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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 115 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
452.1.p.a	$452$	$1$	452.p	452.p	$28$	$12$	$1$	$0.226$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q+\zeta_{28}^{4}q^{2}+\zeta_{28}^{8}q^{4}+(-\zeta_{28}+\zeta_{28}^{10}+\cdots)q^{5}+\cdots$
580.1.bd.a	$580$	$1$	580.bd	580.ad	$28$	$12$	$1$	$0.289$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-\zeta_{28}^{2}q^{2}+\zeta_{28}^{4}q^{4}-\zeta_{28}q^{5}-\zeta_{28}^{6}q^{8}+\cdots$
580.1.bm.a	$580$	$1$	580.bm	580.am	$28$	$12$	$1$	$0.289$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}+\zeta_{28}q^{5}+\zeta_{28}^{9}q^{8}+\cdots$
791.1.x.a	$791$	$1$	791.x	791.x	$28$	$12$	$1$	$0.395$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+(-\zeta_{28}^{3}+\zeta_{28}^{7})q^{2}+(-1+\zeta_{28}^{6}+\cdots)q^{4}+\cdots$
812.1.bi.a	$812$	$1$	812.bi	812.ai	$28$	$12$	$1$	$0.405$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{12}q^{2}-\zeta_{28}^{10}q^{4}-\zeta_{28}^{13}q^{7}+\cdots$
812.1.bi.b	$812$	$1$	812.bi	812.ai	$28$	$12$	$1$	$0.405$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}+\zeta_{28}^{13}q^{7}+\cdots$
904.1.bf.a	$904$	$1$	904.bf	904.af	$28$	$12$	$1$	$0.451$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q-\zeta_{28}^{4}q^{2}+(-\zeta_{28}^{8}+\zeta_{28}^{9})q^{3}+\cdots$
928.1.bs.a	$928$	$1$	928.bs	29.f	$28$	$12$	$1$	$0.463$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{28}^{4}+\zeta_{28}^{12})q^{5}-\zeta_{28}^{3}q^{9}+\cdots$
1011.1.y.a	$1011$	$1$	1011.y	1011.y	$28$	$12$	$1$	$0.505$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots$
1044.1.bi.a	$1044$	$1$	1044.bi	348.v	$28$	$24$	$2$	$0.521$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{56}^{25}q^{2}-\zeta_{56}^{22}q^{4}+(\zeta_{56}^{13}+\cdots)q^{5}+\cdots$
1065.1.l.c	$1065$	$1$	1065.l	1065.l	$4$	$12$	$6$	$0.532$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{28}^{9}+\zeta_{28}^{12})q^{2}+\zeta_{28}q^{3}+(-\zeta_{28}^{4}+\cdots)q^{4}+\cdots$
1065.1.l.d	$1065$	$1$	1065.l	1065.l	$4$	$12$	$6$	$0.532$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+(\zeta_{28}^{9}-\zeta_{28}^{12})q^{2}-\zeta_{28}^{6}q^{3}+(-\zeta_{28}^{4}+\cdots)q^{4}+\cdots$
1136.1.l.b	$1136$	$1$	1136.l	1136.l	$4$	$12$	$6$	$0.567$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$0$	$2$	$-2$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+(\zeta_{28}^{9}-\zeta_{28}^{12})q^{3}+\zeta_{28}^{6}q^{4}+\cdots$
1243.1.v.a	$1243$	$1$	1243.v	1243.v	$28$	$12$	$1$	$0.620$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$2$	$0$	$1$		$q+(\zeta_{28}-\zeta_{28}^{8})q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}+\cdots)q^{5}+\cdots$
1348.1.x.a	$1348$	$1$	1348.x	1348.x	$28$	$12$	$1$	$0.673$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+\zeta_{28}^{6}q^{2}+\zeta_{28}^{12}q^{4}+(-\zeta_{28}^{6}+\cdots)q^{5}+\cdots$
1420.1.l.c	$1420$	$1$	1420.l	1420.l	$4$	$12$	$6$	$0.709$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+(-\zeta_{28}^{2}+\zeta_{28}^{5})q^{3}+\cdots$
1420.1.l.d	$1420$	$1$	1420.l	1420.l	$4$	$12$	$6$	$0.709$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q+\zeta_{28}^{6}q^{2}+(\zeta_{28}^{10}+\zeta_{28}^{11})q^{3}+\cdots$
