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 75 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
3564.1.f.a	$3564$	$1$	3564.f	11.b	$2$	$1$	$1$	$1.779$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓				396.1.m.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-2q^{5}-q^{11}+q^{23}+3q^{25}-q^{31}+\cdots$
3564.1.f.b	$3564$	$1$	3564.f	11.b	$2$	$1$	$1$	$1.779$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓				396.1.m.a	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+q^{11}-q^{23}+2q^{31}+2q^{37}+\cdots$
3564.1.f.c	$3564$	$1$	3564.f	11.b	$2$	$1$	$1$	$1.779$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓				396.1.m.a	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}-q^{11}+q^{23}+2q^{31}+2q^{37}+\cdots$
3564.1.f.d	$3564$	$1$	3564.f	11.b	$2$	$1$	$1$	$1.779$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓				396.1.m.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$		$q+2q^{5}+q^{11}-q^{23}+3q^{25}-q^{31}+\cdots$
3564.1.m.a	$3564$	$1$	3564.m	99.h	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None					44.1.d.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{11}-\zeta_{6}q^{23}+\zeta_{6}q^{31}+\cdots$
3564.1.m.b	$3564$	$1$	3564.m	99.h	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None					44.1.d.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{11}+\zeta_{6}q^{23}+\zeta_{6}q^{31}+\cdots$
3564.1.o.a	$3564$	$1$	3564.o	396.o	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None					1188.1.d.a	$4$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+q^{8}+\cdots$
3564.1.o.b	$3564$	$1$	3564.o	396.o	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None					1188.1.d.a	$4$	$0$	$-1$	$0$	$0$	$1$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+q^{8}+\cdots$
3564.1.o.c	$3564$	$1$	3564.o	396.o	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None					1188.1.d.a	$4$	$0$	$1$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}-q^{8}+\cdots$
3564.1.o.d	$3564$	$1$	3564.o	396.o	$6$	$2$	$1$	$1.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-33}) $	None					1188.1.d.a	$4$	$0$	$1$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}-q^{8}+\cdots$
3564.1.o.e	$3564$	$1$	3564.o	396.o	$6$	$8$	$4$	$1.779$	$\Q(\zeta_{24})$	$D_{4}$	None	$\Q(\sqrt{11}) $			✓		396.1.d.a	$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(-\zeta_{24}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
3564.1.bg.a	$3564$	$1$	3564.bg	297.q	$18$	$6$	$1$	$1.779$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None					1188.1.bg.b	$4$	$0$	$0$	$0$	$-6$	$0$		$1$		$q+(-1-\zeta_{18}^{4})q^{5}+\zeta_{18}^{7}q^{11}+\zeta_{18}^{8}q^{23}+\cdots$
3564.1.bg.b	$3564$	$1$	3564.bg	297.q	$18$	$6$	$1$	$1.779$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None					1188.1.bg.a	$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{5}+\zeta_{18}^{7}q^{11}+\cdots$
3564.1.bl.a	$3564$	$1$	3564.bl	99.n	$30$	$16$	$2$	$1.779$	$\Q(\zeta_{60})$	$A_{5}$	None	None			✓	✓	1188.1.v.a	$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(-\zeta_{60}^{11}-\zeta_{60}^{23})q^{5}+\zeta_{60}^{16}q^{7}+\cdots$
3564.1.bs.a	$3564$	$1$	3564.bs	891.w	$54$	$18$	$1$	$1.779$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-11}) $	None		✓			3564.1.bs.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{54}^{25}q^{3}+(-\zeta_{54}^{15}-\zeta_{54}^{23}+\cdots)q^{5}+\cdots$
3564.1.bs.b	$3564$	$1$	3564.bs	891.w	$54$	$18$	$1$	$1.779$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-11}) $	None		✓			3564.1.bs.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{54}^{7}q^{3}+(-\zeta_{54}^{5}+\zeta_{54}^{6})q^{5}+\cdots$
3564.2.a.a	$3564$	$2$	3564.a	1.a	$1$	$1$	$1$	$28.459$	$\Q$	$_{}$	None	None	✓				396.2.i.c	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+2q^{7}-q^{11}-4q^{13}-4q^{19}+\cdots$
3564.2.a.b	$3564$	$2$	3564.a	1.a	$1$	$1$	$1$	$28.459$	$\Q$	$_{}$	None	None	✓				396.2.i.b	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-q^{11}+4q^{13}-4q^{17}+\cdots$
3564.2.a.c	$3564$	$2$	3564.a	1.a	$1$	$1$	$1$	$28.459$	$\Q$	$_{}$	None	None	✓				396.2.i.a	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-q^{11}+8q^{17}-8q^{19}+\cdots$
3564.2.a.d	$3564$	$2$	3564.a	1.a	$1$	$1$	$1$	$28.459$	$\Q$	$_{}$	None	None	✓				396.2.i.a	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+q^{11}-8q^{17}-8q^{19}+\cdots$
3564.2.a.e	$3564$	$2$	3564.a	1.a	$1$	$1$	$1$	$28.459$	$\Q$	$_{}$	None	None	✓				396.2.i.b	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+q^{11}+4q^{13}+4q^{17}+\cdots$
3564.2.a.f	$3564$	$2$	3564.a	1.a	$1$	$1$	$1$	$28.459$	$\Q$	$_{}$	None	None	✓				396.2.i.c	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}+q^{11}-4q^{13}-4q^{19}+\cdots$
3564.2.a.g	$3564$	$2$	3564.a	1.a	$1$	$2$	$2$	$28.459$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			3564.2.a.g	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}-q^{7}-q^{11}+(-4+\beta )q^{13}+\cdots$
3564.2.a.h	$3564$	$2$	3564.a	1.a	$1$	$2$	$2$	$28.459$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			3564.2.a.h	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-1+2\beta )q^{7}+q^{11}+(2-\beta )q^{13}+\cdots$
