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 213 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
392.1.g.a	$1$	$0.196$	$\Q$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $	$1$	$0$	$0$	$0$		$q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots$
392.1.g.b	$2$	$0.196$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-2}) $	None	$-2$	$0$	$0$	$0$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots$
392.1.j.a	$2$	$0.196$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	$1$	$0$	$0$	$0$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}q^{9}-\zeta_{6}q^{16}+\cdots$
392.1.k.a	$2$	$0.196$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $	$-1$	$0$	$0$	$0$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
392.1.k.b	$4$	$0.196$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-2}) $	None	$2$	$0$	$0$	$0$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots$
392.2.a.a	$1$	$3.130$	$\Q$	None	None	$0$	$-3$	$1$	$0$	$+$	$q-3q^{3}+q^{5}+6q^{9}-q^{11}-2q^{13}+\cdots$
392.2.a.b	$1$	$3.130$	$\Q$	None	None	$0$	$-2$	$4$	$0$	$-$	$q-2q^{3}+4q^{5}+q^{9}-8q^{15}+2q^{17}+\cdots$
392.2.a.c	$1$	$3.130$	$\Q$	None	None	$0$	$-1$	$-1$	$0$	$+$	$q-q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\cdots$
392.2.a.d	$1$	$3.130$	$\Q$	None	None	$0$	$0$	$-2$	$0$	$+$	$q-2q^{5}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots$
392.2.a.e	$1$	$3.130$	$\Q$	None	None	$0$	$1$	$1$	$0$	$-$	$q+q^{3}+q^{5}-2q^{9}+3q^{11}+6q^{13}+\cdots$
392.2.a.f	$1$	$3.130$	$\Q$	None	None	$0$	$3$	$-1$	$0$	$-$	$q+3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\cdots$
392.2.a.g	$2$	$3.130$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta q^{3}+2\beta q^{5}-q^{9}+6q^{11}-4\beta q^{13}+\cdots$
392.2.a.h	$2$	$3.130$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}-\beta q^{13}+\cdots$
392.2.b.a	$2$	$3.130$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $	None	$-1$	$0$	$0$	$0$		$q-\beta q^{2}+(-2+\beta )q^{4}+(2+\beta )q^{8}+3q^{9}+\cdots$
392.2.b.b	$2$	$3.130$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$0$	$0$		$q+\beta q^{2}-\beta q^{3}-2q^{4}+\beta q^{5}+2q^{6}+\cdots$
392.2.b.c	$4$	$3.130$	4.0.2312.1	None	None	$-1$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
392.2.b.d	$4$	$3.130$	4.0.7168.1	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$
392.2.b.e	$6$	$3.130$	6.0.1142512.1	None	None	$2$	$0$	$0$	$0$		$q-\beta _{4}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
392.2.b.f	$6$	$3.130$	6.0.1142512.1	None	None	$2$	$0$	$0$	$0$		$q-\beta _{4}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
392.2.b.g	$12$	$3.130$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$-2$	$0$	$0$	$0$		$q-\beta _{4}q^{2}-\beta _{9}q^{3}-\beta _{1}q^{4}+(\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots$
392.2.e.a	$4$	$3.130$	4.0.2048.2	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}-\beta _{1}q^{6}-2\beta _{2}q^{8}+\cdots$
392.2.e.b	$4$	$3.130$	4.0.2048.2	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{3})q^{6}+\cdots$
392.2.e.c	$8$	$3.130$	8.0.339738624.1	None	None	$0$	$0$	$0$	$0$		$q-\beta _{5}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots$
392.2.e.d	$8$	$3.130$	8.0.$\cdots$.10	None	None	$4$	$0$	$0$	$0$		$q+(1-\beta _{5})q^{2}-\beta _{2}q^{3}+(\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
392.2.e.e	$12$	$3.130$	12.0.$\cdots$.2	None	None	$0$	$0$	$0$	$0$		$q-\beta _{5}q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}-\beta _{9}q^{5}+\cdots$
392.2.i.a	$2$	$3.130$	$\Q(\sqrt{-3}) $	None	None	$0$	$-2$	$4$	$0$		$q+(-2+2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
392.2.i.b	$2$	$3.130$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-1$	$0$		$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$
392.2.i.c	$2$	$3.130$	$\Q(\sqrt{-3}) $	None	None	$0$	$0$	$-2$	$0$		$q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots$
392.2.i.d	$2$	$3.130$	$\Q(\sqrt{-3}) $	None	None	$0$	$0$	$2$	$0$		$q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots$
392.2.i.e	$2$	$3.130$	$\Q(\sqrt{-3}) $	None	None	$0$	$2$	$-4$	$0$		$q+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}-8q^{15}+\cdots$
392.2.i.f	$2$	$3.130$	$\Q(\sqrt{-3}) $	None	None	$0$	$3$	$-1$	$0$		$q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$
392.2.i.g	$4$	$3.130$	$\Q(\sqrt{2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots$
392.2.i.h	$4$	$3.130$	$\Q(\sqrt{2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots$
