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 128 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
891.1.c.a	$1$	$0.445$	$\Q$	$\Q(\sqrt{-11}) $	None	$0$	$0$	$-1$	$0$		$q+q^{4}-q^{5}+q^{11}+q^{16}-q^{20}+2q^{23}+\cdots$
891.1.c.b	$1$	$0.445$	$\Q$	$\Q(\sqrt{-11}) $	None	$0$	$0$	$1$	$0$		$q+q^{4}+q^{5}-q^{11}+q^{16}+q^{20}-2q^{23}+\cdots$
891.1.q.a	$6$	$0.445$	$\Q(\zeta_{18})$	$\Q(\sqrt{-11}) $	None	$0$	$0$	$3$	$0$		$q-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{5}+\zeta_{18}q^{11}+\cdots$
891.1.w.a	$18$	$0.445$	$\Q(\zeta_{54})$	$\Q(\sqrt{-11}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{6}+\zeta_{54}^{8}+\cdots)q^{5}+\cdots$
891.2.a.a	$1$	$7.115$	$\Q$	None	None	$-2$	$0$	$-2$	$4$	$-$	$q-2q^{2}+2q^{4}-2q^{5}+4q^{7}+4q^{10}+\cdots$
891.2.a.b	$1$	$7.115$	$\Q$	None	None	$-1$	$0$	$-1$	$-2$	$+$	$q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots$
891.2.a.c	$1$	$7.115$	$\Q$	None	None	$-1$	$0$	$-1$	$4$	$-$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
891.2.a.d	$1$	$7.115$	$\Q$	None	None	$0$	$0$	$-3$	$-4$	$-$	$q-2q^{4}-3q^{5}-4q^{7}+q^{11}+2q^{13}+\cdots$
891.2.a.e	$1$	$7.115$	$\Q$	None	None	$0$	$0$	$3$	$-4$	$-$	$q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots$
891.2.a.f	$1$	$7.115$	$\Q$	None	None	$1$	$0$	$1$	$-2$	$-$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
891.2.a.g	$1$	$7.115$	$\Q$	None	None	$1$	$0$	$1$	$4$	$-$	$q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots$
891.2.a.h	$1$	$7.115$	$\Q$	None	None	$2$	$0$	$2$	$4$	$-$	$q+2q^{2}+2q^{4}+2q^{5}+4q^{7}+4q^{10}+\cdots$
891.2.a.i	$2$	$7.115$	$\Q(\sqrt{13}) $	None	None	$-1$	$0$	$-1$	$0$	$+$	$q-\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots$
891.2.a.j	$2$	$7.115$	$\Q(\sqrt{13}) $	None	None	$1$	$0$	$1$	$0$	$-$	$q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots$
891.2.a.k	$3$	$7.115$	$\Q(\zeta_{18})^+$	None	None	$0$	$0$	$-3$	$-3$	$+$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
891.2.a.l	$3$	$7.115$	$\Q(\zeta_{18})^+$	None	None	$0$	$0$	$3$	$-3$	$+$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
891.2.a.m	$3$	$7.115$	3.3.837.1	None	None	$0$	$0$	$-6$	$0$	$+$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots$
891.2.a.n	$3$	$7.115$	3.3.837.1	None	None	$0$	$0$	$6$	$0$	$-$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots$
891.2.a.o	$4$	$7.115$	4.4.4752.1	None	None	$-2$	$0$	$-8$	$-2$	$+$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots$
891.2.a.p	$4$	$7.115$	4.4.22545.1	None	None	$-1$	$0$	$-4$	$1$	$-$	$q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots$
891.2.a.q	$4$	$7.115$	4.4.22545.1	None	None	$1$	$0$	$4$	$1$	$-$	$q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots$
891.2.a.r	$4$	$7.115$	4.4.4752.1	None	None	$2$	$0$	$8$	$-2$	$-$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
891.2.d.a	$4$	$7.115$	$\Q(\sqrt{-3}, \sqrt{-11})$	$\Q(\sqrt{-11}) $	None	$0$	$0$	$0$	$0$		$q-2q^{4}+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+4q^{16}+\cdots$
891.2.d.b	$16$	$7.115$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+(2-\beta _{3})q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots$
891.2.d.c	$24$	$7.115$		None	None	$0$	$0$	$0$	$0$
891.2.e.a	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$-2$	$0$	$-2$	$-1$		$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
891.2.e.b	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$-2$	$0$	$1$	$2$		$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
891.2.e.c	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$-1$	$0$	$-4$	$2$		$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots$
891.2.e.d	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$-1$	$0$	$-1$	$2$		$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
891.2.e.e	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$-1$	$0$	$2$	$-4$		$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
891.2.e.f	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$-1$	$0$	$2$	$5$		$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
891.2.e.g	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$1$	$0$	$-2$	$-4$		$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$
891.2.e.h	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$1$	$0$	$-2$	$5$		$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots$
891.2.e.i	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$1$	$0$	$1$	$2$		$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
