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 (displaying matches 1-50 of 309) Next

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
350.2.a.a	$1$	$2.795$	$\Q$	None	$-1$	$-1$	$0$	$-1$	$+$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
350.2.a.b	$1$	$2.795$	$\Q$	None	$-1$	$0$	$0$	$1$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots$
350.2.a.c	$1$	$2.795$	$\Q$	None	$-1$	$3$	$0$	$1$	$-$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots$
350.2.a.d	$1$	$2.795$	$\Q$	None	$1$	$-3$	$0$	$-1$	$+$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}-q^{7}+q^{8}+\cdots$
350.2.a.e	$1$	$2.795$	$\Q$	None	$1$	$1$	$0$	$1$	$-$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
350.2.a.f	$1$	$2.795$	$\Q$	None	$1$	$2$	$0$	$-1$	$-$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots$
350.2.a.g	$2$	$2.795$	$\Q(\sqrt{6}) $	None	$-2$	$0$	$0$	$-2$	$-$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots$
350.2.a.h	$2$	$2.795$	$\Q(\sqrt{6}) $	None	$2$	$0$	$0$	$2$	$-$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots$
350.2.c.a	$2$	$2.795$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{7}+\cdots$
350.2.c.b	$2$	$2.795$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots$
350.2.c.c	$2$	$2.795$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots$
350.2.c.d	$2$	$2.795$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$		$q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots$
350.2.e.a	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$-1$	$-2$	$0$	$-5$		$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.e.b	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$-1$	$-2$	$0$	$4$		$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.e.c	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$0$	$-4$		$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots$
350.2.e.d	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$-1$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots$
350.2.e.e	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$-1$	$1$	$0$	$1$		$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.e.f	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$-1$	$3$	$0$	$5$		$q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.e.g	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$1$	$-3$	$0$	$-5$		$q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.e.h	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$1$	$-2$	$0$	$4$		$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.e.i	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$1$	$0$	$0$	$-1$		$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots$
350.2.e.j	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$1$	$0$	$0$	$4$		$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(3-2\zeta_{6})q^{7}+\cdots$
350.2.e.k	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$1$	$2$	$0$	$5$		$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.e.l	$2$	$2.795$	$\Q(\sqrt{-3}) $	None	$1$	$3$	$0$	$-1$		$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
350.2.g.a	$8$	$2.795$	$\Q(\zeta_{16})$	None	$0$	$0$	$0$	$8$		$q+\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{3}q^{4}+(\zeta_{16}^{4}+\cdots)q^{6}+\cdots$
350.2.g.b	$16$	$2.795$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+\beta _{3}q^{3}+\beta _{10}q^{4}+\beta _{15}q^{6}+\cdots$
350.2.h.a	$8$	$2.795$	$\Q(\zeta_{15})$	None	$-2$	$3$	$0$	$8$		$q+\zeta_{15}^{4}q^{2}+(-\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{6}+\cdots)q^{3}+\cdots$
350.2.h.b	$12$	$2.795$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$3$	$1$	$-5$	$-12$		$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}-\beta _{3}q^{4}+\cdots$
350.2.h.c	$16$	$2.795$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$-4$	$1$	$-4$	$-16$		$q+\beta _{6}q^{2}-\beta _{10}q^{3}-\beta _{1}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
350.2.h.d	$20$	$2.795$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$5$	$3$	$-5$	$20$		$q+\beta _{14}q^{2}+\beta _{1}q^{3}+\beta _{6}q^{4}+(\beta _{10}+\beta _{13}+\cdots)q^{5}+\cdots$
350.2.j.a	$4$	$2.795$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots$
350.2.j.b	$4$	$2.795$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
350.2.j.c	$4$	$2.795$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots$
350.2.j.d	$4$	$2.795$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
350.2.j.e	$4$	$2.795$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
350.2.j.f	$4$	$2.795$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
350.2.m.a	$24$	$2.795$		None	$0$	$0$	$10$	$0$
350.2.m.b	$40$	$2.795$		None	$0$	$0$	$6$	$0$
350.2.o.a	$8$	$2.795$	$\Q(\zeta_{24})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}-\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots$
350.2.o.b	$8$	$2.795$	$\Q(\zeta_{24})$	None	$0$	$0$	$0$	$0$		$q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots$
350.2.o.c	$16$	$2.795$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$0$	$0$	$-8$		$q+\beta _{13}q^{2}+(\beta _{3}-\beta _{7}-\beta _{15})q^{3}+(\beta _{11}+\cdots)q^{4}+\cdots$
350.2.o.d	$16$	$2.795$	16.0.$\cdots$.1	None	$0$	$0$	$0$	$0$		$q+(-\beta _{5}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots$
350.2.q.a	$8$	$2.795$	$\Q(\zeta_{15})$	None	$-1$	$-3$	$0$	$-4$		$q-\zeta_{15}q^{2}+(1-\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\cdots)q^{3}+\cdots$
350.2.q.b	$72$	$2.795$		None	$-9$	$1$	$0$	$8$
350.2.q.c	$80$	$2.795$		None	$10$	$2$	$-2$	$4$
350.2.r.a	$160$	$2.795$		None	$0$	$0$	$0$	$8$
350.2.u.a	$160$	$2.795$		None	$0$	$0$	$-2$	$0$
350.2.x.a	$320$	$2.795$		None	$0$	$0$	$12$	$-8$
350.3.b.a	$4$	$9.537$	4.0.7168.1	None	$0$	$0$	$0$	$-12$		$q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots$
350.3.b.b	$4$	$9.537$	4.0.7168.1	None	$0$	$0$	$0$	$12$		$q-\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$

