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 77 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
2808.1.b.a	$1$	$1.401$	$\Q$	$\Q(\sqrt{-78}) $	None	$-1$	$0$	$0$	$0$		$q-q^{2}+q^{4}-q^{8}-q^{13}+q^{16}+q^{19}+\cdots$
2808.1.b.b	$1$	$1.401$	$\Q$	$\Q(\sqrt{-78}) $	None	$-1$	$0$	$0$	$0$		$q-q^{2}+q^{4}-q^{8}+q^{13}+q^{16}-q^{19}+\cdots$
2808.1.b.c	$1$	$1.401$	$\Q$	$\Q(\sqrt{-78}) $	None	$1$	$0$	$0$	$0$		$q+q^{2}+q^{4}+q^{8}-q^{13}+q^{16}+q^{19}+\cdots$
2808.1.b.d	$1$	$1.401$	$\Q$	$\Q(\sqrt{-78}) $	None	$1$	$0$	$0$	$0$		$q+q^{2}+q^{4}+q^{8}+q^{13}+q^{16}-q^{19}+\cdots$
2808.1.b.e	$8$	$1.401$	$\Q(\zeta_{24})$	$\Q(\sqrt{-39}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2808.1.o.a	$8$	$1.401$	$\Q(\zeta_{24})$	$\Q(\sqrt{-39}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
2808.1.z.a	$4$	$1.401$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$-4$	$0$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+\zeta_{8}^{2})q^{5}+\cdots$
2808.1.z.b	$4$	$1.401$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$4$	$0$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots$
2808.1.bf.a	$4$	$1.401$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$2$		$q+\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{11}+(1-\beta _{2}+\cdots)q^{13}+\cdots$
2808.1.bs.a	$6$	$1.401$	$\Q(\zeta_{18})$	$\Q(\sqrt{-26}) $	None	$-3$	$0$	$0$	$0$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
2808.1.bs.b	$6$	$1.401$	$\Q(\zeta_{18})$	$\Q(\sqrt{-26}) $	None	$3$	$0$	$0$	$0$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
2808.1.dd.a	$8$	$1.401$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+\zeta_{24}^{3}q^{8}+\cdots$
2808.1.dp.a	$4$	$1.401$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$-2$	$0$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{13}+\cdots$
2808.1.dp.b	$4$	$1.401$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$-2$		$q+(\zeta_{12}+\zeta_{12}^{4})q^{7}+(-\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{11}+\cdots$
2808.1.fi.a	$18$	$1.401$	$\Q(\zeta_{54})$	$\Q(\sqrt{-26}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots$
2808.1.fi.b	$18$	$1.401$	$\Q(\zeta_{54})$	$\Q(\sqrt{-26}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots$
2808.2.a.a	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$-3$	$2$	$+$	$q-3q^{5}+2q^{7}+4q^{11}-q^{13}-6q^{17}+\cdots$
2808.2.a.b	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$-2$	$-4$	$-$	$q-2q^{5}-4q^{7}+2q^{11}-q^{13}+q^{19}+\cdots$
2808.2.a.c	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$-2$	$-3$	$-$	$q-2q^{5}-3q^{7}+q^{11}-q^{13}-4q^{17}+\cdots$
2808.2.a.d	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$-1$	$-2$	$+$	$q-q^{5}-2q^{7}+q^{13}+4q^{17}+2q^{19}+\cdots$
2808.2.a.e	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$-1$	$2$	$-$	$q-q^{5}+2q^{7}+4q^{11}-q^{13}+6q^{17}+\cdots$
2808.2.a.f	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$-1$	$3$	$-$	$q-q^{5}+3q^{7}+3q^{11}+q^{13}+2q^{17}+\cdots$
2808.2.a.g	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$0$	$-3$	$-$	$q-3q^{7}-3q^{11}-q^{13}+2q^{17}+6q^{19}+\cdots$
2808.2.a.h	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$0$	$-3$	$+$	$q-3q^{7}+3q^{11}-q^{13}-2q^{17}+6q^{19}+\cdots$
2808.2.a.i	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$1$	$-2$	$-$	$q+q^{5}-2q^{7}+q^{13}-4q^{17}+2q^{19}+\cdots$
2808.2.a.j	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$1$	$2$	$+$	$q+q^{5}+2q^{7}-4q^{11}-q^{13}-6q^{17}+\cdots$
