Properties

Space $M_{34}\left({\textrm{Sp}}(4,\mathbb{Z})\right)$
Name 34_Klingen
Type Klingen Eisenstein series
Weight $34$
Hecke eigenform yes
Field degree $2$

Basic properties

Space: $M_{34}\left({\textrm{Sp}}(4,\mathbb{Z})\right)$
Type: Klingen Eisenstein series
Weight: 34
Hecke eigenform: yes
Integral Fourier coefficients: yes

Coefficient field

Field: $\mathbb{Q}(a)$
Degree: 2
Discriminant: $479 \cdot 4919$
Signature: $(2, 0)$
Is Galois: True
Field polynomial: $x^{2} - x - 589050$
Field generator:$a$

Explicit formula

 (1594 bytes)

Selected eigenvalues $\lambda(l)$ of $T(l)$

$l$$\lambda(l)$
$2$ (too large to render, please specify modulus or download to view)
$3$ (too large to render, please specify modulus or download to view)
$4$ (too large to render, please specify modulus or download to view)
$5$ (too large to render, please specify modulus or download to view)
$6$ (too large to render, please specify modulus or download to view)
$7$ (too large to render, please specify modulus or download to view)
$8$ (too large to render, please specify modulus or download to view)
$9$ (too large to render, please specify modulus or download to view)
$10$ (too large to render, please specify modulus or download to view)
$11$ (too large to render, please specify modulus or download to view)

Selected Fourier coefficients $c(F)$

\(\det(F)\)\(F\)$c(F)$
95 (1, 1, 24) $300533710831750263102356660905870214986184371004021075872106435505535553667072 a + 82082554918398684737234534811022402005470156969147985830190293315256059819324375040$
(2, 1, 12) $18082270125688737905242944140467150541253837171857858145853399420796928 a + 1320919858119514812695885860336454583605231771883632804587626145860364155125760$
(3, 1, 8) $-9914999811530408088041856108242195215560470431130972909944056348672 a - 637151069594004815546687670253036329182343571606804654273783120333252362240$
(4, 1, 6) $-585969379386635619285599811479888273754737691987390917210402684928 a - 18792484606852665104531291996138424504927706412426045250759194257624104960$
(5, 5, 6) $-107866666951869451058748617657473017065514035510412119717973884928 a + 85993672313385383936646680217880019120993131117552135959207289639895040$

Select different $\lambda(l)$ and $c(F)$ to display or specify a modulus $\mathfrak{m}$ to reduce them by

$\lambda(l)$ available for $l$ in: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
$c(F)$ available for $\det(F)$ in: 0 3 4 7 8 11 12 15 16 19 ... 83 84 87 88 91 92 95 96 99 100

List or range of $l$: e.g. 2, or 2,3,5,8, or 2..10
List or range of $\det(F):$ e.g. 3 or 3 7 41
Reduction modulus $\mathfrak{m}$: e.g. 17 or 3*a+14 or 3,a+1
(for best results, specify an ideal of prime norm)

Download

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