[N,k,chi] = [288,7,Mod(271,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.271");
S:= CuspForms(chi, 7);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\)
\(37\)
\(65\)
\(127\)
\(\chi(n)\)
\(-1\)
\(1\)
\(-1\)
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{12} + 107352 T_{5}^{10} + 3991016688 T_{5}^{8} + 71113492512000 T_{5}^{6} + \cdots + 57\!\cdots\!00 \)
T5^12 + 107352*T5^10 + 3991016688*T5^8 + 71113492512000*T5^6 + 661414738278240000*T5^4 + 3095950792825440000000*T5^2 + 5757443062907342400000000
acting on \(S_{7}^{\mathrm{new}}(288, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{12} \)
T^12
$3$
\( T^{12} \)
T^12
$5$
\( T^{12} + 107352 T^{10} + \cdots + 57\!\cdots\!00 \)
T^12 + 107352*T^10 + 3991016688*T^8 + 71113492512000*T^6 + 661414738278240000*T^4 + 3095950792825440000000*T^2 + 5757443062907342400000000
$7$
\( T^{12} + 858216 T^{10} + \cdots + 91\!\cdots\!36 \)
T^12 + 858216*T^10 + 281404850928*T^8 + 44308586427353856*T^6 + 3429289695663761870592*T^4 + 114305825303276548896221184*T^2 + 919211093597842445272959553536
$11$
\( (T^{6} - 1360 T^{5} + \cdots + 23\!\cdots\!12)^{2} \)
(T^6 - 1360*T^5 - 3428416*T^4 + 1598253056*T^3 + 4492836663296*T^2 + 2011661272285184*T + 232358939373862912)^2
$13$
\( T^{12} + 26982528 T^{10} + \cdots + 36\!\cdots\!84 \)
T^12 + 26982528*T^10 + 267033487395840*T^8 + 1183163449428647608320*T^6 + 2284495095063421714732941312*T^4 + 1598534792074580192474601709633536*T^2 + 360809339632287156290367128547291561984
$17$
\( (T^{6} - 2444 T^{5} + \cdots - 15\!\cdots\!24)^{2} \)
(T^6 - 2444*T^5 - 79018756*T^4 + 94550725984*T^3 + 966045296014064*T^2 + 66438011241140032*T - 1564573280130780607424)^2
$19$
\( (T^{6} + 1968 T^{5} + \cdots + 24\!\cdots\!16)^{2} \)
(T^6 + 1968*T^5 - 198025680*T^4 + 267529414144*T^3 + 9291366117643008*T^2 - 37593129778578345984*T + 24229787890059443900416)^2
$23$
\( T^{12} + 879376800 T^{10} + \cdots + 12\!\cdots\!56 \)
T^12 + 879376800*T^10 + 296173629532057344*T^8 + 46863448274898583825858560*T^6 + 3353681881586952874735405766737920*T^4 + 78648208938792218569815106805581857423360*T^2 + 12697512296478014667848098027504115653023891456
$29$
\( T^{12} + 4040599128 T^{10} + \cdots + 28\!\cdots\!04 \)
T^12 + 4040599128*T^10 + 6439053798054291696*T^8 + 5101922939213177215804710144*T^6 + 2074507602419163915571838000808644352*T^4 + 399230347059464462973878222747303682938394624*T^2 + 28298157191824303636481285544064496663190231936405504
$31$
\( T^{12} + 7044987816 T^{10} + \cdots + 12\!\cdots\!84 \)
T^12 + 7044987816*T^10 + 17990785981679259120*T^8 + 20434729581157020630476772096*T^6 + 9994917464236130809778140670772883200*T^4 + 1523446973681561903677449735807709620141729792*T^2 + 1211171530935382424629654924753628649028495201603584
$37$
\( T^{12} + 20697207840 T^{10} + \cdots + 84\!\cdots\!96 \)
T^12 + 20697207840*T^10 + 170718584108032362240*T^8 + 716600614505324148924242706432*T^6 + 1613538231449724487318979970623296438272*T^4 + 1848337366218579939630232233246616457657198837760*T^2 + 841518299660193863500025530742931213257921691112068612096
$41$
\( (T^{6} - 27140 T^{5} + \cdots - 11\!\cdots\!36)^{2} \)
(T^6 - 27140*T^5 - 15459480292*T^4 - 21547433797088*T^3 + 52143570838005350384*T^2 + 935522920958439621168064*T - 11524334588859116789938137536)^2
$43$
