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 153 matches)

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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
370.2.a.a	$1$	$2.954$	$\Q$	None	$-1$	$-2$	$-1$	$-1$	$-$	$q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{7}+\cdots$
370.2.a.b	$1$	$2.954$	$\Q$	None	$-1$	$0$	$-1$	$0$	$+$	$q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots$
370.2.a.c	$1$	$2.954$	$\Q$	None	$-1$	$2$	$1$	$1$	$-$	$q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
370.2.a.d	$1$	$2.954$	$\Q$	None	$1$	$-2$	$1$	$2$	$-$	$q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots$
370.2.a.e	$2$	$2.954$	$\Q(\sqrt{3}) $	None	$-2$	$-2$	$2$	$-6$	$+$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots$
370.2.a.f	$2$	$2.954$	$\Q(\sqrt{33}) $	None	$2$	$4$	$2$	$-3$	$-$	$q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+(-1+\cdots)q^{7}+\cdots$
370.2.a.g	$3$	$2.954$	3.3.892.1	None	$3$	$0$	$-3$	$-1$	$-$	$q+q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}-\beta _{2}q^{6}+\cdots$
370.2.b.a	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$		$q+iq^{2}-q^{4}+(-2-i)q^{5}-2iq^{7}+\cdots$
370.2.b.b	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$2$	$0$		$q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots$
370.2.b.c	$4$	$2.954$	$\Q(i, \sqrt{6})$	None	$0$	$0$	$-8$	$0$		$q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
370.2.b.d	$10$	$2.954$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$0$	$6$	$0$		$q-\beta _{2}q^{2}+(\beta _{4}-\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
370.2.c.a	$10$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$-10$	$0$	$-3$	$0$		$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
370.2.c.b	$10$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$10$	$0$	$3$	$0$		$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
370.2.d.a	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$-4$		$q+iq^{2}-q^{4}+iq^{5}-2q^{7}-iq^{8}+\cdots$
370.2.d.b	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$10$		$q+iq^{2}-q^{4}+iq^{5}+5q^{7}-iq^{8}+\cdots$
370.2.d.c	$6$	$2.954$	6.0.399424.1	None	$0$	$-4$	$0$	$10$		$q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}-q^{4}+\cdots$
370.2.e.a	$2$	$2.954$	$\Q(\sqrt{-3}) $	None	$1$	$-2$	$-1$	$0$		$q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
370.2.e.b	$2$	$2.954$	$\Q(\sqrt{-3}) $	None	$1$	$-1$	$1$	$-2$		$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
370.2.e.c	$2$	$2.954$	$\Q(\sqrt{-3}) $	None	$1$	$3$	$1$	$0$		$q+(1-\zeta_{6})q^{2}+3\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
370.2.e.d	$4$	$2.954$	$\Q(\zeta_{12})$	None	$-2$	$2$	$-2$	$0$		$q+(-1+\zeta_{12})q^{2}+\zeta_{12}q^{3}-\zeta_{12}q^{4}+\cdots$
370.2.e.e	$4$	$2.954$	$\Q(\sqrt{-3}, \sqrt{10})$	None	$2$	$2$	$-2$	$-4$		$q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots$
370.2.e.f	$6$	$2.954$	6.0.2696112.1	None	$-3$	$0$	$3$	$-2$		$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots$
370.2.g.a	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$0$	$-2$	$4$	$2$		$q+iq^{2}+(-1-i)q^{3}-q^{4}+(2+i)q^{5}+\cdots$
370.2.g.b	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$-4$		$q+iq^{2}-q^{4}+(-2+i)q^{5}+(-2-2i)q^{7}+\cdots$
370.2.g.c	$4$	$2.954$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$8$		$q+\zeta_{8}^{2}q^{2}+2\zeta_{8}q^{3}-q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
370.2.g.d	$10$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$0$	$-2$	$2$	$-4$		$q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{3}-\beta _{8})q^{3}-q^{4}+\cdots$
