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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 (1-50 of 55 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
553.1.bg.a	$553$	$1$	553.bg	553.ag	$78$	$24$	$1$	$0.276$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(\zeta_{78}^{16}+\zeta_{78}^{18})q^{2}+(\zeta_{78}^{32}+\zeta_{78}^{34}+\cdots)q^{4}+\cdots$
628.1.u.a	$628$	$1$	628.u	628.u	$78$	$24$	$1$	$0.313$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q-\zeta_{78}^{3}q^{2}+\zeta_{78}^{6}q^{4}+(-\zeta_{78}^{17}+\cdots)q^{5}+\cdots$
676.1.t.a	$676$	$1$	676.t	676.t	$78$	$24$	$1$	$0.337$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q+\zeta_{78}^{8}q^{2}+\zeta_{78}^{16}q^{4}+(\zeta_{78}^{28}+\zeta_{78}^{38}+\cdots)q^{5}+\cdots$
948.1.bb.a	$948$	$1$	948.bb	237.o	$78$	$24$	$1$	$0.473$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q+\zeta_{78}^{4}q^{3}+(-\zeta_{78}^{5}-\zeta_{78}^{29})q^{7}+\cdots$
1185.1.bp.a	$1185$	$1$	1185.bp	1185.ap	$78$	$24$	$1$	$0.591$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{78}^{5}-\zeta_{78}^{14})q^{2}+\zeta_{78}^{17}q^{3}+\cdots$
1185.1.bp.b	$1185$	$1$	1185.bp	1185.ap	$78$	$24$	$1$	$0.591$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{78}^{5}+\zeta_{78}^{14})q^{2}-\zeta_{78}^{17}q^{3}+\cdots$
1252.1.y.a	$1252$	$1$	1252.y	1252.y	$78$	$24$	$1$	$0.625$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-4$	$0$	$1$		$q+\zeta_{78}^{32}q^{2}-\zeta_{78}^{25}q^{4}+(\zeta_{78}^{12}+\cdots)q^{5}+\cdots$
1439.1.b.c	$1439$	$1$	1439.b	1439.b	$2$	$12$	$12$	$0.718$	$\Q(\zeta_{39})^+$	$D_{39}$	$\Q(\sqrt{-1439}) $	None	✓	$2$	$0$	$-2$	$1$	$1$	$0$	$1$		$q+\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
1659.1.cn.a	$1659$	$1$	1659.cn	1659.bn	$78$	$24$	$1$	$0.828$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q+\zeta_{78}^{12}q^{3}-\zeta_{78}^{31}q^{4}-\zeta_{78}^{15}q^{7}+\cdots$
1659.1.cy.a	$1659$	$1$	1659.cy	1659.by	$78$	$24$	$1$	$0.828$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{78}^{10}q^{3}-\zeta_{78}^{15}q^{4}+\zeta_{78}^{14}q^{7}+\cdots$
1719.1.g.c	$1719$	$1$	1719.g	1719.g	$6$	$24$	$12$	$0.858$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-191}) $	None		$4$	$0$	$2$	$1$	$-1$	$0$	$1$		$q+(-\zeta_{78}^{7}-\zeta_{78}^{19})q^{2}-\zeta_{78}^{37}q^{3}+\cdots$
1727.1.bi.a	$1727$	$1$	1727.bi	1727.ai	$78$	$24$	$1$	$0.862$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$-11$	$0$	$1$		$q+(\zeta_{78}^{12}+\zeta_{78}^{20})q^{3}+\zeta_{78}^{36}q^{4}+\cdots$
1884.1.bl.a	$1884$	$1$	1884.bl	471.u	$78$	$24$	$1$	$0.940$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-4$	$1$		$q+\zeta_{78}^{28}q^{3}+(\zeta_{78}^{12}+\zeta_{78}^{18})q^{7}+\cdots$
1896.1.cl.a	$1896$	$1$	1896.cl	1896.bl	$78$	$24$	$1$	$0.946$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$14$	$-1$	$1$		$q-\zeta_{78}^{34}q^{2}-\zeta_{78}^{28}q^{3}-\zeta_{78}^{29}q^{4}+\cdots$
1896.1.cl.b	$1896$	$1$	1896.cl	1896.bl	$78$	$24$	$1$	$0.946$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$-14$	$-1$	$1$		$q+\zeta_{78}^{34}q^{2}+\zeta_{78}^{28}q^{3}-\zeta_{78}^{29}q^{4}+\cdots$
2028.1.bq.a	$2028$	$1$	2028.bq	507.u	$78$	$24$	$1$	$1.012$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q-\zeta_{78}^{37}q^{3}+(-\zeta_{78}^{3}-\zeta_{78}^{25})q^{7}+\cdots$
2133.1.bt.a	$2133$	$1$	2133.bt	237.o	$78$	$24$	$1$	$1.065$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-\zeta_{78}^{35}q^{4}+(-\zeta_{78}^{27}-\zeta_{78}^{37}+\cdots)q^{7}+\cdots$