\( (T^{6} - 24912 T^{5} + \cdots - 19\!\cdots\!32)^{2} \)
(T^6 - 24912*T^5 - 18011705424*T^4 + 162272334673408*T^3 + 70539669873064477440*T^2 - 506648482714625699500032*T - 1903911558445805440869036032)^2
$47$
\( T^{12} + 86670856608 T^{10} + \cdots + 41\!\cdots\!84 \)
T^12 + 86670856608*T^10 + 3016497054495906426624*T^8 + 53577442643395823649810443059200*T^6 + 506820913438461639129655635703234925887488*T^4 + 2379900710129618636421263861869277713756586464247808*T^2 + 4197663422606906109127517011363413633570217529799545437814784
$53$
\( T^{12} + 172945812888 T^{10} + \cdots + 33\!\cdots\!64 \)
T^12 + 172945812888*T^10 + 11971414856530894736880*T^8 + 427202719007547921315383860487424*T^6 + 8310722486714814041781741505296871756164864*T^4 + 83555800781097910707986963385997084388609105433630720*T^2 + 338185568213524774221366231358012323317877150186715666540990464
$59$
\( (T^{6} + 443072 T^{5} + \cdots + 12\!\cdots\!28)^{2} \)
(T^6 + 443072*T^5 - 5635362832*T^4 - 14874702475872256*T^3 - 760523759514921882880*T^2 + 53308323403871741093396480*T + 121261936003004327135597744128)^2
$61$
\( T^{12} + 348717987744 T^{10} + \cdots + 34\!\cdots\!36 \)
T^12 + 348717987744*T^10 + 42569613986144128601856*T^8 + 2088076221606849406049948282044416*T^6 + 33539605628363898682979866915724719836561408*T^4 + 171354238581573212846426169259628165651620640556318720*T^2 + 34212487709195704846733969615371625127439777334712918066855936
$67$
\( (T^{6} + 782976 T^{5} + \cdots - 54\!\cdots\!96)^{2} \)
(T^6 + 782976*T^5 + 76738897392*T^4 - 63007167145668608*T^3 - 17051289323942389585152*T^2 - 1232932597735190460849291264*T - 5478028391792456468496397316096)^2
$71$
\( T^{12} + 671412159648 T^{10} + \cdots + 49\!\cdots\!36 \)
T^12 + 671412159648*T^10 + 167791388005078471819008*T^8 + 19325526785865600523509366792437760*T^6 + 1017023801164364462228690521050104831140626432*T^4 + 19830389825366611732171930716918332474168844240946200576*T^2 + 4974301514253375767055860079795229686901305534006970755355508736
$73$
\( (T^{6} - 277740 T^{5} + \cdots + 11\!\cdots\!24)^{2} \)
(T^6 - 277740*T^5 - 587992202244*T^4 + 50696853976786016*T^3 + 92651434531912059244272*T^2 + 13198861548173459321324935488*T + 111134556068432964364572252687424)^2
$79$
\( T^{12} + 1736387849448 T^{10} + \cdots + 65\!\cdots\!24 \)
T^12 + 1736387849448*T^10 + 1037524740481389109377264*T^8 + 287069511937330285533696974009948928*T^6 + 39497335718011313277546573130955683397330931456*T^4 + 2613077733941340350444354689133614832664603744349595166720*T^2 + 65893161324207208547497553545140763363965595654915793810578200858624
$83$
\( (T^{6} - 1248880 T^{5} + \cdots + 53\!\cdots\!04)^{2} \)
(T^6 - 1248880*T^5 + 242484844736*T^4 + 225639870636775424*T^3 - 99329605424272173076480*T^2 + 8479929827332168242505515008*T + 530829318884003638404169948463104)^2
$89$
\( (T^{6} + 183700 T^{5} + \cdots + 62\!\cdots\!04)^{2} \)
(T^6 + 183700*T^5 - 1361340492292*T^4 + 37986039004278880*T^3 + 313568356307956563742448*T^2 - 85374404681687398971844034240*T + 6295090539816875625506132342615104)^2
$97$
\( (T^{6} + 582828 T^{5} + \cdots - 50\!\cdots\!12)^{2} \)
(T^6 + 582828*T^5 - 2279045333892*T^4 - 1119834103677769312*T^3 + 1045179583596821351416560*T^2 + 163048939196415151522997678784*T - 50652323207507715721293840438168512)^2
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