392.2.m.a	$4$	$3.130$	$\Q(\sqrt{-3}, \sqrt{-7})$	$\Q(\sqrt{-7}) $	None	$-1$	$0$	$0$	$0$		$q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{8}+\cdots$
392.2.m.b	$8$	$3.130$	8.0.339738624.1	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{6}q^{2}+\beta _{3}q^{3}+(-2-2\beta _{4})q^{4}+\cdots$
392.2.m.c	$8$	$3.130$	8.0.339738624.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots$
392.2.m.d	$8$	$3.130$	8.0.339738624.1	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{4})q^{4}+\cdots$
392.2.m.e	$8$	$3.130$	8.0.339738624.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots$
392.2.m.f	$8$	$3.130$	$\Q(\zeta_{24})$	None	None	$4$	$0$	$0$	$0$		$q+(1+\zeta_{24}-\zeta_{24}^{2})q^{2}+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{3}+\cdots$
392.2.m.g	$12$	$3.130$	12.0.$\cdots$.2	None	None	$0$	$6$	$0$	$0$		$q+(\beta _{1}-\beta _{8})q^{2}+(1+\beta _{10})q^{3}+(\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
392.2.m.h	$16$	$3.130$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$-4$	$0$	$0$	$0$		$q+(\beta _{5}+\beta _{14})q^{2}-\beta _{15}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots$
392.2.p.a	$4$	$3.130$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$
392.2.p.b	$4$	$3.130$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots$
392.2.p.c	$4$	$3.130$	$\Q(\sqrt{-3}, \sqrt{-7})$	$\Q(\sqrt{-7}) $	None	$1$	$0$	$0$	$0$		$q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots$
392.2.p.d	$8$	$3.130$	8.0.$\cdots$.10	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{5}q^{2}-\beta _{6}q^{3}+(-2+2\beta _{2})q^{4}+\cdots$
392.2.p.e	$8$	$3.130$	8.0.432972864.2	None	None	$1$	$0$	$0$	$0$		$q+(-\beta _{1}-\beta _{6})q^{2}+(\beta _{5}+\beta _{6})q^{3}+\beta _{5}q^{4}+\cdots$
392.2.p.f	$8$	$3.130$	8.0.432972864.2	None	None	$1$	$0$	$0$	$0$		$q+(-\beta _{1}-\beta _{6})q^{2}+(-\beta _{5}-\beta _{6})q^{3}+\cdots$
392.2.p.g	$12$	$3.130$	12.0.$\cdots$.1	None	None	$-2$	$0$	$0$	$0$		$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots$
392.2.p.h	$24$	$3.130$		None	None	$2$	$0$	$0$	$0$
392.2.q.a	$42$	$3.130$		None	None	$0$	$-7$	$-2$	$1$

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Elliptic curves over $\Q$
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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
392.1.g.a	\(1\)	\(0.196\)	\(\Q\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{14}) \)	\(1\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots\)
392.1.g.b	\(2\)	\(0.196\)	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-2}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots\)
392.1.j.a	\(2\)	\(0.196\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	\(1\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}q^{9}-\zeta_{6}q^{16}+\cdots\)
392.1.k.a	\(2\)	\(0.196\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{14}) \)	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
392.1.k.b	\(4\)	\(0.196\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots\)
392.2.a.a	\(1\)	\(3.130\)	\(\Q\)	None	None	\(0\)	\(-3\)	\(1\)	\(0\)	\(+\)	\(q-3q^{3}+q^{5}+6q^{9}-q^{11}-2q^{13}+\cdots\)
392.2.a.b	\(1\)	\(3.130\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(4\)	\(0\)	\(-\)	\(q-2q^{3}+4q^{5}+q^{9}-8q^{15}+2q^{17}+\cdots\)
392.2.a.c	\(1\)	\(3.130\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(+\)	\(q-q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\cdots\)
392.2.a.d	\(1\)	\(3.130\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(+\)	\(q-2q^{5}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
392.2.a.e	\(1\)	\(3.130\)	\(\Q\)	None	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(q+q^{3}+q^{5}-2q^{9}+3q^{11}+6q^{13}+\cdots\)
392.2.a.f	\(1\)	\(3.130\)	\(\Q\)	None	None	\(0\)	\(3\)	\(-1\)	\(0\)	\(-\)	\(q+3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\cdots\)
392.2.a.g	\(2\)	\(3.130\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+\beta q^{3}+2\beta q^{5}-q^{9}+6q^{11}-4\beta q^{13}+\cdots\)
392.2.a.h	\(2\)	\(3.130\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(q+\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}-\beta q^{13}+\cdots\)
392.2.b.a	\(2\)	\(3.130\)	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)	None	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\beta q^{2}+(-2+\beta )q^{4}+(2+\beta )q^{8}+3q^{9}+\cdots\)
392.2.b.b	\(2\)	\(3.130\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta q^{2}-\beta q^{3}-2q^{4}+\beta q^{5}+2q^{6}+\cdots\)
392.2.b.c	\(4\)	\(3.130\)	4.0.2312.1	None	None	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