2808.2.a.k	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$1$	$3$	$-$	$q+q^{5}+3q^{7}-3q^{11}+q^{13}-2q^{17}+\cdots$
2808.2.a.l	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$2$	$-4$	$-$	$q+2q^{5}-4q^{7}-2q^{11}-q^{13}+q^{19}+\cdots$
2808.2.a.m	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$2$	$-3$	$+$	$q+2q^{5}-3q^{7}-q^{11}-q^{13}+4q^{17}+\cdots$
2808.2.a.n	$1$	$22.422$	$\Q$	None	None	$0$	$0$	$3$	$2$	$-$	$q+3q^{5}+2q^{7}-4q^{11}-q^{13}+6q^{17}+\cdots$
2808.2.a.o	$2$	$22.422$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$-3$	$-4$	$+$	$q+(-1-\beta )q^{5}+(-1-2\beta )q^{7}+(2+\beta )q^{11}+\cdots$
2808.2.a.p	$2$	$22.422$	$\Q(\sqrt{17}) $	None	None	$0$	$0$	$-3$	$5$	$+$	$q+(-1-\beta )q^{5}+(2+\beta )q^{7}+(-4+\beta )q^{11}+\cdots$
2808.2.a.q	$2$	$22.422$	$\Q(\sqrt{6}) $	None	None	$0$	$0$	$-2$	$4$	$+$	$q+(-1+\beta )q^{5}+2q^{7}-2q^{11}-q^{13}+\cdots$
2808.2.a.r	$2$	$22.422$	$\Q(\sqrt{37}) $	None	None	$0$	$0$	$-1$	$6$	$-$	$q-\beta q^{5}+3q^{7}+(-3-\beta )q^{11}-q^{13}+\cdots$
2808.2.a.s	$2$	$22.422$	$\Q(\sqrt{37}) $	None	None	$0$	$0$	$1$	$6$	$-$	$q+\beta q^{5}+3q^{7}+(3+\beta )q^{11}-q^{13}+\cdots$
2808.2.a.t	$2$	$22.422$	$\Q(\sqrt{6}) $	None	None	$0$	$0$	$2$	$4$	$-$	$q+(1+\beta )q^{5}+2q^{7}+2q^{11}-q^{13}+\cdots$
2808.2.a.u	$2$	$22.422$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$3$	$-4$	$+$	$q+(1+\beta )q^{5}+(-1-2\beta )q^{7}+(-2-\beta )q^{11}+\cdots$
2808.2.a.v	$2$	$22.422$	$\Q(\sqrt{17}) $	None	None	$0$	$0$	$3$	$5$	$-$	$q+(1+\beta )q^{5}+(2+\beta )q^{7}+(4-\beta )q^{11}+\cdots$
2808.2.a.w	$3$	$22.422$	3.3.2213.1	None	None	$0$	$0$	$-5$	$0$	$-$	$q+(-2+\beta _{1})q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{11}+\cdots$
2808.2.a.x	$3$	$22.422$	3.3.1101.1	None	None	$0$	$0$	$-2$	$-3$	$+$	$q+(-1+\beta _{1})q^{5}-q^{7}+(2-\beta _{1}+\beta _{2})q^{11}+\cdots$
2808.2.a.y	$3$	$22.422$	3.3.1016.1	None	None	$0$	$0$	$-2$	$-1$	$+$	$q+(-1+\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots$
2808.2.a.z	$3$	$22.422$	3.3.1101.1	None	None	$0$	$0$	$2$	$-3$	$+$	$q+(1-\beta _{1})q^{5}-q^{7}+(-2+\beta _{1}-\beta _{2})q^{11}+\cdots$
2808.2.a.ba	$3$	$22.422$	3.3.1016.1	None	None	$0$	$0$	$2$	$-1$	$-$	$q+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
2808.2.a.bb	$3$	$22.422$	3.3.2213.1	None	None	$0$	$0$	$5$	$0$	$-$	$q+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+(-2-\beta _{1}-\beta _{2})q^{11}+\cdots$
2808.2.c.a	$2$	$22.422$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$0$		$q+3iq^{5}+4iq^{7}-4iq^{11}+(-3-2i)q^{13}+\cdots$
2808.2.c.b	$2$	$22.422$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$0$		$q+3iq^{5}-4iq^{7}-4iq^{11}+(-3+2i)q^{13}+\cdots$
2808.2.c.c	$4$	$22.422$	$\Q(i, \sqrt{17})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
2808.2.c.d	$4$	$22.422$	$\Q(i, \sqrt{17})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
2808.2.c.e	$14$	$22.422$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{7}q^{11}-\beta _{13}q^{13}+\cdots$
2808.2.c.f	$14$	$22.422$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{5}+\beta _{4}q^{7}+\beta _{7}q^{11}-\beta _{10}q^{13}+\cdots$

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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
2808.1.b.a	\(1\)	\(1.401\)	\(\Q\)	\(\Q(\sqrt{-78}) \)	None	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}+q^{4}-q^{8}-q^{13}+q^{16}+q^{19}+\cdots\)
