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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 196 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
176.1.h.a	$176$	$1$	176.h	11.b	$2$	$1$	$1$	$0.088$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓		✓	✓	44.1.d.a	$2$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{5}-q^{11}-q^{15}+q^{23}-q^{27}+\cdots$
176.2.a.a	$176$	$2$	176.a	1.a	$1$	$1$	$1$	$1.405$	$\Q$	$_{}$	None	None	✓		✓	✓	44.2.a.a	$1$	$1$	$0$	$-1$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots$
176.2.a.b	$176$	$2$	176.a	1.a	$1$	$1$	$1$	$1.405$	$\Q$	$_{}$	None	None	✓		✓	✓	11.2.a.a	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots$
176.2.a.c	$176$	$2$	176.a	1.a	$1$	$1$	$1$	$1.405$	$\Q$	$_{}$	None	None	✓				88.2.a.a	$1$	$0$	$0$	$3$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots$
176.2.a.d	$176$	$2$	176.a	1.a	$1$	$2$	$2$	$1.405$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		88.2.a.b	$1$	$0$	$0$	$-1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots$
176.2.e.a	$176$	$2$	176.e	44.c	$2$	$2$	$2$	$1.405$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			176.2.e.a	$4$	$0$	$0$	$0$	$6$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+3q^{5}-8q^{9}+\beta q^{11}-3\beta q^{15}+\cdots$
176.2.e.b	$176$	$2$	176.e	44.c	$2$	$4$	$4$	$1.405$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓	✓		176.2.e.b	$4$	$0$	$0$	$0$	$-6$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{3})q^{9}+\cdots$
176.2.i.a	$176$	$2$	176.i	176.i	$4$	$44$	$22$	$1.405$		$_{}$	None	None		✓	✓	✓	176.2.i.a	$4$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
176.2.j.a	$176$	$2$	176.j	16.e	$4$	$40$	$20$	$1.405$		$_{}$	None	None		✓	✓	✓	176.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
176.2.m.a	$176$	$2$	176.m	11.c	$5$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	$_{}$	None	None					88.2.i.a	$2$	$0$	$0$	$-3$	$3$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
176.2.m.b	$176$	$2$	176.m	11.c	$5$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	$_{}$	None	None					44.2.e.a	$2$	$0$	$0$	$1$	$3$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
176.2.m.c	$176$	$2$	176.m	11.c	$5$	$4$	$1$	$1.405$	$\Q(\zeta_{10})$	$_{}$	None	None					22.2.c.a	$2$	$0$	$0$	$4$	$-6$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots$
176.2.m.d	$176$	$2$	176.m	11.c	$5$	$8$	$2$	$1.405$	8.0.682515625.5	$_{}$	None	None			✓		88.2.i.b	$2$	$0$	$0$	$1$	$-3$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
176.2.q.a	$176$	$2$	176.q	44.g	$10$	$8$	$2$	$1.405$	8.0.484000000.6	$_{}$	None	None		✓			176.2.q.a	$4$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{1}q^{3}+(\beta _{2}-\beta _{3}+\beta _{5})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
176.2.q.b	$176$	$2$	176.q	44.g	$10$	$16$	$4$	$1.405$	16.0.$\cdots$.1	$_{}$	None	None		✓	✓		176.2.q.b	$4$	$0$	$0$	$0$	$6$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{2}+\beta _{4}-\beta _{6}-\beta _{9}+\beta _{11})q^{3}+(1+\cdots)q^{5}+\cdots$
176.2.w.a	$176$	$2$	176.w	176.w	$20$	$176$	$22$	$1.405$		$_{}$	None	None		✓	✓	✓	176.2.w.a	$4$	$0$	$-6$	$-6$	$-6$	$0$			$\mathrm{SU}(2)[C_{20}]$
176.2.x.a	$176$	$2$	176.x	176.x	$20$	$176$	$22$	$1.405$		$_{}$	None	None		✓	✓	✓	176.2.x.a	$4$	$0$	$-10$	$-6$	$-6$	$-20$			$\mathrm{SU}(2)[C_{20}]$
176.3.d.a	$176$	$3$	176.d	4.b	$2$	$2$	$2$	$4.796$	$\Q(\sqrt{-11}) $	$_{}$	None	None		✓			176.3.d.a	$2$	$0$	$0$	$0$	$10$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+5q^{5}-2\beta q^{7}-2q^{9}+\beta q^{11}+\cdots$
