LMFDB - Newform orbit 10002.2.a.h

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Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [10002,2,Mod(1,10002)] 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("10002.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10002, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 10002 = 2 \cdot 3 \cdot 1667 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	10002.a (trivial)

Newform invariants

comment:select newform

sage:traces = [28,-28,-28,28,3,28,5,-28,28,-3,13,-28,-4,-5,-3,28,15,-28,-24, 3,-5,-13,31,28,25,4,-28,5,-9,3,-29,-28,-13,-15,27,28,6,24,4,-3,4,5,-6, 13,3,-31,60,-28,-11,-25,-15,-4,11,28,2,-5,24,9,32,-3,-37,29,5,28,14,13, 12,15,-31,-27,66,-28,0,-6,-25,-24,0,-4,12,3,28,-4,95,-5,9,6,9,-13,16,-3, -54,31,29,-60,87,28,-27,11,13,25] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)

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

Self dual:	yes
Analytic conductor:	$79.8663721017$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) = $ $ 28 q - 28 q^{2} - 28 q^{3} + 28 q^{4} + 3 q^{5} + 28 q^{6} + 5 q^{7} - 28 q^{8} + 28 q^{9} - 3 q^{10} + 13 q^{11} - 28 q^{12} - 4 q^{13} - 5 q^{14} - 3 q^{15} + 28 q^{16} + 15 q^{17} - 28 q^{18} - 24 q^{19}+ \cdots + 13 q^{99}+O(q^{100}) $

28 * q - 28 * q^2 - 28 * q^3 + 28 * q^4 + 3 * q^5 + 28 * q^6 + 5 * q^7 - 28 * q^8 + 28 * q^9 - 3 * q^10 + 13 * q^11 - 28 * q^12 - 4 * q^13 - 5 * q^14 - 3 * q^15 + 28 * q^16 + 15 * q^17 - 28 * q^18 - 24 * q^19 + 3 * q^20 - 5 * q^21 - 13 * q^22 + 31 * q^23 + 28 * q^24 + 25 * q^25 + 4 * q^26 - 28 * q^27 + 5 * q^28 - 9 * q^29 + 3 * q^30 - 29 * q^31 - 28 * q^32 - 13 * q^33 - 15 * q^34 + 27 * q^35 + 28 * q^36 + 6 * q^37 + 24 * q^38 + 4 * q^39 - 3 * q^40 + 4 * q^41 + 5 * q^42 - 6 * q^43 + 13 * q^44 + 3 * q^45 - 31 * q^46 + 60 * q^47 - 28 * q^48 - 11 * q^49 - 25 * q^50 - 15 * q^51 - 4 * q^52 + 11 * q^53 + 28 * q^54 + 2 * q^55 - 5 * q^56 + 24 * q^57 + 9 * q^58 + 32 * q^59 - 3 * q^60 - 37 * q^61 + 29 * q^62 + 5 * q^63 + 28 * q^64 + 14 * q^65 + 13 * q^66 + 12 * q^67 + 15 * q^68 - 31 * q^69 - 27 * q^70 + 66 * q^71 - 28 * q^72 - 6 * q^74 - 25 * q^75 - 24 * q^76 - 4 * q^78 + 12 * q^79 + 3 * q^80 + 28 * q^81 - 4 * q^82 + 95 * q^83 - 5 * q^84 + 9 * q^85 + 6 * q^86 + 9 * q^87 - 13 * q^88 + 16 * q^89 - 3 * q^90 - 54 * q^91 + 31 * q^92 + 29 * q^93 - 60 * q^94 + 87 * q^95 + 28 * q^96 - 27 * q^97 + 11 * q^98 + 13 * q^99

Atkin-Lehner signs

$ p $	Sign
$2$	$ +1 $
$3$	$ +1 $
$1667$	$ -1 $

Inner twists

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

Twists

Twists of this newform have not been computed.

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:	\( N \)	\(=\)	\( 10002 = 2 \cdot 3 \cdot 1667 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	10002.a (trivial)

\( p \)	Sign
\(2\)	\( +1 \)
\(3\)	\( +1 \)
\(1667\)	\( -1 \)

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