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 165 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
2736.1.b.a	$4$	$1.365$	$\Q(\zeta_{8})$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$0$	$0$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
2736.1.b.b	$8$	$1.365$	$\Q(\zeta_{24})$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{6}q^{7}+\cdots$
2736.1.o.a	$1$	$1.365$	$\Q$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{57}) $	$0$	$0$	$0$	$2$		$q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots$
2736.1.o.b	$1$	$1.365$	$\Q$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$1$	$1$		$q+q^{5}+q^{7}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots$
2736.1.o.c	$2$	$1.365$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$0$	$-2$		$q-\beta q^{5}-q^{7}-\beta q^{11}+\beta q^{17}+q^{19}+\cdots$
2736.1.bk.a	$2$	$1.365$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}-q^{19}+\cdots$
2736.1.bk.b	$2$	$1.365$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots$
2736.1.bs.a	$4$	$1.365$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$-2$	$2$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{7}+\cdots$
2736.1.cd.a	$2$	$1.365$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-2$		$q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots$
2736.1.fg.a	$6$	$1.365$	$\Q(\zeta_{18})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots$
2736.1.ga.a	$6$	$1.365$	$\Q(\zeta_{18})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+(\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots$
2736.1.ga.b	$6$	$1.365$	$\Q(\zeta_{18})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{18}^{7}-\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots$
2736.2.a.a	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-4$	$-4$	$-$	$q-4q^{5}-4q^{7}-4q^{11}-4q^{13}-6q^{17}+\cdots$
2736.2.a.b	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-4$	$0$	$-$	$q-4q^{5}-6q^{11}+2q^{13}-4q^{17}+q^{19}+\cdots$
2736.2.a.c	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-3$	$1$	$+$	$q-3q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots$
2736.2.a.d	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-2$	$0$	$-$	$q-2q^{5}-4q^{11}+2q^{13}+6q^{17}+q^{19}+\cdots$
2736.2.a.e	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-2$	$0$	$+$	$q-2q^{5}+2q^{13}-2q^{17}+q^{19}-q^{25}+\cdots$
2736.2.a.f	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-2$	$0$	$+$	$q-2q^{5}+2q^{11}-4q^{13}+q^{19}+8q^{23}+\cdots$
2736.2.a.g	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-2$	$0$	$-$	$q-2q^{5}+2q^{11}+2q^{13}-6q^{17}+q^{19}+\cdots$
2736.2.a.h	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-1$	$-3$	$-$	$q-q^{5}-3q^{7}-3q^{11}-6q^{13}-3q^{17}+\cdots$
2736.2.a.i	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$-1$	$3$	$-$	$q-q^{5}+3q^{7}-5q^{11}-2q^{13}+q^{17}+\cdots$
2736.2.a.j	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$0$	$-4$	$+$	$q-4q^{7}+4q^{11}+2q^{17}-q^{19}-2q^{23}+\cdots$
2736.2.a.k	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$0$	$-3$	$-$	$q-3q^{7}+2q^{11}+q^{13}+5q^{17}-q^{19}+\cdots$
2736.2.a.l	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$0$	$0$	$+$	$q-2q^{11}-2q^{13}+4q^{17}-q^{19}-2q^{23}+\cdots$
2736.2.a.m	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$0$	$0$	$+$	$q+2q^{11}-2q^{13}-4q^{17}-q^{19}+2q^{23}+\cdots$
2736.2.a.n	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$0$	$1$	$+$	$q+q^{7}-6q^{11}+5q^{13}-3q^{17}-q^{19}+\cdots$
2736.2.a.o	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$0$	$4$	$+$	$q+4q^{7}-4q^{13}-6q^{17}-q^{19}-6q^{23}+\cdots$
2736.2.a.p	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$1$	$3$	$+$	$q+q^{5}+3q^{7}-3q^{11}-4q^{13}-5q^{17}+\cdots$
2736.2.a.q	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$1$	$3$	$-$	$q+q^{5}+3q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots$
2736.2.a.r	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$2$	$0$	$+$	$q+2q^{5}-2q^{11}-4q^{13}+q^{19}-8q^{23}+\cdots$
2736.2.a.s	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$2$	$0$	$-$	$q+2q^{5}+6q^{13}+6q^{17}+q^{19}+4q^{23}+\cdots$
2736.2.a.t	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$3$	$-1$	$+$	$q+3q^{5}-q^{7}-5q^{11}-6q^{13}+5q^{17}+\cdots$
2736.2.a.u	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$3$	$3$	$-$	$q+3q^{5}+3q^{7}-q^{11}-2q^{13}+5q^{17}+\cdots$