370.2.g.e	$20$	$2.954$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$0$	$-4$	$2$	$-2$		$q-\beta _{10}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{8}q^{5}+\beta _{4}q^{6}+\cdots$
370.2.h.a	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$2$	$0$	$-2$	$-4$		$q+q^{2}+q^{4}+(-1+2i)q^{5}+(-2+2i)q^{7}+\cdots$
370.2.h.b	$2$	$2.954$	$\Q(\sqrt{-1}) $	None	$2$	$2$	$-2$	$2$		$q+q^{2}+(1-i)q^{3}+q^{4}+(-1-2i)q^{5}+\cdots$
370.2.h.c	$4$	$2.954$	$\Q(\zeta_{8})$	None	$4$	$0$	$0$	$8$		$q+q^{2}+2\zeta_{8}q^{3}+q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$
370.2.h.d	$10$	$2.954$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$10$	$2$	$2$	$-4$		$q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
370.2.h.e	$20$	$2.954$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$-20$	$4$	$-4$	$-2$		$q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{13}q^{5}+\beta _{4}q^{6}+\cdots$
370.2.l.a	$4$	$2.954$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$2$		$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
370.2.l.b	$4$	$2.954$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$4$		$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
370.2.l.c	$12$	$2.954$	12.0.$\cdots$.2	None	$0$	$4$	$0$	$2$		$q-\beta _{2}q^{2}+(1-\beta _{6}+\beta _{10})q^{3}+(1-\beta _{6}+\cdots)q^{4}+\cdots$
370.2.m.a	$4$	$2.954$	$\Q(\sqrt{-3}, \sqrt{-11})$	None	$-2$	$-3$	$-6$	$-12$		$q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
370.2.m.b	$4$	$2.954$	$\Q(\sqrt{-3}, \sqrt{-11})$	None	$2$	$3$	$-3$	$12$		$q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{4}+\cdots$
370.2.m.c	$16$	$2.954$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$-8$	$3$	$6$	$12$		$q+(-1-\beta _{1})q^{2}+\beta _{10}q^{3}+\beta _{1}q^{4}+\cdots$
370.2.m.d	$16$	$2.954$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$8$	$-3$	$0$	$-12$		$q+(1+\beta _{1})q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}+\beta _{8}q^{5}+\cdots$
370.2.n.a	$4$	$2.954$	$\Q(\zeta_{12})$	None	$0$	$0$	$-8$	$-6$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{3})q^{5}+\cdots$
370.2.n.b	$4$	$2.954$	$\Q(\zeta_{12})$	None	$0$	$0$	$4$	$0$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
370.2.n.c	$4$	$2.954$	$\Q(\zeta_{12})$	None	$0$	$0$	$4$	$6$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
370.2.n.d	$4$	$2.954$	$\Q(\zeta_{12})$	None	$0$	$0$	$4$	$0$		$q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
370.2.n.e	$8$	$2.954$	8.0.303595776.1	None	$0$	$0$	$0$	$0$		$q-\beta _{3}q^{2}-2\beta _{5}q^{3}-\beta _{4}q^{4}+(\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots$
370.2.n.f	$12$	$2.954$	12.0.$\cdots$.1	None	$0$	$0$	$0$	$0$		$q+\beta _{3}q^{2}+(\beta _{5}-\beta _{6}-\beta _{7}+\beta _{9})q^{3}+\cdots$
370.2.o.a	$18$	$2.954$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$0$	$0$	$0$	$-3$		$q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{8}-\beta _{17})q^{3}+\beta _{6}q^{4}+\cdots$
370.2.o.b	$18$	$2.954$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$0$	$0$	$0$	$-9$		$q+\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{10}+\beta _{11})q^{4}+\cdots$
370.2.o.c	$24$	$2.954$		None	$0$	$0$	$0$	$-3$
370.2.o.d	$24$	$2.954$		None	$0$	$0$	$0$	$-9$
370.2.q.a	$4$	$2.954$	$\Q(\zeta_{12})$	None	$-2$	$4$	$-4$	$4$		$q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$

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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