2207.1.b.c	$2207$	$1$	2207.b	2207.b	$2$	$12$	$12$	$1.101$	$\Q(\zeta_{39})^+$	$D_{39}$	$\Q(\sqrt{-2207}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots$
2332.1.z.a	$2332$	$1$	2332.z	583.o	$26$	$24$	$2$	$1.164$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$2$	$0$	$13$		$q+(\zeta_{78}^{16}+\zeta_{78}^{38})q^{3}+(-\zeta_{78}-\zeta_{78}^{29}+\cdots)q^{5}+\cdots$
2367.1.f.c	$2367$	$1$	2367.f	2367.f	$6$	$24$	$12$	$1.181$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+(-\zeta_{78}^{25}-\zeta_{78}^{27})q^{2}-\zeta_{78}^{31}q^{3}+\cdots$
2483.1.i.b	$2483$	$1$	2483.i	2483.i	$6$	$24$	$12$	$1.239$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-191}) $	None		$4$	$0$	$-1$	$2$	$2$	$0$	$1$		$q+(-\zeta_{78}^{25}-\zeta_{78}^{27})q^{2}+(-\zeta_{78}^{17}+\cdots)q^{3}+\cdots$
2504.1.bx.a	$2504$	$1$	2504.bx	2504.ax	$78$	$24$	$1$	$1.250$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-14$	$0$	$0$	$1$		$q+\zeta_{78}^{32}q^{2}+(-\zeta_{78}^{9}+\zeta_{78}^{26})q^{3}+\cdots$
2756.1.cj.a	$2756$	$1$	2756.cj	2756.bj	$78$	$24$	$1$	$1.375$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q-\zeta_{78}^{11}q^{2}+\zeta_{78}^{22}q^{4}+(-\zeta_{78}+\cdots)q^{5}+\cdots$
2756.1.cj.b	$2756$	$1$	2756.cj	2756.bj	$78$	$24$	$1$	$1.375$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q-\zeta_{78}^{11}q^{2}+\zeta_{78}^{22}q^{4}+(\zeta_{78}^{14}+\cdots)q^{5}+\cdots$
2765.1.di.a	$2765$	$1$	2765.di	2765.ci	$78$	$24$	$1$	$1.380$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$1$	$1$	$1$		$q+(-\zeta_{78}^{3}-\zeta_{78}^{25})q^{3}+\zeta_{78}^{34}q^{4}+\cdots$
2765.1.di.b	$2765$	$1$	2765.di	2765.ci	$78$	$24$	$1$	$1.380$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q+(\zeta_{78}^{3}+\zeta_{78}^{25})q^{3}+\zeta_{78}^{34}q^{4}+\cdots$
2791.1.b.c	$2791$	$1$	2791.b	2791.b	$2$	$12$	$12$	$1.393$	$\Q(\zeta_{39})^+$	$D_{39}$	$\Q(\sqrt{-2791}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$1$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{5}+\beta _{8})q^{4}+\beta _{1}q^{5}+\cdots$
2811.1.bf.a	$2811$	$1$	2811.bf	2811.af	$78$	$24$	$1$	$1.403$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{78}^{25}q^{3}+\zeta_{78}^{10}q^{4}+(-\zeta_{78}+\cdots)q^{7}+\cdots$
2983.1.cq.a	$2983$	$1$	2983.cq	2983.bq	$78$	$24$	$1$	$1.489$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$2$	$1$		$q-\zeta_{78}^{15}q^{4}+(\zeta_{78}^{18}+\zeta_{78}^{20})q^{5}+\cdots$
3013.1.n.b	$3013$	$1$	3013.n	3013.n	$26$	$24$	$2$	$1.504$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q+(-\zeta_{78}^{5}+\zeta_{78}^{10})q^{2}+(\zeta_{78}^{28}+\zeta_{78}^{38}+\cdots)q^{3}+\cdots$
3081.1.di.a	$3081$	$1$	3081.di	3081.ci	$78$	$24$	$1$	$1.538$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q-\zeta_{78}^{7}q^{3}-\zeta_{78}^{17}q^{4}+(-\zeta_{78}^{15}+\cdots)q^{7}+\cdots$
3081.1.dq.a	$3081$	$1$	3081.dq	3081.cq	$78$	$24$	$1$	$1.538$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-1$	$1$	$-1$	$0$	$1$		$q+(\zeta_{78}^{2}-\zeta_{78}^{33})q^{2}-\zeta_{78}^{19}q^{3}+\cdots$
3081.1.dq.b	$3081$	$1$	3081.dq	3081.cq	$78$	$24$	$1$	$1.538$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$1$	$1$	$1$	$0$	$1$		$q+(-\zeta_{78}^{2}+\zeta_{78}^{33})q^{2}-\zeta_{78}^{19}q^{3}+\cdots$
3081.1.dw.a	$3081$	$1$	3081.dw	3081.cw	$78$	$24$	$1$	$1.538$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$	$1$		$q+\zeta_{78}^{30}q^{3}+\zeta_{78}^{6}q^{4}+(-\zeta_{78}^{5}+\cdots)q^{7}+\cdots$