176.3.d.b	$176$	$3$	176.d	4.b	$2$	$8$	$8$	$4.796$	8.0.$\cdots$.2	$_{}$	None	None		✓	✓		176.3.d.b	$2$	$0$	$0$	$0$	$2$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{4}-\beta _{5}+\beta _{7})q^{7}+\cdots$
176.3.h.a	$176$	$3$	176.h	11.b	$2$	$1$	$1$	$4.796$	$\Q$	$_{}$	$\Q(\sqrt{-11}) $	None	✓				11.3.b.a	$2$	$0$	$0$	$5$	$-1$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5q^{3}-q^{5}+2^{4}q^{9}+11q^{11}-5q^{15}+\cdots$
176.3.h.b	$176$	$3$	176.h	11.b	$2$	$2$	$2$	$4.796$	$\Q(\sqrt{33}) $	$_{}$	$\Q(\sqrt{-11}) $	None	✓				44.3.d.a	$2$	$0$	$0$	$-5$	$1$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-2-\beta )q^{3}+(2-3\beta )q^{5}+(3+5\beta )q^{9}+\cdots$
176.3.h.c	$176$	$3$	176.h	11.b	$2$	$2$	$2$	$4.796$	$\Q(\sqrt{-2}) $	$_{}$	None	None					22.3.b.a	$2$	$0$	$0$	$-2$	$-2$	$0$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-q^{5}+\beta q^{7}-8q^{9}+(-7-\beta )q^{11}+\cdots$
176.3.h.d	$176$	$3$	176.h	11.b	$2$	$6$	$6$	$4.796$	6.0.1750426112.2	$_{}$	None	None			✓		88.3.h.a	$2$	$0$	$0$	$4$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+\beta _{3}q^{5}-\beta _{2}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
176.3.k.a	$176$	$3$	176.k	16.f	$4$	$80$	$40$	$4.796$		$_{}$	None	None		✓	✓	✓	176.3.k.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
176.3.l.a	$176$	$3$	176.l	176.l	$4$	$92$	$46$	$4.796$		$_{}$	None	None		✓	✓	✓	176.3.l.a	$4$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
176.3.n.a	$176$	$3$	176.n	11.d	$10$	$4$	$1$	$4.796$	$\Q(\zeta_{10})$	$_{}$	None	None					11.3.d.a	$2$	$0$	$0$	$0$	$-4$	$-10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(2-3\zeta_{10}+3\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots$
176.3.n.b	$176$	$3$	176.n	11.d	$10$	$8$	$2$	$4.796$	8.0.64000000.1	$_{}$	None	None					22.3.d.a	$2$	$0$	$0$	$2$	$2$	$30$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\beta _{1}+2\beta _{2}+\beta _{3}-2\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
176.3.n.c	$176$	$3$	176.n	11.d	$10$	$8$	$2$	$4.796$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None					44.3.f.a	$2$	$0$	$0$	$5$	$-1$	$-15$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\beta _{2}+\beta _{4})q^{3}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
176.3.n.d	$176$	$3$	176.n	11.d	$10$	$24$	$6$	$4.796$		$_{}$	None	None			✓		88.3.j.a	$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
176.3.r.a	$176$	$3$	176.r	44.h	$10$	$16$	$4$	$4.796$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			176.3.r.a	$4$	$0$	$0$	$0$	$2$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{11}q^{3}+(-2\beta _{4}+\beta _{6}-\beta _{7}+\beta _{10}+\cdots)q^{5}+\cdots$
176.3.r.b	$176$	$3$	176.r	44.h	$10$	$32$	$8$	$4.796$		$_{}$	None	None		✓	✓		176.3.r.b	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{10}]$
176.3.u.a	$176$	$3$	176.u	176.u	$20$	$368$	$46$	$4.796$		$_{}$	None	None		✓	✓	✓	176.3.u.a	$4$	$0$	$-10$	$-6$	$-6$	$0$			$\mathrm{SU}(2)[C_{20}]$
176.3.v.a	$176$	$3$	176.v	176.v	$20$	$368$	$46$	$4.796$		$_{}$	None	None		✓	✓	✓	176.3.v.a	$4$	$0$	$-6$	$-6$	$-6$	$-12$			$\mathrm{SU}(2)[C_{20}]$
176.4.a.a	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	$\Q$	$_{}$	None	None	✓				88.4.a.b	$1$	$1$	$0$	$-7$	$9$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-7q^{3}+9q^{5}-2q^{7}+22q^{9}+11q^{11}+\cdots$
