Properties

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

Basic properties

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

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 $c(F)$

\(\det(F)\)\(F\)$c(F)$
3 (1, 1, 1) $153263258560154463915819029760 a + 41859662617157470859794706703555840$
4 (1, 0, 1) $1174507412027272143668376203894400 a + 320789686164541316627045484102859612800$
7 (1, 1, 2) $46511717288433534460734214738525445652480 a + 12703809477648691414766075931432615393264107520$
8 (1, 0, 2) $3566979597318433682520167825044604007271680 a + 974238422142690360091763229948181311795840472320$
11 (1, 1, 3) $111464940736934680938087191278241166160444358400 a + 30443596336595382997917519972899130575134022937696000$

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

(json file containing all available data)