Introduction	Features
Universe	News

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
350.2.a.a	\(1\)	\(2.795\)	\(\Q\)	None	\(-1\)	\(-1\)	\(0\)	\(-1\)	\(+\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
350.2.a.b	\(1\)	\(2.795\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
350.2.a.c	\(1\)	\(2.795\)	\(\Q\)	None	\(-1\)	\(3\)	\(0\)	\(1\)	\(-\)	\(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
350.2.a.d	\(1\)	\(2.795\)	\(\Q\)	None	\(1\)	\(-3\)	\(0\)	\(-1\)	\(+\)	\(q+q^{2}-3q^{3}+q^{4}-3q^{6}-q^{7}+q^{8}+\cdots\)
350.2.a.e	\(1\)	\(2.795\)	\(\Q\)	None	\(1\)	\(1\)	\(0\)	\(1\)	\(-\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
350.2.a.f	\(1\)	\(2.795\)	\(\Q\)	None	\(1\)	\(2\)	\(0\)	\(-1\)	\(-\)	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
350.2.a.g	\(2\)	\(2.795\)	\(\Q(\sqrt{6}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
350.2.a.h	\(2\)	\(2.795\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
350.2.c.a	\(2\)	\(2.795\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{7}+\cdots\)
350.2.c.b	\(2\)	\(2.795\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
350.2.c.c	\(2\)	\(2.795\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots\)
350.2.c.d	\(2\)	\(2.795\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
350.2.e.a	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(-2\)	\(0\)	\(-5\)		\(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.b	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(-2\)	\(0\)	\(4\)		\(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.c	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(0\)	\(-4\)		\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
350.2.e.d	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(0\)	\(0\)	\(1\)		\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
350.2.e.e	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(1\)	\(0\)	\(1\)		\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.f	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(3\)	\(0\)	\(5\)		\(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.g	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-3\)	\(0\)	\(-5\)		\(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.h	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(-2\)	\(0\)	\(4\)		\(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.i	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(0\)	\(0\)	\(-1\)		\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
350.2.e.j	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(0\)	\(0\)	\(4\)		\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
350.2.e.k	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(2\)	\(0\)	\(5\)		\(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.l	\(2\)	\(2.795\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(3\)	\(0\)	\(-1\)		\(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.g.a	\(8\)	\(2.795\)	\(\Q(\zeta_{16})\)	None	\(0\)	\(0\)	\(0\)	\(8\)		\(q+\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{3}q^{4}+(\zeta_{16}^{4}+\cdots)q^{6}+\cdots\)
350.2.g.b	\(16\)	\(2.795\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+\beta _{3}q^{3}+\beta _{10}q^{4}+\beta _{15}q^{6}+\cdots\)
350.2.h.a	\(8\)	\(2.795\)	\(\Q(\zeta_{15})\)	None	\(-2\)	\(3\)	\(0\)	\(8\)		\(q+\zeta_{15}^{4}q^{2}+(-\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{6}+\cdots)q^{3}+\cdots\)
350.2.h.b	\(12\)	\(2.795\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(3\)	\(1\)	\(-5\)	\(-12\)		\(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}-\beta _{3}q^{4}+\cdots\)
350.2.h.c	\(16\)	\(2.795\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(-4\)	\(1\)	\(-4\)	\(-16\)		\(q+\beta _{6}q^{2}-\beta _{10}q^{3}-\beta _{1}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
350.2.h.d	\(20\)	\(2.795\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(5\)	\(3\)	\(-5\)	\(20\)		\(q+\beta _{14}q^{2}+\beta _{1}q^{3}+\beta _{6}q^{4}+(\beta _{10}+\beta _{13}+\cdots)q^{5}+\cdots\)
350.2.j.a	\(4\)	\(2.795\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
350.2.j.b	\(4\)	\(2.795\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.c	\(4\)	\(2.795\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots\)
350.2.j.d	\(4\)	\(2.795\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.e	\(4\)	\(2.795\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.f	\(4\)	\(2.795\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.m.a	\(24\)	\(2.795\)		None	\(0\)	\(0\)	\(10\)	\(0\)
350.2.m.b	\(40\)	\(2.795\)		None	\(0\)	\(0\)	\(6\)	\(0\)
350.2.o.a	\(8\)	\(2.795\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}-\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
350.2.o.b	\(8\)	\(2.795\)	\(\Q(\zeta_{24})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
350.2.o.c	\(16\)	\(2.795\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\beta _{13}q^{2}+(\beta _{3}-\beta _{7}-\beta _{15})q^{3}+(\beta _{11}+\cdots)q^{4}+\cdots\)
350.2.o.d	\(16\)	\(2.795\)	16.0.\(\cdots\).1	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{5}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
350.2.q.a	\(8\)	\(2.795\)	\(\Q(\zeta_{15})\)	None	\(-1\)	\(-3\)	\(0\)	\(-4\)		\(q-\zeta_{15}q^{2}+(1-\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
350.2.q.b	\(72\)	\(2.795\)		None	\(-9\)	\(1\)	\(0\)	\(8\)
350.2.q.c	\(80\)	\(2.795\)		None	\(10\)	\(2\)	\(-2\)	\(4\)
350.2.r.a	\(160\)	\(2.795\)		None	\(0\)	\(0\)	\(0\)	\(8\)
350.2.u.a	\(160\)	\(2.795\)		None	\(0\)	\(0\)	\(-2\)	\(0\)
350.2.x.a	\(320\)	\(2.795\)		None	\(0\)	\(0\)	\(12\)	\(-8\)
350.3.b.a	\(4\)	\(9.537\)	4.0.7168.1	None	\(0\)	\(0\)	\(0\)	\(-12\)		\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots\)
350.3.b.b	\(4\)	\(9.537\)	4.0.7168.1	None	\(0\)	\(0\)	\(0\)	\(12\)		\(q-\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)

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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.