370.2.a.a	\(1\)	\(2.954\)	\(\Q\)	None	\(-1\)	\(-2\)	\(-1\)	\(-1\)	\(-\)	\(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
370.2.a.b	\(1\)	\(2.954\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(0\)	\(+\)	\(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
370.2.a.c	\(1\)	\(2.954\)	\(\Q\)	None	\(-1\)	\(2\)	\(1\)	\(1\)	\(-\)	\(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
370.2.a.d	\(1\)	\(2.954\)	\(\Q\)	None	\(1\)	\(-2\)	\(1\)	\(2\)	\(-\)	\(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
370.2.a.e	\(2\)	\(2.954\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(-2\)	\(2\)	\(-6\)	\(+\)	\(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
370.2.a.f	\(2\)	\(2.954\)	\(\Q(\sqrt{33}) \)	None	\(2\)	\(4\)	\(2\)	\(-3\)	\(-\)	\(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+(-1+\cdots)q^{7}+\cdots\)
370.2.a.g	\(3\)	\(2.954\)	3.3.892.1	None	\(3\)	\(0\)	\(-3\)	\(-1\)	\(-\)	\(q+q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}-\beta _{2}q^{6}+\cdots\)
370.2.b.a	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+iq^{2}-q^{4}+(-2-i)q^{5}-2iq^{7}+\cdots\)
370.2.b.b	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
370.2.b.c	\(4\)	\(2.954\)	\(\Q(i, \sqrt{6})\)	None	\(0\)	\(0\)	\(-8\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
370.2.b.d	\(10\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(0\)	\(6\)	\(0\)		\(q-\beta _{2}q^{2}+(\beta _{4}-\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
370.2.c.a	\(10\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(-10\)	\(0\)	\(-3\)	\(0\)		\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
370.2.c.b	\(10\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(10\)	\(0\)	\(3\)	\(0\)		\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
370.2.d.a	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+iq^{2}-q^{4}+iq^{5}-2q^{7}-iq^{8}+\cdots\)
370.2.d.b	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(10\)		\(q+iq^{2}-q^{4}+iq^{5}+5q^{7}-iq^{8}+\cdots\)
370.2.d.c	\(6\)	\(2.954\)	6.0.399424.1	None	\(0\)	\(-4\)	\(0\)	\(10\)		\(q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}-q^{4}+\cdots\)
370.2.e.a	\(2\)	\(2.954\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-2\)	\(-1\)	\(0\)		\(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
370.2.e.b	\(2\)	\(2.954\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-1\)	\(1\)	\(-2\)		\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
370.2.e.c	\(2\)	\(2.954\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(3\)	\(1\)	\(0\)		\(q+(1-\zeta_{6})q^{2}+3\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
370.2.e.d	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(-2\)	\(2\)	\(-2\)	\(0\)		\(q+(-1+\zeta_{12})q^{2}+\zeta_{12}q^{3}-\zeta_{12}q^{4}+\cdots\)
370.2.e.e	\(4\)	\(2.954\)	\(\Q(\sqrt{-3}, \sqrt{10})\)	None	\(2\)	\(2\)	\(-2\)	\(-4\)		\(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
370.2.e.f	\(6\)	\(2.954\)	6.0.2696112.1	None	\(-3\)	\(0\)	\(3\)	\(-2\)		\(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
370.2.g.a	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(-2\)	\(4\)	\(2\)		\(q+iq^{2}+(-1-i)q^{3}-q^{4}+(2+i)q^{5}+\cdots\)
370.2.g.b	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(-4\)		\(q+iq^{2}-q^{4}+(-2+i)q^{5}+(-2-2i)q^{7}+\cdots\)
370.2.g.c	\(4\)	\(2.954\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(8\)		\(q+\zeta_{8}^{2}q^{2}+2\zeta_{8}q^{3}-q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
