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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 210 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
167.1.b.a	$167$	$1$	167.b	167.b	$2$	$5$	$5$	$0.083$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+\beta _{4}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$
271.1.b.a	$271$	$1$	271.b	271.b	$2$	$5$	$5$	$0.135$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-271}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
591.1.d.a	$591$	$1$	591.d	591.d	$2$	$5$	$5$	$0.295$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-591}) $	None	✓	$2$	$0$	$-1$	$5$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
591.1.d.b	$591$	$1$	591.d	591.d	$2$	$5$	$5$	$0.295$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-591}) $	None	✓	$2$	$0$	$1$	$-5$	$1$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
623.1.d.a	$623$	$1$	623.d	623.d	$2$	$5$	$5$	$0.311$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-623}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$5$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$
623.1.d.b	$623$	$1$	623.d	623.d	$2$	$5$	$5$	$0.311$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-623}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-5$	$1$		$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
659.1.b.a	$659$	$1$	659.b	659.b	$2$	$5$	$5$	$0.329$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-659}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
767.1.d.a	$767$	$1$	767.d	767.d	$2$	$5$	$5$	$0.383$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-767}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{2}+\beta _{2}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
767.1.d.b	$767$	$1$	767.d	767.d	$2$	$5$	$5$	$0.383$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-767}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+\cdots$
839.1.b.b	$839$	$1$	839.b	839.b	$2$	$5$	$5$	$0.419$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-839}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}+\beta _{4}q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
871.1.d.a	$871$	$1$	871.d	871.d	$2$	$5$	$5$	$0.435$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-871}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots$
871.1.d.b	$871$	$1$	871.d	871.d	$2$	$5$	$5$	$0.435$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-871}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
879.1.d.a	$879$	$1$	879.d	879.d	$2$	$5$	$5$	$0.439$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-879}) $	None	✓	$2$	$0$	$-1$	$5$	$-1$	$0$	$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
879.1.d.b	$879$	$1$	879.d	879.d	$2$	$5$	$5$	$0.439$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-879}) $	None	✓	$2$	$0$	$1$	$-5$	$1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
967.1.b.a	$967$	$1$	967.b	967.b	$2$	$5$	$5$	$0.483$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-967}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-\beta _{1}+\beta _{4})q^{8}+\cdots$
1076.1.d.a	$1076$	$1$	1076.d	1076.d	$2$	$5$	$5$	$0.537$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-269}) $	None	✓	$2$	$0$	$-5$	$1$	$-1$	$1$	$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
1076.1.d.b	$1076$	$1$	1076.d	1076.d	$2$	$5$	$5$	$0.537$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-269}) $	None	✓	$2$	$0$	$5$	$-1$	$-1$	$-1$	$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots$
1111.1.d.a	$1111$	$1$	1111.d	1111.d	$2$	$5$	$5$	$0.554$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1111}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots$
1111.1.d.b	$1111$	$1$	1111.d	1111.d	$2$	$5$	$5$	$0.554$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1111}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
1167.1.d.a	$1167$	$1$	1167.d	1167.d	$2$	$5$	$5$	$0.582$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1167}) $	None	✓	$2$	$0$	$-1$	$5$	$0$	$-1$	$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{4}q^{6}+\cdots$
1167.1.d.b	$1167$	$1$	1167.d	1167.d	$2$	$5$	$5$	$0.582$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1167}) $	None	✓	$2$	$0$	$1$	$-5$	$0$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
1283.1.b.a	$1283$	$1$	1283.b	1283.b	$2$	$5$	$5$	$0.640$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1283}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots$
1303.1.b.a	$1303$	$1$	1303.b	1303.b	$2$	$5$	$5$	$0.650$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1303}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-\beta _{1}+\beta _{4})q^{8}+\cdots$
1304.1.h.a	$1304$	$1$	1304.h	1304.h	$2$	$5$	$5$	$0.651$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-326}) $	None	✓	$2$	$0$	$-5$	$1$	$1$	$0$	$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