2808.1.b.b	\(1\)	\(1.401\)	\(\Q\)	\(\Q(\sqrt{-78}) \)	None	\(-1\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}+q^{4}-q^{8}+q^{13}+q^{16}-q^{19}+\cdots\)
2808.1.b.c	\(1\)	\(1.401\)	\(\Q\)	\(\Q(\sqrt{-78}) \)	None	\(1\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}+q^{8}-q^{13}+q^{16}+q^{19}+\cdots\)
2808.1.b.d	\(1\)	\(1.401\)	\(\Q\)	\(\Q(\sqrt{-78}) \)	None	\(1\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}+q^{4}+q^{8}+q^{13}+q^{16}-q^{19}+\cdots\)
2808.1.b.e	\(8\)	\(1.401\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-39}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)
2808.1.o.a	\(8\)	\(1.401\)	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-39}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)
2808.1.z.a	\(4\)	\(1.401\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+\zeta_{8}^{2})q^{5}+\cdots\)
2808.1.z.b	\(4\)	\(1.401\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots\)
2808.1.bf.a	\(4\)	\(1.401\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{11}+(1-\beta _{2}+\cdots)q^{13}+\cdots\)
2808.1.bs.a	\(6\)	\(1.401\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-26}) \)	None	\(-3\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
2808.1.bs.b	\(6\)	\(1.401\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-26}) \)	None	\(3\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots\)
2808.1.dd.a	\(8\)	\(1.401\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+\zeta_{24}^{3}q^{8}+\cdots\)
2808.1.dp.a	\(4\)	\(1.401\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{13}+\cdots\)
2808.1.dp.b	\(4\)	\(1.401\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+(\zeta_{12}+\zeta_{12}^{4})q^{7}+(-\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{11}+\cdots\)
2808.1.fi.a	\(18\)	\(1.401\)	\(\Q(\zeta_{54})\)	\(\Q(\sqrt{-26}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots\)
2808.1.fi.b	\(18\)	\(1.401\)	\(\Q(\zeta_{54})\)	\(\Q(\sqrt{-26}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{54}^{24}q^{2}-\zeta_{54}^{7}q^{3}-\zeta_{54}^{21}q^{4}+\cdots\)
2808.2.a.a	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-3\)	\(2\)	\(+\)	\(q-3q^{5}+2q^{7}+4q^{11}-q^{13}-6q^{17}+\cdots\)
2808.2.a.b	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(-4\)	\(-\)	\(q-2q^{5}-4q^{7}+2q^{11}-q^{13}+q^{19}+\cdots\)
2808.2.a.c	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-2\)	\(-3\)	\(-\)	\(q-2q^{5}-3q^{7}+q^{11}-q^{13}-4q^{17}+\cdots\)
2808.2.a.d	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(-2\)	\(+\)	\(q-q^{5}-2q^{7}+q^{13}+4q^{17}+2q^{19}+\cdots\)
2808.2.a.e	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(-\)	\(q-q^{5}+2q^{7}+4q^{11}-q^{13}+6q^{17}+\cdots\)
2808.2.a.f	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(3\)	\(-\)	\(q-q^{5}+3q^{7}+3q^{11}+q^{13}+2q^{17}+\cdots\)
2808.2.a.g	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-3\)	\(-\)	\(q-3q^{7}-3q^{11}-q^{13}+2q^{17}+6q^{19}+\cdots\)
2808.2.a.h	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(0\)	\(-3\)	\(+\)	\(q-3q^{7}+3q^{11}-q^{13}-2q^{17}+6q^{19}+\cdots\)
2808.2.a.i	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(-2\)	\(-\)	\(q+q^{5}-2q^{7}+q^{13}-4q^{17}+2q^{19}+\cdots\)
2808.2.a.j	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(2\)	\(+\)	\(q+q^{5}+2q^{7}-4q^{11}-q^{13}-6q^{17}+\cdots\)
2808.2.a.k	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(3\)	\(-\)	\(q+q^{5}+3q^{7}-3q^{11}+q^{13}-2q^{17}+\cdots\)
