LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 113 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1911.1.h.a	$1911$	$1$	1911.h	39.d	$2$	$1$	$1$	$0.954$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓				39.1.d.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
1911.1.h.b	$1911$	$1$	1911.h	39.d	$2$	$2$	$2$	$0.954$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None	✓	✓			1911.1.h.b	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\beta q^{2}-q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{9}+\cdots$
1911.1.h.c	$1911$	$1$	1911.h	39.d	$2$	$2$	$2$	$0.954$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None	✓	✓			1911.1.h.b	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta q^{2}+q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{9}+\cdots$
1911.1.h.d	$1911$	$1$	1911.h	39.d	$2$	$4$	$4$	$0.954$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-39}) $	None	✓	✓			1911.1.h.d	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
1911.1.h.e	$1911$	$1$	1911.h	39.d	$2$	$4$	$4$	$0.954$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-39}) $	None	✓	✓			1911.1.h.d	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
1911.1.s.a	$1911$	$1$	1911.s	273.s	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					273.1.s.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{12}+\cdots$
1911.1.s.b	$1911$	$1$	1911.s	273.s	$6$	$4$	$2$	$0.954$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓		273.1.s.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{4}q^{6}+\cdots$
1911.1.w.a	$1911$	$1$	1911.w	273.w	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $					39.1.d.a	$8$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{12}+\cdots$
1911.1.w.b	$1911$	$1$	1911.w	273.w	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $					39.1.d.a	$8$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
1911.1.w.c	$1911$	$1$	1911.w	273.w	$6$	$4$	$2$	$0.954$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1911.1.h.b	$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots$
1911.1.w.d	$1911$	$1$	1911.w	273.w	$6$	$4$	$2$	$0.954$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1911.1.h.b	$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots$
1911.1.w.e	$1911$	$1$	1911.w	273.w	$6$	$8$	$4$	$0.954$	8.0.339738624.2	$D_{8}$	$\Q(\sqrt{-39}) $	None		✓			1911.1.h.d	$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q+\beta _{3}q^{2}+\beta _{5}q^{3}+(\beta _{5}-\beta _{6})q^{4}+\beta _{1}q^{5}+\cdots$
1911.1.w.f	$1911$	$1$	1911.w	273.w	$6$	$8$	$4$	$0.954$	8.0.339738624.2	$D_{8}$	$\Q(\sqrt{-39}) $	None		✓			1911.1.h.d	$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q+\beta _{3}q^{2}-\beta _{5}q^{3}+(\beta _{5}-\beta _{6})q^{4}-\beta _{1}q^{5}+\cdots$
1911.1.x.a	$1911$	$1$	1911.x	273.x	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓	✓	273.1.x.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+\zeta_{6}q^{4}+q^{9}+\zeta_{6}q^{12}-\zeta_{6}q^{13}+\cdots$
1911.1.bc.a	$1911$	$1$	1911.bc	39.h	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					273.1.x.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}-q^{12}+\cdots$
1911.1.bc.b	$1911$	$1$	1911.bc	39.h	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					273.1.x.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots$
1911.1.be.a	$1911$	$1$	1911.be	39.i	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					273.1.s.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}+q^{12}+\cdots$
1911.1.be.b	$1911$	$1$	1911.be	39.i	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					273.1.s.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots$
1911.1.be.c	$1911$	$1$	1911.be	39.i	$6$	$4$	$2$	$0.954$	$\Q(\zeta_{12})$	$A_{4}$	None	None					273.1.s.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\cdots$
1911.1.be.d	$1911$	$1$	1911.be	39.i	$6$	$4$	$2$	$0.954$	$\Q(\zeta_{12})$	$A_{4}$	None	None					273.1.s.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}^{3}q^{5}+\cdots$
1911.1.bm.a	$1911$	$1$	1911.bm	273.am	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					273.1.s.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-\zeta_{6}q^{4}+q^{9}+\zeta_{6}q^{12}+\zeta_{6}q^{13}+\cdots$
1911.1.bm.b	$1911$	$1$	1911.bm	273.am	$6$	$4$	$2$	$0.954$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓		273.1.s.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{2}q^{6}+\cdots$
1911.1.bp.a	$1911$	$1$	1911.bp	273.ap	$6$	$2$	$1$	$0.954$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓	✓	273.1.x.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}-q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{12}+\cdots$
1911.1.bt.a	$1911$	$1$	1911.bt	273.as	$12$	$4$	$1$	$0.954$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None			✓	✓	273.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}^{4}q^{9}+\cdots$
1911.1.cb.a	$1911$	$1$	1911.cb	273.ba	$12$	$4$	$1$	$0.954$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None					273.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}q^{4}-\zeta_{12}^{4}q^{9}-q^{12}+\cdots$
1911.1.cb.b	$1911$	$1$	1911.cb	273.ba	$12$	$4$	$1$	$0.954$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None					273.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{4}-\zeta_{12}^{4}q^{9}+q^{12}+\cdots$
