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 76 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
343.1.b.a	$343$	$1$	343.b	7.b	$2$	$3$	$3$	$0.171$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-7}) $	None	✓	✓	✓	✓	343.1.b.a	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{8}+\cdots$
343.1.d.a	$343$	$1$	343.d	7.d	$6$	$6$	$3$	$0.171$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	343.1.b.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-1+\cdots)q^{4}+\cdots$
343.2.a.a	$343$	$2$	343.a	1.a	$1$	$3$	$3$	$2.739$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	✓			343.2.a.a	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots$
343.2.a.b	$343$	$2$	343.a	1.a	$1$	$3$	$3$	$2.739$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	✓			343.2.a.b	$2$	$0$	$3$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots$
343.2.a.c	$343$	$2$	343.a	1.a	$1$	$6$	$6$	$2.739$	6.6.1279733.1	$_{}$	None	None	✓	✓	✓		343.2.a.c	$1$	$1$	$-2$	$-5$	$-11$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{3})q^{2}+(\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots$
343.2.a.d	$343$	$2$	343.a	1.a	$1$	$6$	$6$	$2.739$	6.6.1279733.1	$_{}$	None	None	✓	✓			343.2.a.c	$1$	$0$	$-2$	$5$	$11$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{3})q^{2}+(-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
343.2.a.e	$343$	$2$	343.a	1.a	$1$	$6$	$6$	$2.739$	6.6.35650048.1	$_{}$	None	None	✓	✓			343.2.a.e	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{2}-\beta _{1}q^{3}+(1-\beta _{2}-2\beta _{4}+\cdots)q^{4}+\cdots$
343.2.c.a	$343$	$2$	343.c	7.c	$3$	$6$	$3$	$2.739$	6.0.64827.1	$_{}$	$\Q(\sqrt{-7}) $	None		✓			343.2.a.b	$4$	$0$	$-3$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-2+2\beta _{1}+\beta _{4}+2\beta _{5})q^{2}+(-\beta _{1}+\cdots)q^{4}+\cdots$
343.2.c.b	$343$	$2$	343.c	7.c	$3$	$6$	$3$	$2.739$	6.0.64827.1	$_{}$	$\Q(\sqrt{-7}) $	None		✓			343.2.a.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(1+\beta _{4}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$
343.2.c.c	$343$	$2$	343.c	7.c	$3$	$12$	$6$	$2.739$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			343.2.a.e	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2}+\beta _{7})q^{2}+(\beta _{1}+\beta _{3})q^{3}+\cdots$
343.2.c.d	$343$	$2$	343.c	7.c	$3$	$12$	$6$	$2.739$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			343.2.a.c	$2$	$0$	$2$	$-5$	$-11$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}-\beta _{8}+\beta _{9})q^{2}+(-\beta _{7}+\beta _{9}+\cdots)q^{3}+\cdots$
343.2.c.e	$343$	$2$	343.c	7.c	$3$	$12$	$6$	$2.739$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			343.2.a.c	$2$	$0$	$2$	$5$	$11$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}-\beta _{8}+\beta _{9})q^{2}+(\beta _{7}-\beta _{9}+\cdots)q^{3}+\cdots$
343.2.e.a	$343$	$2$	343.e	49.e	$7$	$6$	$1$	$2.739$	$\Q(\zeta_{14})$	$_{}$	None	None					49.2.e.a	$2$	$0$	$-3$	$3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
343.2.e.b	$343$	$2$	343.e	49.e	$7$	$12$	$2$	$2.739$	$\Q(\zeta_{21})$	$_{}$	None	None					49.2.e.b	$2$	$0$	$-2$	$0$	$7$	$0$		$7$	$\mathrm{SU}(2)[C_{7}]$	$q+(\beta_{11}-\beta_{9}+\beta_{5})q^{2}+(\beta_{7}-\beta_{6}+\beta_{2}-\beta_1)q^{3}+\cdots$
343.2.e.c	$343$	$2$	343.e	49.e	$7$	$48$	$8$	$2.739$		$_{}$	None	None					49.2.g.a	$2$	$0$	$5$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{7}]$