2736.2.a.v	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$3$	$5$	$-$	$q+3q^{5}+5q^{7}+q^{11}+2q^{13}+q^{17}+\cdots$
2736.2.a.w	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$4$	$-3$	$-$	$q+4q^{5}-3q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots$
2736.2.a.x	$1$	$21.847$	$\Q$	None	None	$0$	$0$	$4$	$0$	$-$	$q+4q^{5}+6q^{11}+2q^{13}+4q^{17}+q^{19}+\cdots$
2736.2.a.y	$2$	$21.847$	$\Q(\sqrt{33}) $	None	None	$0$	$0$	$-3$	$-1$	$+$	$q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-1+\cdots)q^{11}+\cdots$
2736.2.a.z	$2$	$21.847$	$\Q(\sqrt{17}) $	None	None	$0$	$0$	$-1$	$-1$	$-$	$q-\beta q^{5}-\beta q^{7}+(4-\beta )q^{11}-2\beta q^{13}+\cdots$
2736.2.a.ba	$2$	$21.847$	$\Q(\sqrt{7}) $	None	None	$0$	$0$	$0$	$-6$	$+$	$q+\beta q^{5}-3q^{7}-\beta q^{11}+2q^{13}-3\beta q^{17}+\cdots$
2736.2.a.bb	$2$	$21.847$	$\Q(\sqrt{41}) $	None	None	$0$	$0$	$1$	$3$	$-$	$q+\beta q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots$
2736.2.a.bc	$3$	$21.847$	3.3.892.1	None	None	$0$	$0$	$-2$	$2$	$-$	$q+(-1+\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots$
2736.2.a.bd	$3$	$21.847$	3.3.961.1	None	None	$0$	$0$	$-1$	$-4$	$+$	$q-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
2736.2.a.be	$3$	$21.847$	3.3.892.1	None	None	$0$	$0$	$2$	$2$	$-$	$q+(1-\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{11}+\cdots$
2736.2.a.bf	$4$	$21.847$	4.4.13068.1	None	None	$0$	$0$	$0$	$-2$	$-$	$q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots$
2736.2.d.a	$12$	$21.847$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+(-\beta _{4}+\beta _{9})q^{5}+(\beta _{1}+\beta _{3}-\beta _{8})q^{7}+\cdots$
2736.2.d.b	$24$	$21.847$		None	None	$0$	$0$	$0$	$0$
2736.2.f.a	$2$	$21.847$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$0$	$-4$		$q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots$
2736.2.f.b	$2$	$21.847$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$0$	$-4$		$q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots$
2736.2.f.c	$2$	$21.847$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$0$	$-4$		$q+\beta q^{5}-2q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots$
2736.2.f.d	$2$	$21.847$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$0$	$-4$		$q+\beta q^{5}-2q^{7}+3\beta q^{11}+2\beta q^{13}+\cdots$

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Elliptic curves over $\Q$
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Higher genus families
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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
2736.1.b.a	\(4\)	\(1.365\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
2736.1.b.b	\(8\)	\(1.365\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
2736.1.o.a	\(1\)	\(1.365\)	\(\Q\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{57}) \)	\(0\)	\(0\)	\(0\)	\(2\)		\(q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots\)
2736.1.o.b	\(1\)	\(1.365\)	\(\Q\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(1\)	\(1\)		\(q+q^{5}+q^{7}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots\)
2736.1.o.c	\(2\)	\(1.365\)	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-\beta q^{5}-q^{7}-\beta q^{11}+\beta q^{17}+q^{19}+\cdots\)
2736.1.bk.a	\(2\)	\(1.365\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}-q^{19}+\cdots\)
2736.1.bk.b	\(2\)	\(1.365\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots\)
2736.1.bs.a	\(4\)	\(1.365\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(-2\)	\(2\)		\(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{7}+\cdots\)
2736.1.cd.a	\(2\)	\(1.365\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots\)
2736.1.fg.a	\(6\)	\(1.365\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)
2736.1.ga.a	\(6\)	\(1.365\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)
2736.1.ga.b	\(6\)	\(1.365\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{18}^{7}-\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots\)
2736.2.a.a	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-4\)	\(-4\)	\(-\)	\(q-4q^{5}-4q^{7}-4q^{11}-4q^{13}-6q^{17}+\cdots\)
2736.2.a.b	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(q-4q^{5}-6q^{11}+2q^{13}-4q^{17}+q^{19}+\cdots\)
2736.2.a.c	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-3\)	\(1\)	\(+\)	\(q-3q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.d	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(q-2q^{5}-4q^{11}+2q^{13}+6q^{17}+q^{19}+\cdots\)
2736.2.a.e	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(+\)	\(q-2q^{5}+2q^{13}-2q^{17}+q^{19}-q^{25}+\cdots\)
