[N,k,chi] = [145,4,Mod(86,145)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(145, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("145.86");
S:= CuspForms(chi, 4);
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 \(\left(\mathbb{Z}/145\mathbb{Z}\right)^\times\).
\(n\)
\(31\)
\(117\)
\(\chi(n)\)
\(-1\)
\(1\)
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
\( T_{2}^{16} + 95 T_{2}^{14} + 3576 T_{2}^{12} + 68256 T_{2}^{10} + 700479 T_{2}^{8} + 3754089 T_{2}^{6} + 9373424 T_{2}^{4} + 8978880 T_{2}^{2} + 2560000 \)
T2^16 + 95*T2^14 + 3576*T2^12 + 68256*T2^10 + 700479*T2^8 + 3754089*T2^6 + 9373424*T2^4 + 8978880*T2^2 + 2560000
acting on \(S_{4}^{\mathrm{new}}(145, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{16} + 95 T^{14} + 3576 T^{12} + \cdots + 2560000 \)
T^16 + 95*T^14 + 3576*T^12 + 68256*T^10 + 700479*T^8 + 3754089*T^6 + 9373424*T^4 + 8978880*T^2 + 2560000
$3$
\( T^{16} + 279 T^{14} + \cdots + 276889600 \)
T^16 + 279*T^14 + 30585*T^12 + 1658088*T^10 + 45694736*T^8 + 585429520*T^6 + 2771212976*T^4 + 4261011200*T^2 + 276889600
$5$
\( (T + 5)^{16} \)
(T + 5)^16
$7$
\( (T^{8} - 19 T^{7} - 1665 T^{6} + \cdots - 472329184)^{2} \)
(T^8 - 19*T^7 - 1665*T^6 + 23012*T^5 + 806124*T^4 - 7779336*T^3 - 99477436*T^2 + 708456808*T - 472329184)^2
$11$
\( T^{16} + 11680 T^{14} + \cdots + 20\!\cdots\!00 \)
T^16 + 11680*T^14 + 50972960*T^12 + 103048140352*T^10 + 98294077995184*T^8 + 41308028134317696*T^6 + 7143463267990615040*T^4 + 391478018558627174400*T^2 + 208448220805696000000
$13$
\( (T^{8} + 7 T^{7} - 8177 T^{6} + \cdots - 283267515392)^{2} \)
(T^8 + 7*T^7 - 8177*T^6 + 50228*T^5 + 15159108*T^4 - 327002448*T^3 - 1230762080*T^2 + 61470836224*T - 283267515392)^2
$17$
\( T^{16} + 52631 T^{14} + \cdots + 15\!\cdots\!00 \)
T^16 + 52631*T^14 + 1150581701*T^12 + 13462260357348*T^10 + 90302571430985008*T^8 + 343415768702829010672*T^6 + 678029596281453994388336*T^4 + 561800150539583040814147520*T^2 + 159023982393349251145984000000
$19$
\( T^{16} + 69156 T^{14} + \cdots + 21\!\cdots\!00 \)
T^16 + 69156*T^14 + 1809218912*T^12 + 22734240244928*T^10 + 145481918115038256*T^8 + 476994072852300937024*T^6 + 805356625174752808464384*T^4 + 667513974146728682500275200*T^2 + 215268948667143593825226854400
$23$
\( (T^{8} - 21 T^{7} + \cdots - 69040506420288)^{2} \)
(T^8 - 21*T^7 - 35287*T^6 + 1533172*T^5 + 319710208*T^4 - 19010678592*T^3 - 307169780172*T^2 + 23158770941080*T - 69040506420288)^2
$29$
\( T^{16} - 28 T^{15} + \cdots + 12\!\cdots\!81 \)
T^16 - 28*T^15 + 6308*T^14 + 5226188*T^13 + 583114484*T^12 + 11717555444*T^11 + 28357252145404*T^10 + 3544977695550716*T^9 + 104140085508025206*T^8 + 86458461016786412524*T^7 + 16867554895563582166684*T^6 + 169988287306446493580836*T^5 + 206314524740428945820689844*T^4 + 45097762682432660347074372412*T^3 + 1327564549775505735043564955588*T^2 - 143719595834701119596602752005612*T + 125184900814733057351483732809459681
$31$
\( T^{16} + 132075 T^{14} + \cdots + 54\!\cdots\!00 \)
T^16 + 132075*T^14 + 6601233833*T^12 + 159474693264264*T^10 + 1980576110311061728*T^8 + 12311729494425725657104*T^6 + 31998933078691894827446320*T^4 + 12758743426976627021624960000*T^2 + 544879428144760840824900000000
$37$
\( T^{16} + 356564 T^{14} + \cdots + 15\!\cdots\!00 \)
T^16 + 356564*T^14 + 50926307328*T^12 + 3731719838706912*T^10 + 148602523063768149808*T^8 + 3103486037869809966432192*T^6 + 29240089357217653971441688576*T^4 + 80240758667993840069007894118400*T^2 + 1566662970222583396543510452633600
$41$
\( T^{16} + 327492 T^{14} + \cdots + 83\!\cdots\!00 \)