343.2.e.d	$343$	$2$	343.e	49.e	$7$	$48$	$8$	$2.739$		$_{}$	None	None					49.2.g.a	$2$	$0$	$5$	$7$	$7$	$0$			$\mathrm{SU}(2)[C_{7}]$
343.2.g.a	$343$	$2$	343.g	49.g	$21$	$12$	$1$	$2.739$	$\Q(\zeta_{21})$	$_{}$	None	None					49.2.e.b	$2$	$0$	$1$	$0$	$-14$	$0$		$1$	$\mathrm{SU}(2)[C_{21}]$	$q+(\zeta_{21}+\zeta_{21}^{2}+\zeta_{21}^{8}+\zeta_{21}^{9})q^{2}+\cdots$
343.2.g.b	$343$	$2$	343.g	49.g	$21$	$12$	$1$	$2.739$	$\Q(\zeta_{21})$	$_{}$	None	None					49.2.e.b	$2$	$0$	$1$	$0$	$-7$	$0$		$1$	$\mathrm{SU}(2)[C_{21}]$	$q+(-\zeta_{21}-\zeta_{21}^{9})q^{2}+(-\zeta_{21}+\zeta_{21}^{3}+\cdots)q^{3}+\cdots$
343.2.g.c	$343$	$2$	343.g	49.g	$21$	$12$	$1$	$2.739$	$\Q(\zeta_{21})$	$_{}$	None	None					49.2.e.b	$2$	$0$	$1$	$0$	$7$	$0$		$1$	$\mathrm{SU}(2)[C_{21}]$	$q+(-\zeta_{21}-\zeta_{21}^{9})q^{2}+(\zeta_{21}-\zeta_{21}^{3}+\cdots)q^{3}+\cdots$
343.2.g.d	$343$	$2$	343.g	49.g	$21$	$12$	$1$	$2.739$	$\Q(\zeta_{21})$	$_{}$	None	None					49.2.e.b	$2$	$0$	$1$	$0$	$14$	$0$		$1$	$\mathrm{SU}(2)[C_{21}]$	$q+(\zeta_{21}+\zeta_{21}^{2}+\zeta_{21}^{8}+\zeta_{21}^{9})q^{2}+\cdots$
343.2.g.e	$343$	$2$	343.g	49.g	$21$	$12$	$1$	$2.739$	$\Q(\zeta_{21})$	$_{}$	None	None					49.2.e.a	$4$	$0$	$3$	$-3$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{21}]$	$q+(1-\zeta_{21}^{2}+\zeta_{21}^{3}+\zeta_{21}^{7}-\zeta_{21}^{8}+\cdots)q^{2}+\cdots$
343.2.g.f	$343$	$2$	343.g	49.g	$21$	$12$	$1$	$2.739$	$\Q(\zeta_{21})$	$_{}$	None	None					49.2.e.a	$4$	$0$	$3$	$3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{21}]$	$q+(1-\zeta_{21}^{2}+\zeta_{21}^{3}+\zeta_{21}^{7}-\zeta_{21}^{8}+\cdots)q^{2}+\cdots$
343.2.g.g	$343$	$2$	343.g	49.g	$21$	$48$	$4$	$2.739$		$_{}$	None	None					49.2.g.a	$2$	$0$	$-13$	$14$	$14$	$0$			$\mathrm{SU}(2)[C_{21}]$
343.2.g.h	$343$	$2$	343.g	49.g	$21$	$48$	$4$	$2.739$		$_{}$	None	None					49.2.g.a	$2$	$0$	$8$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{21}]$
343.2.g.i	$343$	$2$	343.g	49.g	$21$	$48$	$4$	$2.739$		$_{}$	None	None					49.2.g.a	$2$	$0$	$8$	$7$	$7$	$0$			$\mathrm{SU}(2)[C_{21}]$
343.2.i.a	$343$	$2$	343.i	343.i	$49$	$1302$	$31$	$2.739$		$_{}$	None	None		✓	✓	✓	343.2.i.a	$2$	$0$	$-42$	$-42$	$-42$	$-42$			$\mathrm{SU}(2)[C_{49}]$
343.2.k.a	$343$	$2$	343.k	343.k	$147$	$2688$	$32$	$2.739$		$_{}$	None	None		✓	✓	✓	343.2.k.a	$2$	$0$	$-84$	$-84$	$-84$	$-84$			$\mathrm{SU}(2)[C_{147}]$
343.3.b.a	$343$	$3$	343.b	7.b	$2$	$3$	$3$	$9.346$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	✓			343.3.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+2\beta _{1}+\beta _{2})q^{2}+(10-3\beta _{1}+\cdots)q^{4}+\cdots$
343.3.b.b	$343$	$3$	343.b	7.b	$2$	$3$	$3$	$9.346$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	✓			343.3.b.b	$2$	$0$	$5$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(2-\beta _{1})q^{2}+(2-4\beta _{1}+\beta _{2})q^{4}+(3+\cdots)q^{8}+\cdots$
343.3.b.c	$343$	$3$	343.b	7.b	$2$	$6$	$6$	$9.346$	6.0.640932544.1	$_{}$	None	None		✓			343.3.b.c	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+2\beta _{4})q^{2}+\beta _{1}q^{3}+(1-4\beta _{2})q^{4}+\cdots$
343.3.b.d	$343$	$3$	343.b	7.b	$2$	$12$	$12$	$9.346$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			343.3.b.d	$2$	$0$	$-2$	$0$	$0$	$0$		$7^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{8}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$
