LMFDB - Newform orbit 1805.4.a.a

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1805,4,Mod(1,1805)] 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("1805.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1805, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1805.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-5,-4,17,5,20,-32,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	yes
Analytic conductor:	$106.498447560$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
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 - 5 q^{2} - 4 q^{3} + 17 q^{4} + 5 q^{5} + 20 q^{6} - 32 q^{7} - 45 q^{8} - 11 q^{9} - 25 q^{10} - 12 q^{11} - 68 q^{12} + 42 q^{13} + 160 q^{14} - 20 q^{15} + 89 q^{16} + 114 q^{17} + 55 q^{18} + 85 q^{20}+ \cdots + 132 q^{99}+O(q^{100}) $

q - 5 * q^2 - 4 * q^3 + 17 * q^4 + 5 * q^5 + 20 * q^6 - 32 * q^7 - 45 * q^8 - 11 * q^9 - 25 * q^10 - 12 * q^11 - 68 * q^12 + 42 * q^13 + 160 * q^14 - 20 * q^15 + 89 * q^16 + 114 * q^17 + 55 * q^18 + 85 * q^20 + 128 * q^21 + 60 * q^22 + 160 * q^23 + 180 * q^24 + 25 * q^25 - 210 * q^26 + 152 * q^27 - 544 * q^28 - 214 * q^29 + 100 * q^30 + 144 * q^31 - 85 * q^32 + 48 * q^33 - 570 * q^34 - 160 * q^35 - 187 * q^36 - 94 * q^37 - 168 * q^39 - 225 * q^40 + 6 * q^41 - 640 * q^42 - 308 * q^43 - 204 * q^44 - 55 * q^45 - 800 * q^46 + 184 * q^47 - 356 * q^48 + 681 * q^49 - 125 * q^50 - 456 * q^51 + 714 * q^52 + 274 * q^53 - 760 * q^54 - 60 * q^55 + 1440 * q^56 + 1070 * q^58 - 276 * q^59 - 340 * q^60 - 826 * q^61 - 720 * q^62 + 352 * q^63 - 287 * q^64 + 210 * q^65 - 240 * q^66 - 52 * q^67 + 1938 * q^68 - 640 * q^69 + 800 * q^70 + 344 * q^71 + 495 * q^72 - 166 * q^73 + 470 * q^74 - 100 * q^75 + 384 * q^77 + 840 * q^78 + 688 * q^79 + 445 * q^80 - 311 * q^81 - 30 * q^82 + 996 * q^83 + 2176 * q^84 + 570 * q^85 + 1540 * q^86 + 856 * q^87 + 540 * q^88 - 1578 * q^89 + 275 * q^90 - 1344 * q^91 + 2720 * q^92 - 576 * q^93 - 920 * q^94 + 340 * q^96 - 786 * q^97 - 3405 * q^98 + 132 * 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

−5.00000

−4.00000

17.0000

5.00000

20.0000

−32.0000

−45.0000

−11.0000

−25.0000

Atkin-Lehner signs

$ p $	Sign
$5$	$ -1 $
$19$	$ -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	1805.4.a.a		1
19.b	odd	2	1		95.4.a.d	✓	1
57.d	even	2	1		855.4.a.a		1
76.d	even	2	1		1520.4.a.c		1
95.d	odd	2	1		475.4.a.a		1
95.g	even	4	2		475.4.b.a		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.4.a.d	✓	1	19.b	odd	2	1
475.4.a.a		1	95.d	odd	2	1
475.4.b.a		2	95.g	even	4	2
855.4.a.a		1	57.d	even	2	1
1520.4.a.c		1	76.d	even	2	1
1805.4.a.a		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1805))$:

$ T_{2} + 5 $

T2 + 5

$ T_{3} + 4 $

T3 + 4

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T + 5 $ T + 5
$3$	$ T + 4 $ T + 4
$5$	$ T - 5 $ T - 5
$7$	$ T + 32 $ T + 32
$11$	$ T + 12 $ T + 12
$13$	$ T - 42 $ T - 42
$17$	$ T - 114 $ T - 114
$19$	$ T $ T
$23$	$ T - 160 $ T - 160
$29$	$ T + 214 $ T + 214
$31$	$ T - 144 $ T - 144
$37$	$ T + 94 $ T + 94
$41$	$ T - 6 $ T - 6
$43$	$ T + 308 $ T + 308
$47$	$ T - 184 $ T - 184
$53$	$ T - 274 $ T - 274
$59$	$ T + 276 $ T + 276
$61$	$ T + 826 $ T + 826
$67$	$ T + 52 $ T + 52
$71$	$ T - 344 $ T - 344
$73$	$ T + 166 $ T + 166
$79$	$ T - 688 $ T - 688
$83$	$ T - 996 $ T - 996
$89$	$ T + 1578 $ T + 1578
$97$	$ T + 786 $ T + 786
show more
show less

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1805.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