1304.1.h.b	$1304$	$1$	1304.h	1304.h	$2$	$5$	$5$	$0.651$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-326}) $	None	✓	$2$	$0$	$5$	$-1$	$-1$	$0$	$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1307.1.b.a	$1307$	$1$	1307.b	1307.b	$2$	$5$	$5$	$0.652$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1307}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
1331.1.b.a	$1331$	$1$	1331.b	11.b	$2$	$5$	$5$	$0.664$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
1391.1.d.c	$1391$	$1$	1391.d	1391.d	$2$	$5$	$5$	$0.694$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1391}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots$
1391.1.d.d	$1391$	$1$	1391.d	1391.d	$2$	$5$	$5$	$0.694$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1391}) $	None	✓	$2$	$0$	$1$	$-1$	$1$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$
1459.1.b.a	$1459$	$1$	1459.b	1459.b	$2$	$5$	$5$	$0.728$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1459}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}+\beta _{4}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
1503.1.d.a	$1503$	$1$	1503.d	167.b	$2$	$5$	$5$	$0.750$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
1531.1.b.a	$1531$	$1$	1531.b	1531.b	$2$	$5$	$5$	$0.764$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1531}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}+\beta _{4}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
1556.1.d.a	$1556$	$1$	1556.d	1556.d	$2$	$5$	$5$	$0.777$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-389}) $	None	✓	$2$	$0$	$-5$	$1$	$-1$	$0$	$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
1556.1.d.b	$1556$	$1$	1556.d	1556.d	$2$	$5$	$5$	$0.777$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-389}) $	None	✓	$2$	$0$	$5$	$-1$	$-1$	$0$	$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1583.1.b.b	$1583$	$1$	1583.b	1583.b	$2$	$5$	$5$	$0.790$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1583}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(1-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
1591.1.d.a	$1591$	$1$	1591.d	1591.d	$2$	$5$	$5$	$0.794$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1591}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
1591.1.d.b	$1591$	$1$	1591.d	1591.d	$2$	$5$	$5$	$0.794$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1591}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
1631.1.d.b	$1631$	$1$	1631.d	1631.d	$2$	$5$	$5$	$0.814$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1631}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$5$	$1$		$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots$
1631.1.d.c	$1631$	$1$	1631.d	1631.d	$2$	$5$	$5$	$0.814$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1631}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$5$	$1$		$q-\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
1639.1.d.a	$1639$	$1$	1639.d	1639.d	$2$	$5$	$5$	$0.818$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1639}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
1639.1.d.b	$1639$	$1$	1639.d	1639.d	$2$	$5$	$5$	$0.818$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1639}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
1655.1.d.c	$1655$	$1$	1655.d	1655.d	$2$	$5$	$5$	$0.826$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1655}) $	None	✓	$2$	$0$	$-1$	$-1$	$5$	$-1$	$1$		$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(1-\beta _{3})q^{4}+q^{5}+\cdots$
1655.1.d.d	$1655$	$1$	1655.d	1655.d	$2$	$5$	$5$	$0.826$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1655}) $	None	✓	$2$	$0$	$1$	$1$	$5$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+\cdots$
1699.1.b.a	$1699$	$1$	1699.b	1699.b	$2$	$5$	$5$	$0.848$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1699}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}+\beta _{4}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
1903.1.d.a	$1903$	$1$	1903.d	1903.d	$2$	$5$	$5$	$0.950$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1903}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1903.1.d.b	$1903$	$1$	1903.d	1903.d	$2$	$5$	$5$	$0.950$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1903}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
1919.1.d.b	$1919$	$1$	1919.d	1919.d	$2$	$5$	$5$	$0.958$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1919}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(1-\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
1919.1.d.c	$1919$	$1$	1919.d	1919.d	$2$	$5$	$5$	$0.958$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1919}) $	None	✓	$2$	$0$	$1$	$1$	$-1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+\cdots$
1951.1.b.b	$1951$	$1$	1951.b	1951.b	$2$	$5$	$5$	$0.974$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1951}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1+\cdots)q^{4}+\cdots$
2027.1.b.a	$2027$	$1$	2027.b	2027.b	$2$	$5$	$5$	$1.012$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2027}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{9}+\beta _{4}q^{12}+\cdots$

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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.