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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	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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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
2003.1.b.b	$2003$	$1$	2003.b	2003.b	$2$	$3$	$3$	$1.000$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2003}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{12}+\cdots$
2007.1.d.b	$2007$	$1$	2007.d	223.b	$2$	$3$	$3$	$1.002$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-223}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
2008.1.c.a	$2008$	$1$	2008.c	2008.c	$2$	$3$	$3$	$1.002$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-502}) $	None	✓	$2$	$0$	$-3$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{9}-\beta _{2}q^{11}+\cdots$
2008.1.c.b	$2008$	$1$	2008.c	2008.c	$2$	$3$	$3$	$1.002$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-502}) $	None	✓	$2$	$0$	$3$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\beta _{2}q^{11}+\cdots$
2011.1.b.a	$2011$	$1$	2011.b	2011.b	$2$	$3$	$3$	$1.004$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2011}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-\beta _{1}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots$
2023.1.c.c	$2023$	$1$	2023.c	7.b	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$
2023.1.c.d	$2023$	$1$	2023.c	7.b	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$
2024.1.o.a	$2024$	$1$	2024.o	2024.o	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-506}) $	None	✓	$2$	$0$	$-3$	$-1$	$-1$	$0$	$1$		$q-q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
2024.1.o.b	$2024$	$1$	2024.o	2024.o	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-506}) $	None	✓	$2$	$0$	$-3$	$-1$	$1$	$0$	$1$		$q-q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
2024.1.o.c	$2024$	$1$	2024.o	2024.o	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-506}) $	None	✓	$2$	$0$	$3$	$-1$	$-1$	$0$	$1$		$q+q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
2024.1.o.d	$2024$	$1$	2024.o	2024.o	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-506}) $	None	✓	$2$	$0$	$3$	$-1$	$1$	$0$	$1$		$q+q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
2039.1.b.c	$2039$	$1$	2039.b	2039.b	$2$	$3$	$3$	$1.018$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2039}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
2047.1.b.c	$2047$	$1$	2047.b	2047.b	$2$	$3$	$3$	$1.022$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2047}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}-\beta _{1}q^{7}+\cdots$
2047.1.b.d	$2047$	$1$	2047.b	2047.b	$2$	$3$	$3$	$1.022$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2047}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\beta _{1}q^{7}+\cdots$
2051.1.c.c	$2051$	$1$	2051.c	2051.c	$2$	$3$	$3$	$1.024$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2051}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}+\cdots$
2051.1.c.d	$2051$	$1$	2051.c	2051.c	$2$	$3$	$3$	$1.024$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2051}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$	$1$		$q-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots$
2055.1.g.b	$2055$	$1$	2055.g	2055.g	$2$	$3$	$3$	$1.026$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2055}) $	None	✓	$2$	$0$	$-1$	$-3$	$-3$	$0$	$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2055.1.g.c	$2055$	$1$	2055.g	2055.g	$2$	$3$	$3$	$1.026$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2055}) $	None	✓	$2$	$0$	$-1$	$3$	$3$	$0$	$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2055.1.g.d	$2055$	$1$	2055.g	2055.g	$2$	$3$	$3$	$1.026$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2055}) $	None	✓	$2$	$0$	$1$	$-3$	$3$	$0$	$1$		$q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{2})q^{4}+q^{5}+\cdots$
2055.1.g.e	$2055$	$1$	2055.g	2055.g	$2$	$3$	$3$	$1.026$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2055}) $	None	✓	$2$	$0$	$1$	$3$	$-3$	$0$	$1$		$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2060.1.f.a	$2060$	$1$	2060.f	515.c	$2$	$3$	$3$	$1.028$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-515}) $	None	✓	$2$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\beta _{1}q^{3}-q^{5}+(1+\beta _{2})q^{9}-\beta _{1}q^{15}+\cdots$
2060.1.f.b	$2060$	$1$	2060.f	515.c	$2$	$3$	$3$	$1.028$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-515}) $	None	✓	$2$	$0$	$0$	$0$	$3$	$0$	$1$		$q-\beta _{1}q^{3}+q^{5}+(1+\beta _{2})q^{9}-\beta _{1}q^{15}+\cdots$
2063.1.b.c	$2063$	$1$	2063.b	2063.b	$2$	$3$	$3$	$1.030$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2063}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2079.1.h.a	$2079$	$1$	2079.h	231.h	$2$	$3$	$3$	$1.038$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots$