392.2.b.d	\(4\)	\(3.130\)	4.0.7168.1	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
392.2.b.e	\(6\)	\(3.130\)	6.0.1142512.1	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{4}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
392.2.b.f	\(6\)	\(3.130\)	6.0.1142512.1	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{4}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
392.2.b.g	\(12\)	\(3.130\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{4}q^{2}-\beta _{9}q^{3}-\beta _{1}q^{4}+(\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
392.2.e.a	\(4\)	\(3.130\)	4.0.2048.2	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}-\beta _{1}q^{6}-2\beta _{2}q^{8}+\cdots\)
392.2.e.b	\(4\)	\(3.130\)	4.0.2048.2	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{3})q^{6}+\cdots\)
392.2.e.c	\(8\)	\(3.130\)	8.0.339738624.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots\)
392.2.e.d	\(8\)	\(3.130\)	8.0.\(\cdots\).10	None	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+(1-\beta _{5})q^{2}-\beta _{2}q^{3}+(\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
392.2.e.e	\(12\)	\(3.130\)	12.0.\(\cdots\).2	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}-\beta _{9}q^{5}+\cdots\)
392.2.i.a	\(2\)	\(3.130\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-2\)	\(4\)	\(0\)		\(q+(-2+2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
392.2.i.b	\(2\)	\(3.130\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-1\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
392.2.i.c	\(2\)	\(3.130\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
392.2.i.d	\(2\)	\(3.130\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
392.2.i.e	\(2\)	\(3.130\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(2\)	\(-4\)	\(0\)		\(q+(2-2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}-8q^{15}+\cdots\)
392.2.i.f	\(2\)	\(3.130\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(3\)	\(-1\)	\(0\)		\(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
392.2.i.g	\(4\)	\(3.130\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)
392.2.i.h	\(4\)	\(3.130\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots\)
392.2.m.a	\(4\)	\(3.130\)	\(\Q(\sqrt{-3}, \sqrt{-7})\)	\(\Q(\sqrt{-7}) \)	None	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{8}+\cdots\)
392.2.m.b	\(8\)	\(3.130\)	8.0.339738624.1	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{6}q^{2}+\beta _{3}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
392.2.m.c	\(8\)	\(3.130\)	8.0.339738624.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{5}-\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)
392.2.m.d	\(8\)	\(3.130\)	8.0.339738624.1	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{4})q^{4}+\cdots\)
392.2.m.e	\(8\)	\(3.130\)	8.0.339738624.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
392.2.m.f	\(8\)	\(3.130\)	\(\Q(\zeta_{24})\)	None	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+(1+\zeta_{24}-\zeta_{24}^{2})q^{2}+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{3}+\cdots\)
392.2.m.g	\(12\)	\(3.130\)	12.0.\(\cdots\).2	None	None	\(0\)	\(6\)	\(0\)	\(0\)		\(q+(\beta _{1}-\beta _{8})q^{2}+(1+\beta _{10})q^{3}+(\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
392.2.m.h	\(16\)	\(3.130\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(\beta _{5}+\beta _{14})q^{2}-\beta _{15}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)
392.2.p.a	\(4\)	\(3.130\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
392.2.p.b	\(4\)	\(3.130\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
392.2.p.c	\(4\)	\(3.130\)	\(\Q(\sqrt{-3}, \sqrt{-7})\)	\(\Q(\sqrt{-7}) \)	None	\(1\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots\)
392.2.p.d	\(8\)	\(3.130\)	8.0.\(\cdots\).10	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{5}q^{2}-\beta _{6}q^{3}+(-2+2\beta _{2})q^{4}+\cdots\)
392.2.p.e	\(8\)	\(3.130\)	8.0.432972864.2	None	None	\(1\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}-\beta _{6})q^{2}+(\beta _{5}+\beta _{6})q^{3}+\beta _{5}q^{4}+\cdots\)
392.2.p.f	\(8\)	\(3.130\)	8.0.432972864.2	None	None	\(1\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}-\beta _{6})q^{2}+(-\beta _{5}-\beta _{6})q^{3}+\cdots\)
392.2.p.g	\(12\)	\(3.130\)	12.0.\(\cdots\).1	None	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots\)
392.2.p.h	\(24\)	\(3.130\)		None	None	\(2\)	\(0\)	\(0\)	\(0\)
392.2.q.a	\(42\)	\(3.130\)		None	None	\(0\)	\(-7\)	\(-2\)	\(1\)

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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.