343.3.b.e	$343$	$3$	343.b	7.b	$2$	$24$	$24$	$9.346$		$_{}$	None	None		✓	✓		343.3.b.e	$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
343.3.d.a	$343$	$3$	343.d	7.d	$6$	$6$	$3$	$9.346$	6.0.64827.1	$_{}$	$\Q(\sqrt{-7}) $	None		✓			343.3.b.b	$4$	$0$	$-5$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5})q^{2}+(2+\cdots)q^{4}+\cdots$
343.3.d.b	$343$	$3$	343.d	7.d	$6$	$6$	$3$	$9.346$	6.0.64827.1	$_{}$	$\Q(\sqrt{-7}) $	None		✓			343.3.b.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(3\beta _{1}-3\beta _{2}+\beta _{3}+\beta _{4}+2\beta _{5})q^{2}+\cdots$
343.3.d.c	$343$	$3$	343.d	7.d	$6$	$12$	$6$	$9.346$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			343.3.b.c	$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2\beta _{2}+2\beta _{3}-\beta _{5}+2\beta _{8}-2\beta _{10}+\cdots)q^{2}+\cdots$
343.3.d.d	$343$	$3$	343.d	7.d	$6$	$24$	$12$	$9.346$		$_{}$	None	None		✓			343.3.b.d	$4$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
343.3.d.e	$343$	$3$	343.d	7.d	$6$	$48$	$24$	$9.346$		$_{}$	None	None		✓	✓		343.3.b.e	$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
343.3.f.a	$343$	$3$	343.f	49.f	$14$	$54$	$9$	$9.346$		$_{}$	None	None					49.3.f.a	$2$	$0$	$-5$	$7$	$7$	$0$			$\mathrm{SU}(2)[C_{14}]$
343.3.f.b	$343$	$3$	343.f	49.f	$14$	$96$	$16$	$9.346$		$_{}$	None	None					49.3.h.a	$2$	$0$	$5$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
343.3.f.c	$343$	$3$	343.f	49.f	$14$	$96$	$16$	$9.346$		$_{}$	None	None					49.3.h.a	$2$	$0$	$5$	$7$	$7$	$0$			$\mathrm{SU}(2)[C_{14}]$
343.3.h.a	$343$	$3$	343.h	49.h	$42$	$96$	$8$	$9.346$		$_{}$	None	None					49.3.h.a	$2$	$0$	$-13$	$14$	$14$	$0$			$\mathrm{SU}(2)[C_{42}]$
343.3.h.b	$343$	$3$	343.h	49.h	$42$	$96$	$8$	$9.346$		$_{}$	None	None					49.3.h.a	$2$	$0$	$8$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{42}]$
343.3.h.c	$343$	$3$	343.h	49.h	$42$	$96$	$8$	$9.346$		$_{}$	None	None					49.3.h.a	$2$	$0$	$8$	$7$	$7$	$0$			$\mathrm{SU}(2)[C_{42}]$
343.3.h.d	$343$	$3$	343.h	49.h	$42$	$108$	$9$	$9.346$		$_{}$	None	None					49.3.f.a	$4$	$0$	$5$	$-7$	$-7$	$0$			$\mathrm{SU}(2)[C_{42}]$
343.3.h.e	$343$	$3$	343.h	49.h	$42$	$108$	$9$	$9.346$		$_{}$	None	None					49.3.f.a	$4$	$0$	$5$	$7$	$7$	$0$			$\mathrm{SU}(2)[C_{42}]$
343.3.j.a	$343$	$3$	343.j	343.j	$98$	$2730$	$65$	$9.346$		$_{}$	None	None		✓	✓	✓	343.3.j.a	$2$	$0$	$-42$	$-42$	$-42$	$-42$			$\mathrm{SU}(2)[C_{98}]$
343.3.l.a	$343$	$3$	343.l	343.l	$294$	$5376$	$64$	$9.346$		$_{}$	None	None		✓	✓	✓	343.3.l.a	$2$	$0$	$-84$	$-84$	$-84$	$-84$			$\mathrm{SU}(2)[C_{294}]$
343.4.a.a	$343$	$4$	343.a	1.a	$1$	$3$	$3$	$20.238$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	✓			343.4.a.a	$2$	$0$	$-1$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1+3\beta _{1}+\beta _{2})q^{2}+(18-5\beta _{1}+\cdots)q^{4}+\cdots$
343.4.a.b	$343$	$4$	343.a	1.a	$1$	$3$	$3$	$20.238$	$\Q(\zeta_{14})^+$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	✓			343.4.a.b	$2$	$1$	$6$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(2-\beta _{1}-\beta _{2})q^{2}+(1-3\beta _{1}-2\beta _{2})q^{4}+\cdots$
343.4.a.c	$343$	$4$	343.a	1.a	$1$	$12$	$12$	$20.238$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓			343.4.a.c	$2$	$1$	$-22$	$0$	$0$	$0$	$-$	$7^{3}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$

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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.