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 69 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
3312.1.c.a	$3312$	$1$	3312.c	23.b	$2$	$1$	$1$	$1.653$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓		✓	✓	23.1.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{13}+q^{23}+q^{25}+q^{29}+q^{31}+\cdots$
3312.1.w.a	$3312$	$1$	3312.w	368.k	$4$	$2$	$1$	$1.653$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None					368.1.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{8}+(-i-1)q^{13}+\cdots$
3312.1.w.b	$3312$	$1$	3312.w	368.k	$4$	$4$	$2$	$1.653$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None			✓		368.1.k.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots$
3312.1.bm.a	$3312$	$1$	3312.bm	207.f	$6$	$6$	$3$	$1.653$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None			✓	✓	207.1.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{9}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
3312.1.bp.a	$3312$	$1$	3312.bp	3312.ap	$12$	$12$	$3$	$1.653$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-23}) $	None		✓			3312.1.bp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{5}q^{2}+\zeta_{36}^{8}q^{3}+\zeta_{36}^{10}q^{4}+\cdots$
3312.1.bp.b	$3312$	$1$	3312.bp	3312.ap	$12$	$12$	$3$	$1.653$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-23}) $	None		✓			3312.1.bp.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{13}q^{2}-\zeta_{36}^{11}q^{3}-\zeta_{36}^{8}q^{4}+\cdots$
3312.1.bw.a	$3312$	$1$	3312.bw	3312.aw	$12$	$12$	$3$	$1.653$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-23}) $	None		✓			3312.1.bw.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{13}q^{2}+\zeta_{36}^{11}q^{3}-\zeta_{36}^{8}q^{4}+\cdots$
3312.1.bw.b	$3312$	$1$	3312.bw	3312.aw	$12$	$12$	$3$	$1.653$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-23}) $	None		✓			3312.1.bw.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{11}q^{2}+\zeta_{36}^{14}q^{3}-\zeta_{36}^{4}q^{4}+\cdots$
3312.2.a.a	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				552.2.a.d	$1$	$1$	$0$	$0$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-2q^{7}+2q^{13}+4q^{17}+6q^{19}+\cdots$
3312.2.a.b	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				46.2.a.a	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+4q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots$
3312.2.a.c	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				828.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots$
3312.2.a.d	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				138.2.a.c	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{13}-2q^{17}+8q^{19}-q^{23}+\cdots$
3312.2.a.e	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				552.2.a.c	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots$
3312.2.a.f	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				184.2.a.c	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}+6q^{11}-2q^{13}-6q^{17}+6q^{19}+\cdots$
3312.2.a.g	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				92.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-q^{13}+6q^{17}-2q^{19}-q^{23}+\cdots$
3312.2.a.h	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				138.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{13}-2q^{19}-q^{23}-5q^{25}+\cdots$
3312.2.a.i	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				184.2.a.d	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-5q^{13}+6q^{17}-6q^{19}+q^{23}+\cdots$
3312.2.a.j	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				552.2.a.b	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+2q^{13}-8q^{17}-6q^{19}+q^{23}+\cdots$
3312.2.a.k	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				69.2.a.a	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+4q^{11}-6q^{13}-4q^{17}-2q^{19}+\cdots$
3312.2.a.l	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				828.2.a.a	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots$
3312.2.a.m	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				552.2.a.a	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-2q^{11}-2q^{13}+4q^{17}+\cdots$
3312.2.a.n	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				138.2.a.a	$1$	$1$	$0$	$0$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-6q^{11}-2q^{13}-q^{23}+\cdots$
3312.2.a.o	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				184.2.a.b	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-2q^{11}+7q^{13}+4q^{17}+\cdots$
3312.2.a.p	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				552.2.a.e	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-2q^{13}+2q^{17}+4q^{19}+\cdots$
3312.2.a.q	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				92.2.a.a	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+2q^{11}-5q^{13}-4q^{17}+\cdots$