370.2.g.d	\(10\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(0\)	\(-2\)	\(2\)	\(-4\)		\(q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{3}-\beta _{8})q^{3}-q^{4}+\cdots\)
370.2.g.e	\(20\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(0\)	\(-4\)	\(2\)	\(-2\)		\(q-\beta _{10}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{8}q^{5}+\beta _{4}q^{6}+\cdots\)
370.2.h.a	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(2\)	\(0\)	\(-2\)	\(-4\)		\(q+q^{2}+q^{4}+(-1+2i)q^{5}+(-2+2i)q^{7}+\cdots\)
370.2.h.b	\(2\)	\(2.954\)	\(\Q(\sqrt{-1}) \)	None	\(2\)	\(2\)	\(-2\)	\(2\)		\(q+q^{2}+(1-i)q^{3}+q^{4}+(-1-2i)q^{5}+\cdots\)
370.2.h.c	\(4\)	\(2.954\)	\(\Q(\zeta_{8})\)	None	\(4\)	\(0\)	\(0\)	\(8\)		\(q+q^{2}+2\zeta_{8}q^{3}+q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
370.2.h.d	\(10\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(10\)	\(2\)	\(2\)	\(-4\)		\(q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
370.2.h.e	\(20\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(-20\)	\(4\)	\(-4\)	\(-2\)		\(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{13}q^{5}+\beta _{4}q^{6}+\cdots\)
370.2.l.a	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.l.b	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.l.c	\(12\)	\(2.954\)	12.0.\(\cdots\).2	None	\(0\)	\(4\)	\(0\)	\(2\)		\(q-\beta _{2}q^{2}+(1-\beta _{6}+\beta _{10})q^{3}+(1-\beta _{6}+\cdots)q^{4}+\cdots\)
370.2.m.a	\(4\)	\(2.954\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None	\(-2\)	\(-3\)	\(-6\)	\(-12\)		\(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
370.2.m.b	\(4\)	\(2.954\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None	\(2\)	\(3\)	\(-3\)	\(12\)		\(q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
370.2.m.c	\(16\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(-8\)	\(3\)	\(6\)	\(12\)		\(q+(-1-\beta _{1})q^{2}+\beta _{10}q^{3}+\beta _{1}q^{4}+\cdots\)
370.2.m.d	\(16\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(8\)	\(-3\)	\(0\)	\(-12\)		\(q+(1+\beta _{1})q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}+\beta _{8}q^{5}+\cdots\)
370.2.n.a	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(-8\)	\(-6\)		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{3})q^{5}+\cdots\)
370.2.n.b	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
370.2.n.c	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(4\)	\(6\)		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
370.2.n.d	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.n.e	\(8\)	\(2.954\)	8.0.303595776.1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{3}q^{2}-2\beta _{5}q^{3}-\beta _{4}q^{4}+(\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
370.2.n.f	\(12\)	\(2.954\)	12.0.\(\cdots\).1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}+(\beta _{5}-\beta _{6}-\beta _{7}+\beta _{9})q^{3}+\cdots\)
370.2.o.a	\(18\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-3\)		\(q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{8}-\beta _{17})q^{3}+\beta _{6}q^{4}+\cdots\)
370.2.o.b	\(18\)	\(2.954\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-9\)		\(q+\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{10}+\beta _{11})q^{4}+\cdots\)
370.2.o.c	\(24\)	\(2.954\)		None	\(0\)	\(0\)	\(0\)	\(-3\)
370.2.o.d	\(24\)	\(2.954\)		None	\(0\)	\(0\)	\(0\)	\(-9\)
370.2.q.a	\(4\)	\(2.954\)	\(\Q(\zeta_{12})\)	None	\(-2\)	\(4\)	\(-4\)	\(4\)		\(q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)

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