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 $T(l)$

$l$	$\lambda(l)$
$5$	(too large to render, please specify modulus or download to view)

Selected Fourier coefficients $c(F)$

\(\det(F)\)	\(F\)	$c(F)$
0	(0, 0, 0)	$0$
	(0, 0, 1)	$-2280861281627370805040680524288361203419712 a - 622954812264770711063750705259242086562528715840$
	(0, 0, 2)	$-1178822696210821943443662247582546235755613184 a - 86113651539208755894210427242289206627710853598817280$
	(0, 0, 3)	$418290949993006435978023288053498742599463737088 a + 26881251499776673862536604740208672087642280708599688960$
	(0, 0, 4)	$318824167483534443254150358982022524321628658057216 a + 10526210736199809647336368734832101517386349753985860485120$
	(0, 0, 5)	$65981915334703747238946640359970536659862919724688000 a - 68113701467302780696450210157264039645633074765523827440000$
	(0, 0, 6)	$6013397116332206199358239766755020956269980122647023616 a - 1612715173017944352411985044692794293145297783342456103546880$
	(0, 0, 7)	$188763764101613279535648113478664259389547620487183248896 a + 120325830865587193561218565837296548633388439753912949511544320$
	(0, 0, 8)	$2355431351200721318277670153533236338784943330519491543040 a + 116629800820600025431794367298520629219981536402771020172492800$
	(0, 0, 9)	$10803256847220727070952539679441083902770673656691310172864 a + 3965615514680479319473261450898813072956354327430197112442636480$
	(0, 0, 10)	$-19316006282151669775494938027718884815585004273343638784000 a + 7731593776427406129626513374609798888816715739546054333745920000$
	(0, 0, 11)	$-341125022566644402827223937571333646921496044660162319497984 a - 208697058860269779261175034940725976756057690898249419498744410880$
	(0, 0, 12)	$-731742325266616130173344047624891379606372362948977935581184 a + 194168169708699329287956287145711817995008874514708606807958814720$
	(0, 0, 13)	$2877116830223508310418778301140284220795804525747913990328448 a + 465065239514154432611765895465480742296594680895141401798394668160$
	(0, 0, 14)	$15546709683532998133849296774764421321508427250046728714166272 a + 2942768606709030439454418524972966538343661552192097693600581591040$
	(0, 0, 15)	$6025133120425810628990550386030722314780871968240510708288000 a - 2410749220894864628878852765225375427473060994463060254589205440000$
	(0, 0, 16)	$-119842091092452957276855716138370921835579091294865616212590592 a + 30553561407585838151657892859023958809237026278682453927591474626560$
	(0, 0, 17)	$-282044183199812535792488483272737370887736067338751692925679744 a - 305417901342959340812247585728463688645875505445670477304130357988480$
	(0, 0, 18)	$233602570963424852517286109166901182755987632259586595426280448 a + 346122885132669876628571463864334237108483679841624939760886944220160$
	(0, 0, 19)	$2235376650201866236230977425014604883124413856792193951495975680 a + 1029598861106139291788951248557480125960490332541213936704057383545600$
	(0, 0, 20)	$2345298017290230078723653070548093135040588195379656505430016000 a - 935542781587410092635102920101043955015786415245264150914076078080000$
	(0, 0, 21)	$-4854752650999505135769899842958917079013513886332165595950434304 a - 920807819188581597575223958839203305549965624340086113105567047649280$
	(0, 0, 22)	$-26129574589417387312032582676518946707403646847342388973952012288 a - 5850392934017895749462130837180175386726268544822991036643563783720960$
	(0, 0, 23)	$-6798793820590391412995033878607282957557551269648295995292513792 a + 12266912238602526775246451207821865141711184685280837175465513051855360$
	(0, 0, 24)	$36484115402279625499778242206521567085568399803449614314677207040 a - 37746165401333083420082960769267946165723723486441518828120834126643200$
	(0, 0, 25)	$244190933437987142278339013707749934174086967813804498474113000000 a + 82289777079500446176407883922763204733429907064209429839264214185000000$

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)