LMFDB - Newform orbit 350.4.a.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,4,Mod(1,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-2,-7,4,0,14,-7,-8,22,0,-33] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$

$=$

$ q - 2 q^{2} - 7 q^{3} + 4 q^{4} + 14 q^{6} - 7 q^{7} - 8 q^{8} + 22 q^{9} - 33 q^{11} - 28 q^{12} + 43 q^{13} + 14 q^{14} + 16 q^{16} - 111 q^{17} - 44 q^{18} - 70 q^{19} + 49 q^{21} + 66 q^{22} - 42 q^{23}+ \cdots - 726 q^{99}+O(q^{100}) $

q - 2 * q^2 - 7 * q^3 + 4 * q^4 + 14 * q^6 - 7 * q^7 - 8 * q^8 + 22 * q^9 - 33 * q^11 - 28 * q^12 + 43 * q^13 + 14 * q^14 + 16 * q^16 - 111 * q^17 - 44 * q^18 - 70 * q^19 + 49 * q^21 + 66 * q^22 - 42 * q^23 + 56 * q^24 - 86 * q^26 + 35 * q^27 - 28 * q^28 - 225 * q^29 - 88 * q^31 - 32 * q^32 + 231 * q^33 + 222 * q^34 + 88 * q^36 + 34 * q^37 + 140 * q^38 - 301 * q^39 + 432 * q^41 - 98 * q^42 + 178 * q^43 - 132 * q^44 + 84 * q^46 - 411 * q^47 - 112 * q^48 + 49 * q^49 + 777 * q^51 + 172 * q^52 + 708 * q^53 - 70 * q^54 + 56 * q^56 + 490 * q^57 + 450 * q^58 + 480 * q^59 + 812 * q^61 + 176 * q^62 - 154 * q^63 + 64 * q^64 - 462 * q^66 - 596 * q^67 - 444 * q^68 + 294 * q^69 + 432 * q^71 - 176 * q^72 + 358 * q^73 - 68 * q^74 - 280 * q^76 + 231 * q^77 + 602 * q^78 + 425 * q^79 - 839 * q^81 - 864 * q^82 - 972 * q^83 + 196 * q^84 - 356 * q^86 + 1575 * q^87 + 264 * q^88 + 960 * q^89 - 301 * q^91 - 168 * q^92 + 616 * q^93 + 822 * q^94 + 224 * q^96 + 709 * q^97 - 98 * q^98 - 726 * q^99

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment:embeddings in the coefficient field

gp:mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

1.1

−2.00000

−7.00000

4.00000

14.0000

−7.00000

−8.00000

22.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$5$	$ +1 $
$7$	$ +1 $

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	350.4.a.b		1
5.b	even	2	1		70.4.a.f	✓	1
5.c	odd	4	2		350.4.c.l		2
7.b	odd	2	1		2450.4.a.s		1
15.d	odd	2	1		630.4.a.j		1
20.d	odd	2	1		560.4.a.c		1
35.c	odd	2	1		490.4.a.i		1
35.i	odd	6	2		490.4.e.h		2
35.j	even	6	2		490.4.e.b		2
40.e	odd	2	1		2240.4.a.bh		1
40.f	even	2	1		2240.4.a.f		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
70.4.a.f	✓	1	5.b	even	2	1
350.4.a.b		1	1.a	even	1	1	trivial
350.4.c.l		2	5.c	odd	4	2
490.4.a.i		1	35.c	odd	2	1
490.4.e.b		2	35.j	even	6	2
490.4.e.h		2	35.i	odd	6	2
560.4.a.c		1	20.d	odd	2	1
630.4.a.j		1	15.d	odd	2	1
2240.4.a.f		1	40.f	even	2	1
2240.4.a.bh		1	40.e	odd	2	1
2450.4.a.s		1	7.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(350))$:

$ T_{3} + 7 $

T3 + 7

$ T_{11} + 33 $

T11 + 33

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 2 $ T + 2
$3$	$ T + 7 $ T + 7
$5$	$ T $ T
$7$	$ T + 7 $ T + 7
$11$	$ T + 33 $ T + 33
$13$	$ T - 43 $ T - 43
$17$	$ T + 111 $ T + 111
$19$	$ T + 70 $ T + 70
$23$	$ T + 42 $ T + 42
$29$	$ T + 225 $ T + 225
$31$	$ T + 88 $ T + 88
$37$	$ T - 34 $ T - 34
$41$	$ T - 432 $ T - 432
$43$	$ T - 178 $ T - 178
$47$	$ T + 411 $ T + 411
$53$	$ T - 708 $ T - 708
$59$	$ T - 480 $ T - 480
$61$	$ T - 812 $ T - 812
$67$	$ T + 596 $ T + 596
$71$	$ T - 432 $ T - 432
$73$	$ T - 358 $ T - 358
$79$	$ T - 425 $ T - 425
$83$	$ T + 972 $ T + 972
$89$	$ T - 960 $ T - 960
$97$	$ T - 709 $ T - 709
show more
show less

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

\(n\):		e.g. 2-40 or 80-90
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more