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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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Results (21 matches)

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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
1081.1.l.b	$1081$	$1$	1081.l	1081.l	$46$	$44$	$2$	$0.539$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q+(-\zeta_{138}^{25}-\zeta_{138}^{41})q^{2}+(-\zeta_{138}^{5}+\cdots)q^{3}+\cdots$
1108.1.u.a	$1108$	$1$	1108.u	1108.u	$138$	$44$	$1$	$0.553$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q+\zeta_{138}^{12}q^{2}+\zeta_{138}^{24}q^{4}+(-\zeta_{138}^{19}+\cdots)q^{5}+\cdots$
1112.1.bd.a	$1112$	$1$	1112.bd	1112.ad	$138$	$44$	$1$	$0.555$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$2$	$0$	$0$	$1$		$q-\zeta_{138}^{31}q^{2}+(-\zeta_{138}^{59}+\zeta_{138}^{68}+\cdots)q^{3}+\cdots$
1457.1.s.b	$1457$	$1$	1457.s	1457.s	$46$	$44$	$2$	$0.727$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$2$	$2$	$23$		$q+(\zeta_{138}^{58}-\zeta_{138}^{59})q^{2}+(-\zeta_{138}^{47}+\cdots)q^{4}+\cdots$
1668.1.bb.a	$1668$	$1$	1668.bb	417.n	$138$	$44$	$1$	$0.832$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q-\zeta_{138}^{53}q^{3}+(-\zeta_{138}^{31}+\zeta_{138}^{36}+\cdots)q^{7}+\cdots$
1939.1.bo.a	$1939$	$1$	1939.bo	1939.ao	$138$	$44$	$1$	$0.968$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(-\zeta_{138}^{31}-\zeta_{138}^{47})q^{2}+(-\zeta_{138}^{9}+\cdots)q^{4}+\cdots$
2068.1.r.a	$2068$	$1$	2068.r	517.k	$46$	$44$	$2$	$1.032$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$2$	$0$	$23$		$q+(\zeta_{138}^{28}-\zeta_{138}^{35})q^{3}+(\zeta_{138}^{4}+\zeta_{138}^{44}+\cdots)q^{5}+\cdots$
2085.1.bp.a	$2085$	$1$	2085.bp	2085.ap	$138$	$44$	$1$	$1.041$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$1$	$1$	$0$	$1$		$q+(-\zeta_{138}^{39}-\zeta_{138}^{61})q^{2}-\zeta_{138}^{49}q^{3}+\cdots$
2085.1.bp.b	$2085$	$1$	2085.bp	2085.ap	$138$	$44$	$1$	$1.041$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{138}^{39}+\zeta_{138}^{61})q^{2}+\zeta_{138}^{49}q^{3}+\cdots$
2487.1.ba.a	$2487$	$1$	2487.ba	2487.aa	$138$	$44$	$1$	$1.241$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{138}^{11}q^{3}-\zeta_{138}^{43}q^{4}+(-\zeta_{138}^{25}+\cdots)q^{7}+\cdots$
2641.1.bp.a	$2641$	$1$	2641.bp	2641.ap	$138$	$44$	$1$	$1.318$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q-\zeta_{138}^{41}q^{4}+(\zeta_{138}^{34}+\zeta_{138}^{42})q^{5}+\cdots$
2919.1.co.a	$2919$	$1$	2919.co	2919.bo	$138$	$44$	$1$	$1.457$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q-\zeta_{138}^{31}q^{3}+\zeta_{138}^{52}q^{4}-\zeta_{138}^{65}q^{7}+\cdots$
2919.1.cy.a	$2919$	$1$	2919.cy	2919.by	$138$	$44$	$1$	$1.457$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$1$	$1$		$q+\zeta_{138}^{36}q^{3}-\zeta_{138}^{27}q^{4}-\zeta_{138}^{11}q^{7}+\cdots$
3119.1.b.d	$3119$	$1$	3119.b	3119.b	$2$	$22$	$22$	$1.557$	$\Q(\zeta_{69})^+$	$D_{69}$	$\Q(\sqrt{-3119}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$0$	$1$		$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{9}+\cdots)q^{5}+\cdots$
3191.1.b.c	$3191$	$1$	3191.b	3191.b	$2$	$22$	$22$	$1.593$	$\Q(\zeta_{69})^+$	$D_{69}$	$\Q(\sqrt{-3191}) $	None	✓	$2$	$0$	$1$	$1$	$1$	$-2$	$1$		$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{21})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
3197.1.o.b	$3197$	$1$	3197.o	3197.o	$46$	$44$	$2$	$1.596$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q+(\zeta_{138}^{16}-\zeta_{138}^{17})q^{2}+(-\zeta_{138}^{47}+\cdots)q^{3}+\cdots$
3316.1.ba.a	$3316$	$1$	3316.ba	3316.aa	$138$	$44$	$1$	$1.655$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+\zeta_{138}^{38}q^{2}-\zeta_{138}^{7}q^{4}+(-\zeta_{138}^{11}+\cdots)q^{5}+\cdots$
3324.1.bn.a	$3324$	$1$	3324.bn	831.u	$138$	$44$	$1$	$1.659$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+\zeta_{138}^{16}q^{3}+(-\zeta_{138}^{27}+\zeta_{138}^{34}+\cdots)q^{7}+\cdots$
3359.1.b.c	$3359$	$1$	3359.b	3359.b	$2$	$22$	$22$	$1.676$	$\Q(\zeta_{69})^+$	$D_{69}$	$\Q(\sqrt{-3359}) $	None	✓	$2$	$0$	$1$	$1$	$-2$	$1$	$1$		$q+\beta _{1}q^{2}+(-\beta _{5}-\beta _{18})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
3572.1.bc.a	$3572$	$1$	3572.bc	893.o	$46$	$44$	$2$	$1.783$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$2$	$1$		$q+(\zeta_{138}^{52}+\zeta_{138}^{56})q^{5}+(\zeta_{138}^{16}-\zeta_{138}^{59}+\cdots)q^{7}+\cdots$
3753.1.br.a	$3753$	$1$	3753.br	417.n	$138$	$44$	$1$	$1.873$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\zeta_{138}^{49}q^{4}+(-\zeta_{138}^{37}-\zeta_{138}^{67}+\cdots)q^{7}+\cdots$

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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.