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 286 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
234.2.a.a	$234$	$2$	234.a	1.a	$1$	$1$	$1$	$1.868$	$\Q$	None	✓	✓	✓	✓	234.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots$
234.2.a.b	$234$	$2$	234.a	1.a	$1$	$1$	$1$	$1.868$	$\Q$	None	✓		✓	✓	26.2.a.b	$1$	$0$	$-1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
234.2.a.c	$234$	$2$	234.a	1.a	$1$	$1$	$1$	$1.868$	$\Q$	None	✓				78.2.a.a	$1$	$0$	$1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+4q^{7}+q^{8}-2q^{10}+\cdots$
234.2.a.d	$234$	$2$	234.a	1.a	$1$	$1$	$1$	$1.868$	$\Q$	None	✓	✓	✓	✓	234.2.a.a	$1$	$0$	$1$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots$
234.2.a.e	$234$	$2$	234.a	1.a	$1$	$1$	$1$	$1.868$	$\Q$	None	✓				26.2.a.a	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots$
234.2.b.a	$234$	$2$	234.b	13.b	$2$	$2$	$2$	$1.868$	$\Q(\sqrt{-1}) $	None					78.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}+2 i q^{7}-i q^{8}+\cdots$
234.2.b.b	$234$	$2$	234.b	13.b	$2$	$2$	$2$	$1.868$	$\Q(\sqrt{-1}) $	None					26.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-3 i q^{5}-3 i q^{7}-i q^{8}+\cdots$
234.2.e.a	$234$	$2$	234.e	9.c	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None		✓			234.2.e.a	$2$	$0$	$-1$	$3$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
234.2.e.b	$234$	$2$	234.e	9.c	$3$	$4$	$2$	$1.868$	$\Q(\zeta_{12})$	None		✓			234.2.e.b	$2$	$0$	$2$	$0$	$-2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{2}-\beta_{2} q^{3}+(\beta_1-1)q^{4}+\cdots$
234.2.e.c	$234$	$2$	234.e	9.c	$3$	$4$	$2$	$1.868$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			234.2.e.c	$2$	$0$	$2$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
234.2.e.d	$234$	$2$	234.e	9.c	$3$	$6$	$3$	$1.868$	6.0.309123.1	None		✓			234.2.e.d	$2$	$0$	$3$	$-2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots$
234.2.e.e	$234$	$2$	234.e	9.c	$3$	$8$	$4$	$1.868$	8.0.508277025.1	None		✓	✓		234.2.e.e	$2$	$0$	$-4$	$3$	$-2$	$-4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{7})q^{2}+(-\beta _{3}+\beta _{4})q^{3}-\beta _{7}q^{4}+\cdots$
234.2.f.a	$234$	$2$	234.f	117.h	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None		✓			234.2.f.a	$2$	$0$	$-2$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
234.2.f.b	$234$	$2$	234.f	117.h	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None		✓			234.2.f.b	$2$	$0$	$2$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
234.2.f.c	$234$	$2$	234.f	117.h	$3$	$12$	$6$	$1.868$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			234.2.f.c	$2$	$0$	$-12$	$0$	$-3$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-\beta _{3}-\beta _{6})q^{3}+q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
234.2.f.d	$234$	$2$	234.f	117.h	$3$	$12$	$6$	$1.868$	12.0.$\cdots$.1	None		✓			234.2.f.d	$2$	$0$	$12$	$0$	$1$	$-5$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{9}+\beta _{10})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
234.2.g.a	$234$	$2$	234.g	117.f	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None		✓			234.2.f.b	$2$	$0$	$-1$	$-3$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
234.2.g.b	$234$	$2$	234.g	117.f	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None		✓			234.2.f.a	$2$	$0$	$1$	$3$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
234.2.g.c	$234$	$2$	234.g	117.f	$3$	$12$	$6$	$1.868$	12.0.$\cdots$.1	None		✓			234.2.f.d	$2$	$0$	$-6$	$3$	$1$	$10$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-1-\beta _{1})q^{4}+\cdots$
234.2.g.d	$234$	$2$	234.g	117.f	$3$	$12$	$6$	$1.868$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			234.2.f.c	$2$	$0$	$6$	$-3$	$-3$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{8}q^{2}+\beta _{6}q^{3}+(-1+\beta _{8})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
234.2.h.a	$234$	$2$	234.h	13.c	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None					78.2.e.a	$2$	$0$	$-1$	$0$	$-6$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}-2\zeta_{6}q^{7}+\cdots$
234.2.h.b	$234$	$2$	234.h	13.c	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None					78.2.e.b	$2$	$0$	$-1$	$0$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+2\zeta_{6}q^{7}+\cdots$
234.2.h.c	$234$	$2$	234.h	13.c	$3$	$2$	$1$	$1.868$	$\Q(\sqrt{-3}) $	None					26.2.c.a	$2$	$0$	$1$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-4\zeta_{6}q^{7}+\cdots$
234.2.h.d	$234$	$2$	234.h	13.c	$3$	$4$	$2$	$1.868$	$\Q(\sqrt{-3}, \sqrt{10})$	None		✓			234.2.h.d	$2$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots$
234.2.h.e	$234$	$2$	234.h	13.c	$3$	$4$	$2$	$1.868$	$\Q(\sqrt{-3}, \sqrt{10})$	None		✓			234.2.h.d	$2$	$0$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+\cdots$