1421.1.cl.a	$1421$	$1$	1421.cl	29.f	$28$	$12$	$1$	$0.709$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(\zeta_{28}^{3}-\zeta_{28}^{12})q^{2}+(\zeta_{28}+\zeta_{28}^{6}+\cdots)q^{4}+\cdots$
1421.1.dr.a	$1421$	$1$	1421.dr	203.w	$84$	$24$	$1$	$0.709$	$\Q(\zeta_{84})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{84}^{5}-\zeta_{84}^{20})q^{2}+(\zeta_{84}^{10}+\zeta_{84}^{25}+\cdots)q^{4}+\cdots$
1508.1.cc.a	$1508$	$1$	1508.cc	1508.bc	$28$	$12$	$1$	$0.753$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$2$	$0$	$1$		$q-\zeta_{28}^{12}q^{2}-\zeta_{28}^{10}q^{4}+(\zeta_{28}^{6}+\zeta_{28}^{11}+\cdots)q^{5}+\cdots$
1508.1.cd.a	$1508$	$1$	1508.cd	1508.bd	$28$	$12$	$1$	$0.753$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}+(-\zeta_{28}^{5}+\zeta_{28}^{8}+\cdots)q^{5}+\cdots$
1624.1.ct.a	$1624$	$1$	1624.ct	1624.bt	$28$	$12$	$1$	$0.810$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{9}q^{2}-\zeta_{28}^{4}q^{4}+\zeta_{28}^{11}q^{7}+\cdots$
1624.1.ct.b	$1624$	$1$	1624.ct	1624.bt	$28$	$12$	$1$	$0.810$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\zeta_{28}^{8}q^{2}-\zeta_{28}^{2}q^{4}-\zeta_{28}^{11}q^{7}+\cdots$
1677.1.cx.a	$1677$	$1$	1677.cx	1677.bx	$28$	$12$	$1$	$0.837$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{28}q^{3}-\zeta_{28}^{5}q^{4}+(-\zeta_{28}^{10}-\zeta_{28}^{11}+\cdots)q^{7}+\cdots$
1677.1.cx.b	$1677$	$1$	1677.cx	1677.bx	$28$	$12$	$1$	$0.837$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{28}q^{3}-\zeta_{28}^{5}q^{4}+(\zeta_{28}^{3}-\zeta_{28}^{4}+\cdots)q^{7}+\cdots$
1695.1.bt.a	$1695$	$1$	1695.bt	1695.at	$28$	$24$	$2$	$0.846$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{56}+\zeta_{56}^{7})q^{2}-\zeta_{56}^{19}q^{3}+(\zeta_{56}^{2}+\cdots)q^{4}+\cdots$
1740.1.cf.a	$1740$	$1$	1740.cf	1740.bf	$28$	$24$	$2$	$0.868$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\zeta_{56}^{17}q^{2}-\zeta_{56}^{25}q^{3}-\zeta_{56}^{6}q^{4}+\cdots$
1740.1.cf.b	$1740$	$1$	1740.cf	1740.bf	$28$	$24$	$2$	$0.868$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+\zeta_{56}^{17}q^{2}-\zeta_{56}^{5}q^{3}-\zeta_{56}^{6}q^{4}+\cdots$
1796.1.p.a	$1796$	$1$	1796.p	1796.p	$28$	$12$	$1$	$0.896$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{4}q^{4}+(\zeta_{28}-\zeta_{28}^{9}+\cdots)q^{5}+\cdots$
1827.1.cw.a	$1827$	$1$	1827.cw	609.aj	$28$	$24$	$2$	$0.912$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(\zeta_{56}^{19}-\zeta_{56}^{27})q^{2}+(-\zeta_{56}^{10}+\cdots)q^{4}+\cdots$
1827.1.cw.b	$1827$	$1$	1827.cw	609.aj	$28$	$24$	$2$	$0.912$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+(\zeta_{56}^{19}+\zeta_{56}^{27})q^{2}+(-\zeta_{56}^{10}+\cdots)q^{4}+\cdots$
1856.1.ca.a	$1856$	$1$	1856.ca	29.f	$28$	$12$	$1$	$0.926$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{28}^{4}-\zeta_{28}^{12})q^{5}-\zeta_{28}^{3}q^{9}+(-\zeta_{28}^{9}+\cdots)q^{13}+\cdots$
1911.1.cv.a	$1911$	$1$	1911.cv	1911.bv	$28$	$12$	$1$	$0.954$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{9}q^{4}+\zeta_{28}^{8}q^{7}+\cdots$
1911.1.cv.b	$1911$	$1$	1911.cv	1911.bv	$28$	$12$	$1$	$0.954$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{3}q^{3}-\zeta_{28}^{9}q^{4}+\zeta_{28}q^{7}+\zeta_{28}^{6}q^{9}+\cdots$