3312.2.a.r	$3312$	$2$	3312.a	1.a	$1$	$1$	$1$	$26.446$	$\Q$	$_{}$	None	None	✓				184.2.a.a	$1$	$1$	$0$	$0$	$4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-2q^{7}-4q^{11}-5q^{13}+2q^{17}+\cdots$
3312.2.a.s	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				276.2.a.b	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+\beta q^{7}+4\beta q^{11}+4\beta q^{13}+\cdots$
3312.2.a.t	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				184.2.a.e	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(2-2\beta )q^{11}+(3-\beta )q^{13}+\cdots$
3312.2.a.u	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				207.2.a.b	$1$	$1$	$0$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+(2+\beta )q^{7}-2\beta q^{11}+\cdots$
3312.2.a.v	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓				414.2.a.e	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}-2q^{7}+(-1+\beta )q^{11}+\cdots$
3312.2.a.w	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		552.2.a.f	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-2q^{7}+(1+\beta )q^{11}+\cdots$
3312.2.a.x	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				1656.2.a.k	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+(1-\beta )q^{7}+(-2+2\beta )q^{11}+\cdots$
3312.2.a.y	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓		✓		276.2.a.a	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2-\beta )q^{7}+4q^{13}+(-4+\cdots)q^{17}+\cdots$
3312.2.a.z	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓				414.2.a.e	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-2q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots$
3312.2.a.ba	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				23.2.a.a	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(-3+\beta )q^{11}+\cdots$
3312.2.a.bb	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				69.2.a.b	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(-1+\beta )q^{7}+4q^{11}+\cdots$
3312.2.a.bc	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				138.2.a.d	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-2\beta q^{7}+(-3+\beta )q^{11}+\cdots$
3312.2.a.bd	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				1656.2.a.k	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(1+\beta )q^{7}+(2+2\beta )q^{11}+\cdots$
3312.2.a.be	$3312$	$2$	3312.a	1.a	$1$	$2$	$2$	$26.446$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				207.2.a.b	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(2-\beta )q^{7}-2\beta q^{11}+(6+\cdots)q^{17}+\cdots$
3312.2.a.bf	$3312$	$2$	3312.a	1.a	$1$	$3$	$3$	$26.446$	3.3.148.1	$_{}$	None	None	✓		✓		552.2.a.g	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots$
3312.2.a.bg	$3312$	$2$	3312.a	1.a	$1$	$4$	$4$	$26.446$	4.4.44688.2	$_{}$	None	None	✓		✓		1656.2.a.o	$1$	$1$	$0$	$0$	$-4$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+(\beta _{2}-\beta _{3})q^{11}+\cdots$
3312.2.a.bh	$3312$	$2$	3312.a	1.a	$1$	$4$	$4$	$26.446$	4.4.44688.2	$_{}$	None	None	✓		✓		1656.2.a.o	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots$
3312.2.e.a	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			3312.2.e.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+2\beta q^{7}-4q^{11}-4q^{13}+3\beta q^{17}+\cdots$
3312.2.e.b	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			3312.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}-\beta q^{7}-2q^{11}+2q^{13}-5\beta q^{19}+\cdots$
3312.2.e.c	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			3312.2.e.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3\beta q^{7}-2q^{11}+2q^{13}+2\beta q^{17}+\cdots$
3312.2.e.d	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			3312.2.e.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3\beta q^{7}+2q^{11}+2q^{13}+2\beta q^{17}+\cdots$
3312.2.e.e	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			3312.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+\beta q^{7}+2q^{11}+2q^{13}+5\beta q^{19}+\cdots$
3312.2.e.f	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			3312.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2\beta q^{7}+4q^{11}-4q^{13}+3\beta q^{17}+\cdots$
3312.2.e.g	$3312$	$2$	3312.e	12.b	$2$	$16$	$16$	$26.446$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			3312.2.e.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}-\beta _{8}q^{7}+\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots$
3312.2.e.h	$3312$	$2$	3312.e	12.b	$2$	$16$	$16$	$26.446$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			3312.2.e.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+\beta _{8}q^{7}-\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots$

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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.