3564.2.a.i	$3564$	$2$	3564.a	1.a	$1$	$2$	$2$	$28.459$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			3564.2.a.g	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+q^{11}+(-4+\beta )q^{13}+\cdots$
3564.2.a.j	$3564$	$2$	3564.a	1.a	$1$	$2$	$2$	$28.459$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			3564.2.a.h	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+2\beta )q^{7}-q^{11}+(2-\beta )q^{13}+\cdots$
3564.2.a.k	$3564$	$2$	3564.a	1.a	$1$	$3$	$3$	$28.459$	3.3.321.1	$_{}$	None	None	✓		✓		396.2.i.d	$1$	$1$	$0$	$0$	$-5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{5}+(-2-\beta _{2})q^{7}+q^{11}+\cdots$
3564.2.a.l	$3564$	$2$	3564.a	1.a	$1$	$3$	$3$	$28.459$	3.3.321.1	$_{}$	None	None	✓				396.2.i.d	$1$	$1$	$0$	$0$	$5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{5}+(-2-\beta _{2})q^{7}-q^{11}+\cdots$
3564.2.a.m	$3564$	$2$	3564.a	1.a	$1$	$4$	$4$	$28.459$	4.4.72153.1	$_{}$	None	None	✓				396.2.i.e	$1$	$0$	$0$	$0$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots$
3564.2.a.n	$3564$	$2$	3564.a	1.a	$1$	$4$	$4$	$28.459$	4.4.72153.1	$_{}$	None	None	✓		✓		396.2.i.e	$1$	$0$	$0$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}-q^{11}+\cdots$
3564.2.a.o	$3564$	$2$	3564.a	1.a	$1$	$6$	$6$	$28.459$	6.6.1166692032.1	$_{}$	None	None	✓	✓	✓		3564.2.a.o	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{4}q^{7}-q^{11}+(-1-\beta _{1}+\cdots)q^{13}+\cdots$
3564.2.a.p	$3564$	$2$	3564.a	1.a	$1$	$6$	$6$	$28.459$	6.6.1166692032.1	$_{}$	None	None	✓	✓	✓		3564.2.a.o	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{11}+(-1-\beta _{1}+\cdots)q^{13}+\cdots$
3564.2.b.a	$3564$	$2$	3564.b	33.d	$2$	$4$	$4$	$28.459$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None					396.2.q.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{2}-\beta _{3})q^{11}+(\beta _{2}+\cdots)q^{23}+\cdots$
3564.2.b.b	$3564$	$2$	3564.b	33.d	$2$	$4$	$4$	$28.459$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None					396.2.q.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+(2\beta _{2}-\beta _{3})q^{23}+\cdots$
3564.2.b.c	$3564$	$2$	3564.b	33.d	$2$	$16$	$16$	$28.459$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					396.2.q.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{9})q^{5}+\beta _{6}q^{7}+(\beta _{3}-\beta _{11}+\cdots)q^{11}+\cdots$
3564.2.b.d	$3564$	$2$	3564.b	33.d	$2$	$24$	$24$	$28.459$		$_{}$	None	None		✓	✓		3564.2.b.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3564.2.i.a	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					44.2.a.a	$2$	$0$	$0$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$
3564.2.i.b	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					132.2.a.a	$2$	$0$	$0$	$0$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$
3564.2.i.c	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					1188.2.a.a	$2$	$0$	$0$	$0$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$
3564.2.i.d	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					132.2.a.b	$2$	$0$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$
3564.2.i.e	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					1188.2.a.b	$2$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+4\zeta_{6}q^{13}+\cdots$
3564.2.i.f	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					1188.2.a.b	$2$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+4\zeta_{6}q^{13}+\cdots$
3564.2.i.g	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					132.2.a.a	$2$	$0$	$0$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$
3564.2.i.h	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					1188.2.a.a	$2$	$0$	$0$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$
3564.2.i.i	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					132.2.a.b	$2$	$0$	$0$	$0$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$
3564.2.i.j	$3564$	$2$	3564.i	9.c	$3$	$2$	$1$	$28.459$	$\Q(\sqrt{-3}) $	$_{}$	None	None					44.2.a.a	$2$	$0$	$0$	$0$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$
3564.2.i.k	$3564$	$2$	3564.i	9.c	$3$	$4$	$2$	$28.459$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None					1188.2.a.e	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
3564.2.i.l	$3564$	$2$	3564.i	9.c	$3$	$4$	$2$	$28.459$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			3564.2.a.h	$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{5}+(-2+2\beta _{1}-\beta _{2}+2\beta _{3})q^{7}+\cdots$
3564.2.i.m	$3564$	$2$	3564.i	9.c	$3$	$4$	$2$	$28.459$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			3564.2.a.g	$2$	$0$	$0$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{2}q^{11}+(4-\beta _{1}+\cdots)q^{13}+\cdots$
3564.2.i.n	$3564$	$2$	3564.i	9.c	$3$	$4$	$2$	$28.459$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			3564.2.a.h	$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}+(-2+2\beta _{1}-\beta _{2}+2\beta _{3})q^{7}+\cdots$

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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.