T^16 + 327492*T^14 + 37723308272*T^12 + 2065643447491840*T^10 + 60789458203273204992*T^8 + 1005542852466270780283904*T^6 + 9279732364392954481690931200*T^4 + 44207090208807359383332963942400*T^2 + 83886825198167513433137741824000000
$43$
\( T^{16} + 889827 T^{14} + \cdots + 39\!\cdots\!00 \)
T^16 + 889827*T^14 + 309446941273*T^12 + 54236963923133640*T^10 + 5175576586993891883792*T^8 + 271268420541572247771210576*T^6 + 7515747458580685647282018946736*T^4 + 97134469347436369440176229945324800*T^2 + 399620236288350687971774935147846041600
$47$
\( T^{16} + 1325828 T^{14} + \cdots + 53\!\cdots\!00 \)
T^16 + 1325828*T^14 + 722752935248*T^12 + 209664421491787456*T^10 + 35013794821478271389872*T^8 + 3406649584460927019868273728*T^6 + 186491450246088453282186985925376*T^4 + 5170913902110027805359144292214702080*T^2 + 53823306423640441657744286080010199040000
$53$
\( (T^{8} - 307 T^{7} + \cdots + 17\!\cdots\!92)^{2} \)
(T^8 - 307*T^7 - 830113*T^6 + 253927448*T^5 + 200201937572*T^4 - 53738539750560*T^3 - 12384368219000992*T^2 + 1253754907480491520*T + 177270995131193659392)^2
$59$
\( (T^{8} + 1043 T^{7} + \cdots + 73\!\cdots\!00)^{2} \)
(T^8 + 1043*T^7 - 239071*T^6 - 580743436*T^5 - 197095454248*T^4 - 4423496636720*T^3 + 8503753342971856*T^2 + 1465349816274109376*T + 73116092692667289600)^2
$61$
\( T^{16} + 656315 T^{14} + \cdots + 26\!\cdots\!00 \)
T^16 + 656315*T^14 + 159284708825*T^12 + 18584493951973448*T^10 + 1168572556181620506944*T^8 + 41014646372479036164344704*T^6 + 782745170683272985141166129920*T^4 + 7346674567917771067165588183040000*T^2 + 26291759131041756355970143257600000000
$67$
\( (T^{8} + 802 T^{7} + \cdots + 19\!\cdots\!64)^{2} \)
(T^8 + 802*T^7 - 1600532*T^6 - 931781364*T^5 + 963411925348*T^4 + 281149893551120*T^3 - 216407460423021248*T^2 - 3098321952822971616*T + 1903809708141266756864)^2
$71$
\( (T^{8} - 396 T^{7} + \cdots + 31\!\cdots\!00)^{2} \)
(T^8 - 396*T^7 - 1707604*T^6 + 503867712*T^5 + 647320616560*T^4 - 83194194003904*T^3 - 53006653833196736*T^2 + 6354505519616519680*T + 315662261693126246400)^2
$73$
\( T^{16} + 2549615 T^{14} + \cdots + 35\!\cdots\!00 \)
T^16 + 2549615*T^14 + 2511466487733*T^12 + 1251194458972869492*T^10 + 340161713968960181612016*T^8 + 49516879065108833270964674992*T^6 + 3356204784090463089515719063007856*T^4 + 62973710130448478326486735733534827200*T^2 + 3501297488544206065177061240293093401600
$79$
\( T^{16} + 5069151 T^{14} + \cdots + 32\!\cdots\!00 \)
T^16 + 5069151*T^14 + 10659038938241*T^12 + 12039262510811037960*T^10 + 7898012010137998695267136*T^8 + 3037504130767316615823098108176*T^6 + 658876589193905112356491761771287344*T^4 + 73248338185061595905676388487992841123840*T^2 + 3208385122585636294501079236530694088912697600
$83$
\( (T^{8} - 2200 T^{7} + \cdots - 54\!\cdots\!12)^{2} \)
(T^8 - 2200*T^7 - 1209700*T^6 + 4913512476*T^5 - 759273283228*T^4 - 3029490113034984*T^3 + 1018480613961777664*T^2 + 305216967032358066944*T - 54147748266856545050112)^2
$89$
\( T^{16} + 5882764 T^{14} + \cdots + 76\!\cdots\!00 \)
T^16 + 5882764*T^14 + 12564102863824*T^12 + 13273050854547106048*T^10 + 7698984337355337895579648*T^8 + 2499791915469184796522983260160*T^6 + 431991595019626665100248467682361344*T^4 + 33907582753899015810454800109308445982720*T^2 + 764250111159416246590143389536083100303360000
$97$
\( T^{16} + 10761167 T^{14} + \cdots + 40\!\cdots\!00 \)
T^16 + 10761167*T^14 + 47746615229029*T^12 + 112869011062434532804*T^10 + 153108310015757285871136976*T^8 + 119153204423132848339494584656496*T^6 + 49785008993784670847262088998709923056*T^4 + 9268158937854283628162162681519211888386240*T^2 + 405851897039750602415024873017708712427632870400
show more
show less