2736.2.a.f	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(+\)	\(q-2q^{5}+2q^{11}-4q^{13}+q^{19}+8q^{23}+\cdots\)
2736.2.a.g	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(q-2q^{5}+2q^{11}+2q^{13}-6q^{17}+q^{19}+\cdots\)
2736.2.a.h	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(-3\)	\(-\)	\(q-q^{5}-3q^{7}-3q^{11}-6q^{13}-3q^{17}+\cdots\)
2736.2.a.i	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(3\)	\(-\)	\(q-q^{5}+3q^{7}-5q^{11}-2q^{13}+q^{17}+\cdots\)
2736.2.a.j	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(+\)	\(q-4q^{7}+4q^{11}+2q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.k	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-3\)	\(-\)	\(q-3q^{7}+2q^{11}+q^{13}+5q^{17}-q^{19}+\cdots\)
2736.2.a.l	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q-2q^{11}-2q^{13}+4q^{17}-q^{19}-2q^{23}+\cdots\)
2736.2.a.m	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q+2q^{11}-2q^{13}-4q^{17}-q^{19}+2q^{23}+\cdots\)
2736.2.a.n	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(1\)	\(+\)	\(q+q^{7}-6q^{11}+5q^{13}-3q^{17}-q^{19}+\cdots\)
2736.2.a.o	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	\(+\)	\(q+4q^{7}-4q^{13}-6q^{17}-q^{19}-6q^{23}+\cdots\)
2736.2.a.p	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(3\)	\(+\)	\(q+q^{5}+3q^{7}-3q^{11}-4q^{13}-5q^{17}+\cdots\)
2736.2.a.q	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(3\)	\(-\)	\(q+q^{5}+3q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots\)
2736.2.a.r	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	\(+\)	\(q+2q^{5}-2q^{11}-4q^{13}+q^{19}-8q^{23}+\cdots\)
2736.2.a.s	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	\(-\)	\(q+2q^{5}+6q^{13}+6q^{17}+q^{19}+4q^{23}+\cdots\)
2736.2.a.t	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(3\)	\(-1\)	\(+\)	\(q+3q^{5}-q^{7}-5q^{11}-6q^{13}+5q^{17}+\cdots\)
2736.2.a.u	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(3\)	\(3\)	\(-\)	\(q+3q^{5}+3q^{7}-q^{11}-2q^{13}+5q^{17}+\cdots\)
2736.2.a.v	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(3\)	\(5\)	\(-\)	\(q+3q^{5}+5q^{7}+q^{11}+2q^{13}+q^{17}+\cdots\)
2736.2.a.w	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(4\)	\(-3\)	\(-\)	\(q+4q^{5}-3q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots\)
2736.2.a.x	\(1\)	\(21.847\)	\(\Q\)	None	None	\(0\)	\(0\)	\(4\)	\(0\)	\(-\)	\(q+4q^{5}+6q^{11}+2q^{13}+4q^{17}+q^{19}+\cdots\)
2736.2.a.y	\(2\)	\(21.847\)	\(\Q(\sqrt{33}) \)	None	None	\(0\)	\(0\)	\(-3\)	\(-1\)	\(+\)	\(q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-1+\cdots)q^{11}+\cdots\)
2736.2.a.z	\(2\)	\(21.847\)	\(\Q(\sqrt{17}) \)	None	None	\(0\)	\(0\)	\(-1\)	\(-1\)	\(-\)	\(q-\beta q^{5}-\beta q^{7}+(4-\beta )q^{11}-2\beta q^{13}+\cdots\)
2736.2.a.ba	\(2\)	\(21.847\)	\(\Q(\sqrt{7}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-6\)	\(+\)	\(q+\beta q^{5}-3q^{7}-\beta q^{11}+2q^{13}-3\beta q^{17}+\cdots\)
2736.2.a.bb	\(2\)	\(21.847\)	\(\Q(\sqrt{41}) \)	None	None	\(0\)	\(0\)	\(1\)	\(3\)	\(-\)	\(q+\beta q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots\)
2736.2.a.bc	\(3\)	\(21.847\)	3.3.892.1	None	None	\(0\)	\(0\)	\(-2\)	\(2\)	\(-\)	\(q+(-1+\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2736.2.a.bd	\(3\)	\(21.847\)	3.3.961.1	None	None	\(0\)	\(0\)	\(-1\)	\(-4\)	\(+\)	\(q-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
2736.2.a.be	\(3\)	\(21.847\)	3.3.892.1	None	None	\(0\)	\(0\)	\(2\)	\(2\)	\(-\)	\(q+(1-\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{11}+\cdots\)
2736.2.a.bf	\(4\)	\(21.847\)	4.4.13068.1	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots\)
2736.2.d.a	\(12\)	\(21.847\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{4}+\beta _{9})q^{5}+(\beta _{1}+\beta _{3}-\beta _{8})q^{7}+\cdots\)
2736.2.d.b	\(24\)	\(21.847\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
2736.2.f.a	\(2\)	\(21.847\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.b	\(2\)	\(21.847\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots\)
2736.2.f.c	\(2\)	\(21.847\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta q^{5}-2q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots\)
2736.2.f.d	\(2\)	\(21.847\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta q^{5}-2q^{7}+3\beta q^{11}+2\beta q^{13}+\cdots\)

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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.