176.4.a.b	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	$\Q$	$_{}$	None	None	✓				22.4.a.b	$1$	$0$	$0$	$-4$	$14$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+14q^{5}+8q^{7}-11q^{9}+11q^{11}+\cdots$
176.4.a.c	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	$\Q$	$_{}$	None	None	✓				22.4.a.c	$1$	$1$	$0$	$-1$	$-3$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+10q^{7}-26q^{9}-11q^{11}+\cdots$
176.4.a.d	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	$\Q$	$_{}$	None	None	✓				88.4.a.a	$1$	$1$	$0$	$1$	$-7$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-7q^{5}+6q^{7}-26q^{9}+11q^{11}+\cdots$
176.4.a.e	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	$\Q$	$_{}$	None	None	✓				44.4.a.a	$1$	$0$	$0$	$5$	$-7$	$26$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{3}-7q^{5}+26q^{7}-2q^{9}+11q^{11}+\cdots$
176.4.a.f	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	$\Q$	$_{}$	None	None	✓				22.4.a.a	$1$	$1$	$0$	$7$	$-19$	$-14$	$-$	$1$	$\mathrm{SU}(2)$	$q+7q^{3}-19q^{5}-14q^{7}+22q^{9}-11q^{11}+\cdots$
176.4.a.g	$176$	$4$	176.a	1.a	$1$	$2$	$2$	$10.384$	$\Q(\sqrt{97}) $	$_{}$	None	None	✓		✓		44.4.a.b	$1$	$1$	$0$	$-9$	$11$	$-10$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-4-\beta )q^{3}+(6-\beta )q^{5}+(-8+6\beta )q^{7}+\cdots$
176.4.a.h	$176$	$4$	176.a	1.a	$1$	$2$	$2$	$10.384$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				88.4.a.c	$1$	$0$	$0$	$2$	$-6$	$56$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-3+4\beta )q^{5}+(28+\beta )q^{7}+\cdots$
176.4.a.i	$176$	$4$	176.a	1.a	$1$	$2$	$2$	$10.384$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		11.4.a.a	$1$	$0$	$0$	$2$	$2$	$-20$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+2\beta )q^{5}+(-10+\beta )q^{7}+\cdots$
176.4.a.j	$176$	$4$	176.a	1.a	$1$	$3$	$3$	$10.384$	3.3.11109.1	$_{}$	None	None	✓		✓		88.4.a.d	$1$	$0$	$0$	$-2$	$8$	$-24$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(3+\beta _{2})q^{5}+(-8+\cdots)q^{7}+\cdots$
176.4.e.a	$176$	$4$	176.e	44.c	$2$	$2$	$2$	$10.384$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			176.4.e.a	$4$	$0$	$0$	$0$	$-36$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-2\beta q^{3}-18q^{5}-17q^{9}+11\beta q^{11}+\cdots$
176.4.e.b	$176$	$4$	176.e	44.c	$2$	$2$	$2$	$10.384$	$\Q(\sqrt{-19}) $	$_{}$	None	None		✓			176.4.e.b	$2$	$0$	$0$	$0$	$14$	$-40$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+7q^{5}-20q^{7}+8q^{9}+(20+\cdots)q^{11}+\cdots$
176.4.e.c	$176$	$4$	176.e	44.c	$2$	$2$	$2$	$10.384$	$\Q(\sqrt{-19}) $	$_{}$	None	None		✓			176.4.e.b	$2$	$0$	$0$	$0$	$14$	$40$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+7q^{5}+20q^{7}+8q^{9}+(-20+\cdots)q^{11}+\cdots$
176.4.e.d	$176$	$4$	176.e	44.c	$2$	$4$	$4$	$10.384$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			176.4.e.d	$4$	$0$	$0$	$0$	$36$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+(-2\beta _{1}-\beta _{2})q^{3}+(9+\beta _{3})q^{5}+(-2^{5}+\cdots)q^{9}+\cdots$
176.4.e.e	$176$	$4$	176.e	44.c	$2$	$8$	$8$	$10.384$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	✓		176.4.e.e	$4$	$0$	$0$	$0$	$-28$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}+\beta _{3})q^{3}+(-4+\beta _{1})q^{5}-\beta _{4}q^{7}+\cdots$
176.4.i.a	$176$	$4$	176.i	176.i	$4$	$140$	$70$	$10.384$		$_{}$	None	None		✓	✓	✓	176.4.i.a	$4$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
176.4.j.a	$176$	$4$	176.j	16.e	$4$	$120$	$60$	$10.384$		$_{}$	None	None		✓	✓	✓	176.4.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.