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 $c(F)$

\(\det(F)\)\(F\)$c(F)$
100 (1, 0, 25) $1591754263879773159054195979279079196263934436889712026333364650395446977124480 a + 434744097159377678508579234219769800709378714138660676633287746270668791771150953600$
(2, 2, 13) $95771387818887505719522274051576721766546912080279517132167869220411520 a + 6996152979265572648638959666775781137112058640587808558088291458343628769078400$
(5, 0, 5) $-791055799017678207984299959165044583476449318319585690492712800000 a + 816630778155295251207075186586057928546583572975971418333728673604000000$

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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