Siegel modular forms sample Sp4Z.34_Klingen

• 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

 

(-1384742489310021254894997497327602008379*a - 29109667357863906416025353168772901787784492755)*A^7*B + (1449542107307906627243304876432772764779*a + 57858828458630144596481406160891149590289744355)*A^4*B^3 + (119935548350558612607346051814237862230856192*a + 2117971759834753062100343813853695865225387862909440)*A^6*C + (-64799617997885372348307379105170756400*a - 28749161100766238180456052992118247802505251600)*A*B^5 + (-334272744425207755719061896401506832451379200*a - 17468086185480992925972214355332658910884988075417600)*A^3*B^2*C + (113160940226326219119353861969193304874591232*a + 4896407659068404068099853128059003276882243021358080)*A^4*B*D + 992959356415346480009338423094404674068298485760000*B^4*C + (19758598580718068761929471007261502627624779776000*a + 1152973267168272013793035782021492358438003363499212800000)*A^2*B*C^2 + (37312139962756694714481488092465467469209600*a + 9443304675419075777712556587735767176080014604902400)*A*B^3*D + (-4221644059179269523210735132023156123791628697600*a - 23851803761821168937062893212284929784033712021490892800)*A^3*C*D + (-320333702103205781914393432329864916294583294361600000*a - 21172972247919068556684011872161338659050945573036648038400000)*A*C^3 + (-200604133548354211962257009782526587777843200000*a - 239477168369468686562493072314528761367556707387965440000)*B^2*C*D + (-5672301031158859031659192085820665467931040153600*a - 744590597049320972905271825480057158329914530813339238400)*A*B*D^2 + (78306208917126605372035025847030196791822149222400000*a + 10903282489849133395297625521851855044288917266138755235840000)*C*D^2

(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 $c(F)$

\(\det(F)\)	\(F\)	$c(F)$
96	(1, 0, 24)	$422368086068389110478310654564071475628876961424450919991215915778608737241600 a + 115358278858428935584316550066123080781936413878316173067828932732342800164429683200$
	(2, 0, 12)	$25412702639588230822019975575943306314974862793486568466982072272281600 a + 1856412017505441861091243397345554404499136008225905420931049861725920168960000$
	(3, 0, 8)	$-13934473512497566969812589178090016543113052357106526760514806412800 a - 895447887024650362196267551022319396776257589662404551406129235463063692800$
	(4, 0, 6)	$-823448302470965669873550679108763362498600840399098661845351014400 a - 26410814127636692645916264677518104386520405833275574913806704415929344000$
	(4, 4, 7)	$-809178727303452684318829827714154022492288601435725666903777932800 a - 26422829556801717420560216271787596040745824099284341540133725283829900800$
	(5, 2, 5)	$-210599703452294732110764602688355472035061434208530609149175641600 a + 216659673210455189455144776740570797392445722601217976415072432930675200$

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)

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