[N,k,chi] = [5,20,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 20);
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
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
\( p \)
Sign
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 1006T_{2}^{2} - 757856T_{2} - 578651136 \)
T2^3 + 1006*T2^2 - 757856*T2 - 578651136
acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(5))\).
$p$
$F_p(T)$
$2$
\( T^{3} + 1006 T^{2} + \cdots - 578651136 \)
T^3 + 1006*T^2 - 757856*T - 578651136
$3$
\( T^{3} + 73452 T^{2} + \cdots - 20870112837888 \)
T^3 + 73452*T^2 + 249267456*T - 20870112837888
$5$
\( (T - 1953125)^{3} \)
(T - 1953125)^3
$7$
\( T^{3} + 54910456 T^{2} + \cdots - 37\!\cdots\!16 \)
T^3 + 54910456*T^2 - 10144649913300336*T - 376394687498859820713216
$11$
\( T^{3} + 8566943524 T^{2} + \cdots - 30\!\cdots\!88 \)
T^3 + 8566943524*T^2 - 5126752331383873808*T - 30044120772155793419806375488
$13$
\( T^{3} + 85630509662 T^{2} + \cdots + 87\!\cdots\!12 \)
T^3 + 85630509662*T^2 + 2044306680832326796076*T + 8767941875516283982713696622312
$17$
\( T^{3} - 87257923094 T^{2} + \cdots - 64\!\cdots\!76 \)
T^3 - 87257923094*T^2 - 466314996751661733814196*T - 64407979353069961805029776609429576
$19$
\( T^{3} - 1282010076580 T^{2} + \cdots + 34\!\cdots\!00 \)
T^3 - 1282010076580*T^2 - 1175803772717625091186000*T + 348655321680731054061948028108744000
$23$
\( T^{3} - 4088829256728 T^{2} + \cdots - 58\!\cdots\!88 \)
T^3 - 4088829256728*T^2 - 12262229392390518681761904*T - 5880105579040640464795290357396933888
$29$
\( T^{3} + 73280209082030 T^{2} + \cdots - 72\!\cdots\!00 \)
T^3 + 73280209082030*T^2 - 6939646870623016134237924500*T - 72471079420882013406503240146950887319000
$31$
\( T^{3} + 284526134418784 T^{2} + \cdots - 25\!\cdots\!48 \)
T^3 + 284526134418784*T^2 + 2840841136599733165011999552*T - 2563847878339560738959683837202091323317248
$37$
\( T^{3} + 432614295273606 T^{2} + \cdots - 10\!\cdots\!96 \)
T^3 + 432614295273606*T^2 - 2035440875961946975102342998516*T - 1023656290077418948372526012211515823278216696
$41$
\( T^{3} + \cdots + 93\!\cdots\!72 \)
T^3 - 2081433692967886*T^2 - 5638876232655574997046726843668*T + 9343537530183649169675881534058920153953622872
$43$
\( T^{3} + \cdots - 66\!\cdots\!88 \)
T^3 - 1100001003168508*T^2 - 13026608725158198750835910577664*T - 6687613326337645772863656737698120073390194688
$47$
\( T^{3} + \cdots - 16\!\cdots\!56 \)
T^3 + 20429801107275856*T^2 + 93001771372056733483879055971024*T - 16876656412894807896495164559151411688127075456
$53$
\( T^{3} + \cdots + 57\!\cdots\!12 \)
T^3 - 9015898015717898*T^2 - 548969574731011294857273109307444*T + 5743798078645326488642482929350042661691425056712
$59$
\( T^{3} + \cdots - 87\!\cdots\!00 \)
T^3 - 3004038355564940*T^2 - 4553998087348204941193781495042000*T - 87456993762294869899421367923033652256907775912000
$61$
\( T^{3} + \cdots + 21\!\cdots\!12 \)
T^3 + 40826301921185774*T^2 - 24083858168983862553929428081340308*T + 210912936458456740478184517723589821578300221513512
$67$
\( T^{3} + \cdots + 43\!\cdots\!24 \)
T^3 + 1055285157192202156*T^2 + 369679084589987941244027188772853504*T + 43006456957861605993606244303358172199626397025562624
$71$
\( T^{3} + \cdots + 76\!\cdots\!32 \)
T^3 - 295447643020954696*T^2 - 249972386799012413330763469932182528*T + 76932771658365238071140216583374862097144792119416832
$73$
\( T^{3} + \cdots + 55\!\cdots\!12 \)
T^3 - 481254292945206478*T^2 + 27409354441180892934275981480425196*T + 5510543913459236597498339433013641516959792051476312
$79$
\( T^{3} + \cdots + 95\!\cdots\!00 \)
T^3 - 1996757185645655120*T^2 + 170702117343664507393031033410560000*T + 955386318914562873516658413229832661800520123488256000
$83$
\( T^{3} + \cdots - 65\!\cdots\!88 \)
T^3 + 1502750763410367132*T^2 - 5967284176807541319445515643601280384*T - 6508163731172611891475297339152811260818193939588754688
$89$
\( T^{3} + \cdots - 14\!\cdots\!00 \)
T^3 - 1042000807550316510*T^2 - 3671713161196664915917491224495980500*T - 1485254541549938644488165838036148708543570561267553000
$97$
\( T^{3} + \cdots - 44\!\cdots\!56 \)
T^3 - 1619779467732499494*T^2 - 122182325126128912315317267068683548276*T - 441246341827060838702145162838065858685643543130196779656
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