3127.1.i.b	$3127$	$1$	3127.i	3127.i	$26$	$24$	$2$	$1.561$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$2$	$2$	$2$	$1$		$q+(\zeta_{78}^{8}-\zeta_{78}^{37})q^{3}-\zeta_{78}^{21}q^{4}+\cdots$
3297.1.de.a	$3297$	$1$	3297.de	3297.ce	$78$	$24$	$1$	$1.645$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$1$	$1$		$q+\zeta_{78}^{24}q^{3}+\zeta_{78}^{28}q^{4}+\zeta_{78}^{14}q^{7}+\cdots$
3297.1.dl.a	$3297$	$1$	3297.dl	3297.cl	$78$	$24$	$1$	$1.645$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{78}^{8}q^{3}-\zeta_{78}^{31}q^{4}+\zeta_{78}^{20}q^{7}+\cdots$
3397.1.by.a	$3397$	$1$	3397.by	3397.ay	$78$	$24$	$1$	$1.695$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{78}^{2}q^{4}+\zeta_{78}^{20}q^{9}+(-\zeta_{78}^{5}+\cdots)q^{11}+\cdots$
3419.1.h.b	$3419$	$1$	3419.h	3419.h	$6$	$24$	$12$	$1.706$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-263}) $	None		$4$	$0$	$2$	$-1$	$0$	$0$	$1$		$q+(-\zeta_{78}^{5}+\zeta_{78}^{8})q^{2}+(-\zeta_{78}^{25}+\cdots)q^{3}+\cdots$
3443.1.bn.a	$3443$	$1$	3443.bn	3443.an	$78$	$24$	$1$	$1.718$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$2$	$0$	$1$		$q+(-\zeta_{78}^{21}+\zeta_{78}^{38})q^{3}-\zeta_{78}^{31}q^{4}+\cdots$
3513.1.bc.a	$3513$	$1$	3513.bc	3513.ac	$78$	$24$	$1$	$1.753$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-14$	$1$		$q+\zeta_{78}^{20}q^{3}+\zeta_{78}^{38}q^{4}+(\zeta_{78}^{26}+\cdots)q^{7}+\cdots$
3549.1.dd.a	$3549$	$1$	3549.dd	3549.cd	$78$	$24$	$1$	$1.771$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$1$	$1$		$q+\zeta_{78}^{18}q^{3}+\zeta_{78}^{20}q^{4}+\zeta_{78}^{22}q^{7}+\cdots$
3549.1.dx.a	$3549$	$1$	3549.dx	3549.cx	$78$	$24$	$1$	$1.771$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{78}^{20}q^{3}-\zeta_{78}^{15}q^{4}-\zeta_{78}^{35}q^{7}+\cdots$
3713.1.u.a	$3713$	$1$	3713.u	3713.u	$78$	$24$	$1$	$1.853$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$-1$	$0$	$25$	$1$		$q+(\zeta_{78}^{8}-\zeta_{78}^{27})q^{2}+(-\zeta_{78}^{9}-\zeta_{78}^{29}+\cdots)q^{3}+\cdots$
3748.1.bg.a	$3748$	$1$	3748.bg	3748.ag	$78$	$24$	$1$	$1.870$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q-\zeta_{78}^{29}q^{2}-\zeta_{78}^{19}q^{4}+(\zeta_{78}^{4}-\zeta_{78}^{21}+\cdots)q^{5}+\cdots$
3756.1.bt.a	$3756$	$1$	3756.bt	939.x	$78$	$24$	$1$	$1.874$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-4$	$1$		$q+\zeta_{78}^{28}q^{3}+(-\zeta_{78}^{9}+\zeta_{78}^{36})q^{7}+\cdots$
3767.1.b.c	$3767$	$1$	3767.b	3767.b	$2$	$12$	$12$	$1.880$	$\Q(\zeta_{39})^+$	$D_{39}$	$\Q(\sqrt{-3767}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots$
3792.1.da.a	$3792$	$1$	3792.da	237.o	$78$	$24$	$1$	$1.892$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{78}^{28}q^{3}+(-\zeta_{78}^{8}+\zeta_{78}^{35})q^{7}+\cdots$
3829.1.cd.a	$3829$	$1$	3829.cd	3829.bd	$78$	$24$	$1$	$1.911$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(-\zeta_{78}^{7}-\zeta_{78}^{15})q^{2}+(\zeta_{78}^{14}+\zeta_{78}^{22}+\cdots)q^{4}+\cdots$
3857.1.x.c	$3857$	$1$	3857.x	3857.x	$6$	$24$	$12$	$1.925$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-551}) $	None		$4$	$0$	$-2$	$1$	$-1$	$-2$	$1$		$q+(\zeta_{78}^{7}+\zeta_{78}^{19})q^{2}+(\zeta_{78}^{25}+\zeta_{78}^{27}+\cdots)q^{3}+\cdots$

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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.