1967.1.bc.a	$1967$	$1$	1967.bc	1967.ac	$28$	$12$	$1$	$0.982$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$4$	$0$	$0$	$0$	$1$		$q+(\zeta_{28}^{2}+\zeta_{28}^{10})q^{2}+(\zeta_{28}^{4}-\zeta_{28}^{6}+\cdots)q^{4}+\cdots$
1972.1.bw.a	$1972$	$1$	1972.bw	1972.aw	$28$	$12$	$1$	$0.984$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{28}^{11}q^{2}-\zeta_{28}^{8}q^{4}+(\zeta_{28}^{2}+\zeta_{28}^{13}+\cdots)q^{5}+\cdots$
1972.1.bw.b	$1972$	$1$	1972.bw	1972.aw	$28$	$12$	$1$	$0.984$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{28}^{11}q^{2}-\zeta_{28}^{8}q^{4}+(\zeta_{28}^{6}+\zeta_{28}^{9}+\cdots)q^{5}+\cdots$
1991.1.d.f	$1991$	$1$	1991.d	1991.d	$2$	$12$	$12$	$0.994$	$\Q(\zeta_{56})^+$	$D_{28}$	$\Q(\sqrt{-1991}) $	None	✓	$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q+\beta _{9}q^{2}+\beta _{8}q^{3}+(1-\beta _{10})q^{4}+\beta _{6}q^{5}+\cdots$
2001.1.bf.a	$2001$	$1$	2001.bf	2001.af	$28$	$12$	$1$	$0.999$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{28}^{7}-\zeta_{28}^{10})q^{2}-\zeta_{28}^{9}q^{3}+\cdots$
2001.1.bf.b	$2001$	$1$	2001.bf	2001.af	$28$	$12$	$1$	$0.999$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+(\zeta_{28}^{7}+\zeta_{28}^{10})q^{2}-\zeta_{28}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots$
2019.1.y.a	$2019$	$1$	2019.y	2019.y	$28$	$12$	$1$	$1.008$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+\zeta_{28}^{10}q^{3}-q^{4}+(\zeta_{28}^{3}-\zeta_{28}^{5}+\cdots)q^{7}+\cdots$
2088.1.cn.a	$2088$	$1$	2088.cn	232.u	$28$	$24$	$2$	$1.042$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{56}^{5}q^{2}+\zeta_{56}^{10}q^{4}+(-\zeta_{56}^{3}+\cdots)q^{5}+\cdots$
2233.1.bv.a	$2233$	$1$	2233.bv	2233.av	$28$	$12$	$1$	$1.114$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{28}+\zeta_{28}^{4})q^{2}+(\zeta_{28}^{2}+\zeta_{28}^{5}+\cdots)q^{4}+\cdots$
2233.1.bv.b	$2233$	$1$	2233.bv	2233.av	$28$	$12$	$1$	$1.114$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{28}-\zeta_{28}^{4})q^{2}+(\zeta_{28}^{2}+\zeta_{28}^{5}+\cdots)q^{4}+\cdots$
2248.1.bl.a	$2248$	$1$	2248.bl	2248.al	$28$	$12$	$1$	$1.122$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$2$	$0$	$0$	$1$		$q+\zeta_{28}^{4}q^{2}+(\zeta_{28}^{2}+\zeta_{28}^{13})q^{3}+\zeta_{28}^{8}q^{4}+\cdots$
2279.1.d.f	$2279$	$1$	2279.d	2279.d	$2$	$12$	$12$	$1.137$	$\Q(\zeta_{56})^+$	$D_{28}$	$\Q(\sqrt{-2279}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{9}q^{2}+\beta _{1}q^{3}+(1-\beta _{10})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
2320.1.dr.a	$2320$	$1$	2320.dr	580.ad	$28$	$12$	$1$	$1.158$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{28}^{13}q^{5}-\zeta_{28}^{12}q^{9}+(\zeta_{28}^{3}-\zeta_{28}^{8}+\cdots)q^{13}+\cdots$
2320.1.fg.a	$2320$	$1$	2320.fg	580.am	$28$	$12$	$1$	$1.158$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{9}q^{5}+\zeta_{28}^{12}q^{9}+(\zeta_{28}-\zeta_{28}^{10}+\cdots)q^{13}+\cdots$
2359.1.by.a	$2359$	$1$	2359.by	2359.ay	$28$	$12$	$1$	$1.177$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{28}^{9}-\zeta_{28}^{11})q^{2}+(-\zeta_{28}^{4}+\cdots)q^{4}+\cdots$
2416.1.m.b	$2416$	$1$	2416.m	2416.m	$4$	$12$	$6$	$1.206$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{28}^{13}q^{2}-\zeta_{28}^{12}q^{4}+(\zeta_{28}^{10}+\cdots)q^{5}+\cdots$

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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.