2079.1.h.b	$2079$	$1$	2079.h	231.h	$2$	$3$	$3$	$1.038$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
2079.1.h.c	$2079$	$1$	2079.h	231.h	$2$	$3$	$3$	$1.038$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$	$1$		$q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
2079.1.h.d	$2079$	$1$	2079.h	231.h	$2$	$3$	$3$	$1.038$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-231}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$	$1$		$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots$
2083.1.b.a	$2083$	$1$	2083.b	2083.b	$2$	$3$	$3$	$1.040$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2083}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-\beta _{1}q^{13}+q^{16}+\beta _{2}q^{17}+\cdots$
2087.1.b.b	$2087$	$1$	2087.b	2087.b	$2$	$3$	$3$	$1.042$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2087}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2111.1.b.a	$2111$	$1$	2111.b	2111.b	$2$	$3$	$3$	$1.054$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2111}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
2120.1.p.b	$2120$	$1$	2120.p	2120.p	$2$	$3$	$3$	$1.058$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-530}) $	None	✓	$2$	$0$	$-3$	$1$	$-3$	$-1$	$1$		$q-q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}+\beta _{2}q^{6}+\cdots$
2120.1.p.c	$2120$	$1$	2120.p	2120.p	$2$	$3$	$3$	$1.058$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-530}) $	None	✓	$2$	$0$	$-3$	$1$	$3$	$1$	$1$		$q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2120.1.p.d	$2120$	$1$	2120.p	2120.p	$2$	$3$	$3$	$1.058$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-530}) $	None	✓	$2$	$0$	$3$	$-1$	$-3$	$1$	$1$		$q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
2120.1.p.e	$2120$	$1$	2120.p	2120.p	$2$	$3$	$3$	$1.058$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-530}) $	None	✓	$2$	$0$	$3$	$-1$	$3$	$-1$	$1$		$q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2123.1.b.a	$2123$	$1$	2123.b	2123.b	$2$	$3$	$3$	$1.060$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2123}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-q^{11}+\cdots$
2123.1.b.b	$2123$	$1$	2123.b	2123.b	$2$	$3$	$3$	$1.060$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2123}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}+q^{11}+\cdots$
2124.1.h.a	$2124$	$1$	2124.h	59.b	$2$	$3$	$3$	$1.060$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{17}-\beta _{1}q^{19}+\cdots$
2127.1.d.b	$2127$	$1$	2127.d	2127.d	$2$	$3$	$3$	$1.062$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2127}) $	None	✓	$2$	$0$	$-1$	$3$	$0$	$-1$	$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
2127.1.d.c	$2127$	$1$	2127.d	2127.d	$2$	$3$	$3$	$1.062$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2127}) $	None	✓	$2$	$0$	$1$	$3$	$0$	$-1$	$1$		$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2144.1.h.a	$2144$	$1$	2144.h	536.h	$2$	$3$	$3$	$1.070$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-134}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$	$1$		$q+\beta _{2}q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
2144.1.h.b	$2144$	$1$	2144.h	536.h	$2$	$3$	$3$	$1.070$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-134}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q-\beta _{2}q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
2147.1.c.a	$2147$	$1$	2147.c	2147.c	$2$	$3$	$3$	$1.071$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2147}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
2147.1.c.b	$2147$	$1$	2147.c	2147.c	$2$	$3$	$3$	$1.071$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2147}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
2167.1.d.c	$2167$	$1$	2167.d	2167.d	$2$	$3$	$3$	$1.081$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2167}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{1})q^{8}+\cdots$
2167.1.d.d	$2167$	$1$	2167.d	2167.d	$2$	$3$	$3$	$1.081$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2167}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{1})q^{8}+\cdots$
2171.1.c.a	$2171$	$1$	2171.c	2171.c	$2$	$3$	$3$	$1.083$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2171}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
2171.1.c.b	$2171$	$1$	2171.c	2171.c	$2$	$3$	$3$	$1.083$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2171}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
2175.1.h.c	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots$
2175.1.h.d	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(1-\beta _{1})q^{4}+\cdots$
2175.1.h.e	$2175$	$1$	2175.h	87.d	$2$	$3$	$3$	$1.085$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(1-\beta _{1})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$

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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.