1911.1.cc.a	$1911$	$1$	1911.cc	273.bb	$12$	$4$	$1$	$0.954$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-3}) $	None					273.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{2}q^{12}+\cdots$
1911.1.cc.b	$1911$	$1$	1911.cc	273.bb	$12$	$4$	$1$	$0.954$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-3}) $	None					273.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}+\zeta_{12}q^{4}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{2}q^{12}+\cdots$
1911.1.ci.a	$1911$	$1$	1911.ci	273.bh	$12$	$4$	$1$	$0.954$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None			✓	✓	273.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}-q^{9}+\zeta_{12}^{2}q^{12}+\cdots$
1911.1.cj.a	$1911$	$1$	1911.cj	1911.bj	$14$	$6$	$1$	$0.954$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		✓			1911.1.cj.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{14}^{3}q^{3}-\zeta_{14}^{2}q^{4}-\zeta_{14}q^{7}+\zeta_{14}^{6}q^{9}+\cdots$
1911.1.cj.b	$1911$	$1$	1911.cj	1911.bj	$14$	$6$	$1$	$0.954$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		✓			1911.1.cj.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{14}^{3}q^{3}-\zeta_{14}^{2}q^{4}+\zeta_{14}q^{7}+\zeta_{14}^{6}q^{9}+\cdots$
1911.1.cv.a	$1911$	$1$	1911.cv	1911.bv	$28$	$12$	$1$	$0.954$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		✓			1911.1.cv.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{9}q^{4}+\zeta_{28}^{8}q^{7}+\cdots$
1911.1.cv.b	$1911$	$1$	1911.cv	1911.bv	$28$	$12$	$1$	$0.954$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		✓			1911.1.cv.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{3}q^{3}-\zeta_{28}^{9}q^{4}+\zeta_{28}q^{7}+\zeta_{28}^{6}q^{9}+\cdots$
1911.1.da.a	$1911$	$1$	1911.da	1911.ca	$42$	$12$	$1$	$0.954$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1911.1.da.a	$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{42}^{19}q^{3}+\zeta_{42}^{15}q^{4}-\zeta_{42}^{4}q^{7}+\cdots$
1911.1.dd.a	$1911$	$1$	1911.dd	1911.cd	$42$	$12$	$1$	$0.954$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1911.1.dd.a	$4$	$0$	$0$	$-2$	$0$	$1$		$1$		$q+\zeta_{42}^{6}q^{3}-\zeta_{42}^{11}q^{4}+\zeta_{42}^{16}q^{7}+\cdots$
1911.1.ds.a	$1911$	$1$	1911.ds	1911.cs	$42$	$12$	$1$	$0.954$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1911.1.da.a	$4$	$0$	$0$	$2$	$0$	$1$		$1$		$q-\zeta_{42}^{6}q^{3}-\zeta_{42}^{4}q^{4}+\zeta_{42}^{2}q^{7}+\cdots$
1911.1.dx.a	$1911$	$1$	1911.dx	1911.cx	$42$	$12$	$1$	$0.954$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1911.1.dd.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{42}^{20}q^{3}+\zeta_{42}^{18}q^{4}+\zeta_{42}^{2}q^{7}+\cdots$
1911.1.ea.a	$1911$	$1$	1911.ea	1911.da	$84$	$24$	$1$	$0.954$	$\Q(\zeta_{84})$	$D_{84}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1911.1.ea.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{84}^{33}q^{3}+\zeta_{84}q^{4}+\zeta_{84}^{32}q^{7}+\cdots$
1911.1.ep.a	$1911$	$1$	1911.ep	1911.dp	$84$	$24$	$1$	$0.954$	$\Q(\zeta_{84})$	$D_{84}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1911.1.ea.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{84}^{13}q^{3}+\zeta_{84}^{39}q^{4}+\zeta_{84}^{37}q^{7}+\cdots$
1911.2.a.a	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	$\Q$	$_{}$	None	None	✓				273.2.a.a	$1$	$1$	$-2$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots$
1911.2.a.b	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	$\Q$	$_{}$	None	None	✓				273.2.i.a	$1$	$1$	$-1$	$-1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-4q^{5}+q^{6}+3q^{8}+\cdots$
1911.2.a.c	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	$\Q$	$_{}$	None	None	✓				273.2.i.a	$1$	$0$	$-1$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+4q^{5}-q^{6}+3q^{8}+\cdots$
1911.2.a.d	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	$\Q$	$_{}$	None	None	✓	✓			1911.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{9}-2q^{11}+2q^{12}+\cdots$
1911.2.a.e	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	$\Q$	$_{}$	None	None	✓	✓			1911.2.a.d	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{9}-2q^{11}-2q^{12}+\cdots$
1911.2.a.f	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	$\Q$	$_{}$	None	None	✓				39.2.a.a	$1$	$1$	$1$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots$
1911.2.a.g	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	$\Q$	$_{}$	None	None	✓				273.2.a.b	$1$	$1$	$2$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
1911.2.a.h	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				39.2.a.b	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots$
1911.2.a.i	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1911.2.a.i	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{5}-\beta q^{6}-2\beta q^{8}+\cdots$
1911.2.a.j	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1911.2.a.i	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}-q^{5}+\beta q^{6}-2\beta q^{8}+\cdots$
1911.2.a.k	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				273.2.a.c	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots$

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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.