2808.2.a.l	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(-4\)	\(-\)	\(q+2q^{5}-4q^{7}-2q^{11}-q^{13}+q^{19}+\cdots\)
2808.2.a.m	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(2\)	\(-3\)	\(+\)	\(q+2q^{5}-3q^{7}-q^{11}-q^{13}+4q^{17}+\cdots\)
2808.2.a.n	\(1\)	\(22.422\)	\(\Q\)	None	None	\(0\)	\(0\)	\(3\)	\(2\)	\(-\)	\(q+3q^{5}+2q^{7}-4q^{11}-q^{13}+6q^{17}+\cdots\)
2808.2.a.o	\(2\)	\(22.422\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(-3\)	\(-4\)	\(+\)	\(q+(-1-\beta )q^{5}+(-1-2\beta )q^{7}+(2+\beta )q^{11}+\cdots\)
2808.2.a.p	\(2\)	\(22.422\)	\(\Q(\sqrt{17}) \)	None	None	\(0\)	\(0\)	\(-3\)	\(5\)	\(+\)	\(q+(-1-\beta )q^{5}+(2+\beta )q^{7}+(-4+\beta )q^{11}+\cdots\)
2808.2.a.q	\(2\)	\(22.422\)	\(\Q(\sqrt{6}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(4\)	\(+\)	\(q+(-1+\beta )q^{5}+2q^{7}-2q^{11}-q^{13}+\cdots\)
2808.2.a.r	\(2\)	\(22.422\)	\(\Q(\sqrt{37}) \)	None	None	\(0\)	\(0\)	\(-1\)	\(6\)	\(-\)	\(q-\beta q^{5}+3q^{7}+(-3-\beta )q^{11}-q^{13}+\cdots\)
2808.2.a.s	\(2\)	\(22.422\)	\(\Q(\sqrt{37}) \)	None	None	\(0\)	\(0\)	\(1\)	\(6\)	\(-\)	\(q+\beta q^{5}+3q^{7}+(3+\beta )q^{11}-q^{13}+\cdots\)
2808.2.a.t	\(2\)	\(22.422\)	\(\Q(\sqrt{6}) \)	None	None	\(0\)	\(0\)	\(2\)	\(4\)	\(-\)	\(q+(1+\beta )q^{5}+2q^{7}+2q^{11}-q^{13}+\cdots\)
2808.2.a.u	\(2\)	\(22.422\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(3\)	\(-4\)	\(+\)	\(q+(1+\beta )q^{5}+(-1-2\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
2808.2.a.v	\(2\)	\(22.422\)	\(\Q(\sqrt{17}) \)	None	None	\(0\)	\(0\)	\(3\)	\(5\)	\(-\)	\(q+(1+\beta )q^{5}+(2+\beta )q^{7}+(4-\beta )q^{11}+\cdots\)
2808.2.a.w	\(3\)	\(22.422\)	3.3.2213.1	None	None	\(0\)	\(0\)	\(-5\)	\(0\)	\(-\)	\(q+(-2+\beta _{1})q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{11}+\cdots\)
2808.2.a.x	\(3\)	\(22.422\)	3.3.1101.1	None	None	\(0\)	\(0\)	\(-2\)	\(-3\)	\(+\)	\(q+(-1+\beta _{1})q^{5}-q^{7}+(2-\beta _{1}+\beta _{2})q^{11}+\cdots\)
2808.2.a.y	\(3\)	\(22.422\)	3.3.1016.1	None	None	\(0\)	\(0\)	\(-2\)	\(-1\)	\(+\)	\(q+(-1+\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2808.2.a.z	\(3\)	\(22.422\)	3.3.1101.1	None	None	\(0\)	\(0\)	\(2\)	\(-3\)	\(+\)	\(q+(1-\beta _{1})q^{5}-q^{7}+(-2+\beta _{1}-\beta _{2})q^{11}+\cdots\)
2808.2.a.ba	\(3\)	\(22.422\)	3.3.1016.1	None	None	\(0\)	\(0\)	\(2\)	\(-1\)	\(-\)	\(q+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2808.2.a.bb	\(3\)	\(22.422\)	3.3.2213.1	None	None	\(0\)	\(0\)	\(5\)	\(0\)	\(-\)	\(q+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+(-2-\beta _{1}-\beta _{2})q^{11}+\cdots\)
2808.2.c.a	\(2\)	\(22.422\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+3iq^{5}+4iq^{7}-4iq^{11}+(-3-2i)q^{13}+\cdots\)
2808.2.c.b	\(2\)	\(22.422\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+3iq^{5}-4iq^{7}-4iq^{11}+(-3+2i)q^{13}+\cdots\)
2808.2.c.c	\(4\)	\(22.422\)	\(\Q(i, \sqrt{17})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2808.2.c.d	\(4\)	\(22.422\)	\(\Q(i, \sqrt{17})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
2808.2.c.e	\(14\)	\(22.422\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{7}q^{11}-\beta _{13}q^{13}+\cdots\)
2808.2.c.f	\(14\)	\(22.422\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{5}+\beta _{4}q^{7}+\beta _{7}q^{11}-\beta _{10}q^{13}+\cdots\)

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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.