891.2.e.j	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$1$	$0$	$4$	$2$		$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
891.2.e.k	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$2$	$0$	$-1$	$2$		$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
891.2.e.l	$2$	$7.115$	$\Q(\sqrt{-3}) $	None	None	$2$	$0$	$2$	$-1$		$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$
891.2.e.m	$4$	$7.115$	$\Q(\zeta_{12})$	None	None	$-2$	$0$	$-2$	$4$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots$
891.2.e.n	$4$	$7.115$	$\Q(\sqrt{-3}, \sqrt{13})$	None	None	$-1$	$0$	$-1$	$0$		$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
891.2.e.o	$4$	$7.115$	$\Q(\sqrt{-3}, \sqrt{13})$	None	None	$1$	$0$	$1$	$0$		$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
891.2.e.p	$4$	$7.115$	$\Q(\zeta_{12})$	None	None	$2$	$0$	$2$	$4$		$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
891.2.e.q	$6$	$7.115$	6.0.954288.1	None	None	$-1$	$0$	$2$	$-7$		$q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$
891.2.e.r	$6$	$7.115$	6.0.2101707.2	None	None	$0$	$0$	$-6$	$0$		$q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots$
891.2.e.s	$6$	$7.115$	6.0.2101707.2	None	None	$0$	$0$	$6$	$0$		$q+(\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots$
891.2.e.t	$6$	$7.115$	6.0.954288.1	None	None	$1$	$0$	$-2$	$-7$		$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
891.2.e.u	$8$	$7.115$	8.0.22581504.2	None	None	$-2$	$0$	$-8$	$2$		$q+(-1+\beta _{1}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
891.2.e.v	$8$	$7.115$	8.0.22581504.2	None	None	$2$	$0$	$8$	$2$		$q+(1-\beta _{1}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots$
891.2.f.a	$4$	$7.115$	$\Q(\zeta_{10})$	None	None	$-4$	$0$	$6$	$1$		$q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots$
891.2.f.b	$4$	$7.115$	$\Q(\zeta_{10})$	None	None	$4$	$0$	$-6$	$1$		$q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots$
891.2.f.c	$24$	$7.115$		None	None	$-2$	$0$	$4$	$7$

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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
891.1.c.a	\(1\)	\(0.445\)	\(\Q\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(-1\)	\(0\)		\(q+q^{4}-q^{5}+q^{11}+q^{16}-q^{20}+2q^{23}+\cdots\)
891.1.c.b	\(1\)	\(0.445\)	\(\Q\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(1\)	\(0\)		\(q+q^{4}+q^{5}-q^{11}+q^{16}+q^{20}-2q^{23}+\cdots\)
891.1.q.a	\(6\)	\(0.445\)	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(3\)	\(0\)		\(q-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{5}+\zeta_{18}q^{11}+\cdots\)
891.1.w.a	\(18\)	\(0.445\)	\(\Q(\zeta_{54})\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{6}+\zeta_{54}^{8}+\cdots)q^{5}+\cdots\)
891.2.a.a	\(1\)	\(7.115\)	\(\Q\)	None	None	\(-2\)	\(0\)	\(-2\)	\(4\)	\(-\)	\(q-2q^{2}+2q^{4}-2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.b	\(1\)	\(7.115\)	\(\Q\)	None	None	\(-1\)	\(0\)	\(-1\)	\(-2\)	\(+\)	\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.c	\(1\)	\(7.115\)	\(\Q\)	None	None	\(-1\)	\(0\)	\(-1\)	\(4\)	\(-\)	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.d	\(1\)	\(7.115\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-3\)	\(-4\)	\(-\)	\(q-2q^{4}-3q^{5}-4q^{7}+q^{11}+2q^{13}+\cdots\)
891.2.a.e	\(1\)	\(7.115\)	\(\Q\)	None	None	\(0\)	\(0\)	\(3\)	\(-4\)	\(-\)	\(q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots\)
891.2.a.f	\(1\)	\(7.115\)	\(\Q\)	None	None	\(1\)	\(0\)	\(1\)	\(-2\)	\(-\)	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.g	\(1\)	\(7.115\)	\(\Q\)	None	None	\(1\)	\(0\)	\(1\)	\(4\)	\(-\)	\(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.h	\(1\)	\(7.115\)	\(\Q\)	None	None	\(2\)	\(0\)	\(2\)	\(4\)	\(-\)	\(q+2q^{2}+2q^{4}+2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.i	\(2\)	\(7.115\)	\(\Q(\sqrt{13}) \)	None	None	\(-1\)	\(0\)	\(-1\)	\(0\)	\(+\)	\(q-\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.j	\(2\)	\(7.115\)	\(\Q(\sqrt{13}) \)	None	None	\(1\)	\(0\)	\(1\)	\(0\)	\(-\)	\(q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.k	\(3\)	\(7.115\)	\(\Q(\zeta_{18})^+\)	None	None	\(0\)	\(0\)	\(-3\)	\(-3\)	\(+\)	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.l	\(3\)	\(7.115\)	\(\Q(\zeta_{18})^+\)	None	None	\(0\)	\(0\)	\(3\)	\(-3\)	\(+\)	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.m	\(3\)	\(7.115\)	3.3.837.1	None	None	\(0\)	\(0\)	\(-6\)	\(0\)	\(+\)	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
891.2.a.n	\(3\)	\(7.115\)	3.3.837.1	None	None	\(0\)	\(0\)	\(6\)	\(0\)	\(-\)	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