234.2.j.a	$234$	$2$	234.j	39.f	$4$	$4$	$2$	$1.868$	$\Q(\zeta_{8})$	None		✓	✓	✓	234.2.j.a	$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(2+2\zeta_{8}^{2})q^{7}+\cdots$
234.2.l.a	$234$	$2$	234.l	13.e	$6$	$4$	$2$	$1.868$	$\Q(\zeta_{12})$	None					78.2.i.b	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-1+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
234.2.l.b	$234$	$2$	234.l	13.e	$6$	$4$	$2$	$1.868$	$\Q(\zeta_{12})$	None		✓			234.2.l.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+3\zeta_{12}^{3}q^{5}+\cdots$
234.2.l.c	$234$	$2$	234.l	13.e	$6$	$4$	$2$	$1.868$	$\Q(\zeta_{12})$	None					78.2.i.a	$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(1-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
234.2.p.a	$234$	$2$	234.p	117.r	$6$	$28$	$14$	$1.868$		None		✓	✓	✓	234.2.p.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
234.2.s.a	$234$	$2$	234.s	117.l	$6$	$28$	$14$	$1.868$		None		✓	✓	✓	234.2.p.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
234.2.t.a	$234$	$2$	234.t	117.t	$6$	$28$	$14$	$1.868$		None		✓	✓	✓	234.2.t.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
234.2.x.a	$234$	$2$	234.x	39.k	$12$	$8$	$2$	$1.868$	$\Q(\zeta_{24})$	None		✓			234.2.x.a	$4$	$0$	$0$	$0$	$0$	$16$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
234.2.x.b	$234$	$2$	234.x	39.k	$12$	$16$	$4$	$1.868$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		234.2.x.b	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{6}$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{3}q^{2}+\beta _{4}q^{4}+\beta _{14}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
234.2.y.a	$234$	$2$	234.y	117.x	$12$	$56$	$14$	$1.868$		None		✓	✓	✓	234.2.y.a	$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{12}]$
234.2.z.a	$234$	$2$	234.z	117.ac	$12$	$56$	$14$	$1.868$		None		✓	✓	✓	234.2.y.a	$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{12}]$
234.2.bd.a	$234$	$2$	234.bd	117.z	$12$	$56$	$14$	$1.868$		None		✓	✓	✓	234.2.bd.a	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{12}]$
234.3.c.a	$234$	$3$	234.c	3.b	$2$	$4$	$4$	$6.376$	$\Q(\sqrt{-2}, \sqrt{13})$	None		✓			234.3.c.a	$2$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-2q^{4}+(-\beta _{1}-3\beta _{2})q^{5}+\cdots$
234.3.c.b	$234$	$3$	234.c	3.b	$2$	$4$	$4$	$6.376$	$\Q(\sqrt{-2}, \sqrt{13})$	None		✓			234.3.c.b	$2$	$0$	$0$	$0$	$0$	$12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-2q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(3+\cdots)q^{7}+\cdots$
234.3.d.a	$234$	$3$	234.d	39.d	$2$	$4$	$4$	$6.376$	$\Q(\zeta_{8})$	None		✓			234.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{2}+2 q^{4}-6\beta_{2} q^{5}-2\beta_1 q^{7}+\cdots$
234.3.d.b	$234$	$3$	234.d	39.d	$2$	$4$	$4$	$6.376$	$\Q(\zeta_{8})$	None		✓			234.3.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{3} q^{2}+2 q^{4}+\beta_{3} q^{5}+8\beta_1 q^{7}+\cdots$
234.3.d.c	$234$	$3$	234.d	39.d	$2$	$4$	$4$	$6.376$	$\Q(\zeta_{8})$	None		✓			234.3.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{2}+2 q^{4}-6\beta_{2} q^{5}+\beta_1 q^{7}+\cdots$
234.3.i.a	$234$	$3$	234.i	13.d	$4$	$2$	$1$	$6.376$	$\Q(\sqrt{-1}) $	None					26.3.d.a	$2$	$0$	$-2$	$0$	$6$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(3 i+3)q^{5}+\cdots$
234.3.i.b	$234$	$3$	234.i	13.d	$4$	$4$	$2$	$6.376$	$\Q(\zeta_{12})$	None					78.3.f.a	$2$	$0$	$-4$	$0$	$-12$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta_1-1)q^{2}+2\beta_1 q^{4}+(\beta_{2}-3\beta_1-3)q^{5}+\cdots$
234.3.i.c	$234$	$3$	234.i	13.d	$4$	$6$	$3$	$6.376$	6.0.353139264.2	None		✓			234.3.i.c	$2$	$0$	$-6$	$0$	$6$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
234.3.i.d	$234$	$3$	234.i	13.d	$4$	$6$	$3$	$6.376$	6.0.353139264.2	None		✓			234.3.i.c	$2$	$0$	$6$	$0$	$-6$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
234.3.i.e	$234$	$3$	234.i	13.d	$4$	$8$	$4$	$6.376$	8.0.$\cdots$.1	None			✓		78.3.f.b	$2$	$0$	$8$	$0$	$0$	$4$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{3})q^{2}+2\beta _{3}q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots$
234.3.k.a	$234$	$3$	234.k	39.i	$6$	$4$	$2$	$6.376$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			234.3.k.a	$4$	$0$	$0$	$0$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{3}q^{5}+5\beta _{2}q^{7}+\cdots$
234.3.k.b	$234$	$3$	234.k	39.i	$6$	$12$	$6$	$6.376$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		234.3.k.b	$4$	$0$	$0$	$0$	$0$	$-14$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{5}+\beta _{8})q^{2}+(2+2\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
234.3.m.a	$234$	$3$	234.m	117.m	$6$	$56$	$28$	$6.376$		None		✓	✓	✓	234.3.m.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.