12$	$8.283$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots\)
304.3.e.a	$1$	$8.283$	\(\Q\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-9\)	\(5\)	$-$	\(q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots\)
304.3.e.b	$2$	$8.283$	\(\Q(\sqrt{-29}) \)	None	None	\(0\)	\(0\)	\(-8\)	\(2\)	$-$	\(q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots\)
304.3.e.c	$2$	$8.283$	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(-10\)	$-$	\(q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots\)
304.3.e.d	$2$	$8.283$	\(\Q(\sqrt{-13}) \)	None	None	\(0\)	\(0\)	\(8\)	\(10\)	$-$	\(q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots\)
304.3.e.e	$2$	$8.283$	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(9\)	\(-5\)	$-$	\(q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots\)
304.3.e.f	$2$	$8.283$	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(14\)	\(-22\)	$-$	\(q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots\)
304.3.e.g	$8$	$8.283$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	None	\(0\)	\(0\)	\(-14\)	\(6\)	$-$	\(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots\)