891.2.a.o	\(4\)	\(7.115\)	4.4.4752.1	None	None	\(-2\)	\(0\)	\(-8\)	\(-2\)	\(+\)	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
891.2.a.p	\(4\)	\(7.115\)	4.4.22545.1	None	None	\(-1\)	\(0\)	\(-4\)	\(1\)	\(-\)	\(q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
891.2.a.q	\(4\)	\(7.115\)	4.4.22545.1	None	None	\(1\)	\(0\)	\(4\)	\(1\)	\(-\)	\(q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots\)
891.2.a.r	\(4\)	\(7.115\)	4.4.4752.1	None	None	\(2\)	\(0\)	\(8\)	\(-2\)	\(-\)	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
891.2.d.a	\(4\)	\(7.115\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-2q^{4}+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+4q^{16}+\cdots\)
891.2.d.b	\(16\)	\(7.115\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+(2-\beta _{3})q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)
891.2.d.c	\(24\)	\(7.115\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
891.2.e.a	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(-2\)	\(0\)	\(-2\)	\(-1\)		\(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
891.2.e.b	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(-2\)	\(0\)	\(1\)	\(2\)		\(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
891.2.e.c	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(-1\)	\(0\)	\(-4\)	\(2\)		\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
891.2.e.d	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(-1\)	\(0\)	\(-1\)	\(2\)		\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.e	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(-1\)	\(0\)	\(2\)	\(-4\)		\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.f	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(-1\)	\(0\)	\(2\)	\(5\)		\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.g	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(1\)	\(0\)	\(-2\)	\(-4\)		\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
891.2.e.h	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(1\)	\(0\)	\(-2\)	\(5\)		\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots\)
891.2.e.i	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(1\)	\(0\)	\(1\)	\(2\)		\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
891.2.e.j	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(1\)	\(0\)	\(4\)	\(2\)		\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.k	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(2\)	\(0\)	\(-1\)	\(2\)		\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.l	\(2\)	\(7.115\)	\(\Q(\sqrt{-3}) \)	None	None	\(2\)	\(0\)	\(2\)	\(-1\)		\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.m	\(4\)	\(7.115\)	\(\Q(\zeta_{12})\)	None	None	\(-2\)	\(0\)	\(-2\)	\(4\)		\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
891.2.e.n	\(4\)	\(7.115\)	\(\Q(\sqrt{-3}, \sqrt{13})\)	None	None	\(-1\)	\(0\)	\(-1\)	\(0\)		\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.o	\(4\)	\(7.115\)	\(\Q(\sqrt{-3}, \sqrt{13})\)	None	None	\(1\)	\(0\)	\(1\)	\(0\)		\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.p	\(4\)	\(7.115\)	\(\Q(\zeta_{12})\)	None	None	\(2\)	\(0\)	\(2\)	\(4\)		\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
891.2.e.q	\(6\)	\(7.115\)	6.0.954288.1	None	None	\(-1\)	\(0\)	\(2\)	\(-7\)		\(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
891.2.e.r	\(6\)	\(7.115\)	6.0.2101707.2	None	None	\(0\)	\(0\)	\(-6\)	\(0\)		\(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.s	\(6\)	\(7.115\)	6.0.2101707.2	None	None	\(0\)	\(0\)	\(6\)	\(0\)		\(q+(\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.t	\(6\)	\(7.115\)	6.0.954288.1	None	None	\(1\)	\(0\)	\(-2\)	\(-7\)		\(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.u	\(8\)	\(7.115\)	8.0.22581504.2	None	None	\(-2\)	\(0\)	\(-8\)	\(2\)		\(q+(-1+\beta _{1}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.v	\(8\)	\(7.115\)	8.0.22581504.2	None	None	\(2\)	\(0\)	\(8\)	\(2\)		\(q+(1-\beta _{1}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)
891.2.f.a	\(4\)	\(7.115\)	\(\Q(\zeta_{10})\)	None	None	\(-4\)	\(0\)	\(6\)	\(1\)		\(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
891.2.f.b	\(4\)	\(7.115\)	\(\Q(\zeta_{10})\)	None	None	\(4\)	\(0\)	\(-6\)	\(1\)		\(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots\)
891.2.f.c	\(24\)	\(7.115\)		None	None	\(-2\)	\(0\)	\(4\)	\(7\)

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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.