[N,k,chi] = [1560,4,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.1");
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
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(5\)
\(1\)
\(13\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{6} + 6T_{7}^{5} - 1459T_{7}^{4} - 7528T_{7}^{3} + 578468T_{7}^{2} + 2643120T_{7} - 46869120 \)
T7^6 + 6*T7^5 - 1459*T7^4 - 7528*T7^3 + 578468*T7^2 + 2643120*T7 - 46869120
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1560))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( (T - 3)^{6} \)
(T - 3)^6
$5$
\( (T + 5)^{6} \)
(T + 5)^6
$7$
\( T^{6} + 6 T^{5} - 1459 T^{4} + \cdots - 46869120 \)
T^6 + 6*T^5 - 1459*T^4 - 7528*T^3 + 578468*T^2 + 2643120*T - 46869120
$11$
\( T^{6} + 8 T^{5} + \cdots - 2813910016 \)
T^6 + 8*T^5 - 6595*T^4 - 62770*T^3 + 8836632*T^2 + 39677760*T - 2813910016
$13$
\( (T + 13)^{6} \)
(T + 13)^6
$17$
\( T^{6} - 88 T^{5} + \cdots + 45378853184 \)
T^6 - 88*T^5 - 20895*T^4 + 1690370*T^3 + 61954620*T^2 - 4058231368*T + 45378853184
$19$
\( T^{6} + 20 T^{5} + \cdots - 3101487910400 \)
T^6 + 20*T^5 - 48632*T^4 - 1089920*T^3 + 727805776*T^2 + 13690631360*T - 3101487910400
$23$
\( T^{6} - 12 T^{5} + \cdots - 187866479360 \)
T^6 - 12*T^5 - 31903*T^4 + 1071434*T^3 + 170762224*T^2 - 1618401760*T - 187866479360
$29$
\( T^{6} - 126 T^{5} + \cdots + 779991110528 \)
T^6 - 126*T^5 - 77280*T^4 + 9500176*T^3 + 204806800*T^2 - 38524448864*T + 779991110528
$31$
\( T^{6} + 110 T^{5} + \cdots - 22819448422400 \)
T^6 + 110*T^5 - 107108*T^4 - 9958040*T^3 + 3125805376*T^2 + 183668956160*T - 22819448422400
$37$
\( T^{6} + 306 T^{5} + \cdots - 11230108888080 \)
T^6 + 306*T^5 - 118011*T^4 - 24277020*T^3 + 4409295904*T^2 + 226189517520*T - 11230108888080
$41$
\( T^{6} - 274 T^{5} + \cdots - 40785543888 \)
T^6 - 274*T^5 - 234795*T^4 + 58689788*T^3 + 4823982032*T^2 - 15759624144*T - 40785543888
$43$
\( T^{6} - 752 T^{5} + \cdots + 63173993136128 \)
T^6 - 752*T^5 + 40176*T^4 + 65347392*T^3 - 8332650496*T^2 - 824224809984*T + 63173993136128
$47$
\( T^{6} - 362 T^{5} + \cdots - 31354450927616 \)
T^6 - 362*T^5 - 233780*T^4 + 72639240*T^3 + 5762900992*T^2 - 555238254080*T - 31354450927616
$53$
\( T^{6} - 394 T^{5} + \cdots + 55\!\cdots\!24 \)
T^6 - 394*T^5 - 913863*T^4 + 398257256*T^3 + 195625605848*T^2 - 99714478704384*T + 5501985957641424
$59$
\( T^{6} - 834 T^{5} + \cdots + 98545717477376 \)
T^6 - 834*T^5 - 28616*T^4 + 111081792*T^3 - 17456984064*T^2 - 253243228160*T + 98545717477376
$61$
\( T^{6} - 202 T^{5} + \cdots + 12\!\cdots\!56 \)
T^6 - 202*T^5 - 829807*T^4 + 54705872*T^3 + 151060538808*T^2 + 26419939776288*T + 1256233545567056
$67$
\( T^{6} - 1490 T^{5} + \cdots - 10\!\cdots\!40 \)
T^6 - 1490*T^5 + 564520*T^4 + 110635712*T^3 - 107068355072*T^2 + 19570221606400*T - 1048421853501440
$71$
\( T^{6} - 376 T^{5} + \cdots - 26845782835200 \)
T^6 - 376*T^5 - 622923*T^4 + 74465822*T^3 + 22811126192*T^2 - 218992270080*T - 26845782835200
$73$
\( T^{6} - 638 T^{5} + \cdots + 18\!\cdots\!24 \)
T^6 - 638*T^5 - 839880*T^4 + 588074320*T^3 + 131775558992*T^2 - 134894072788320*T + 18050328184391424
$79$
\( T^{6} - 1822 T^{5} + \cdots + 19\!\cdots\!20 \)
T^6 - 1822*T^5 - 335019*T^4 + 1743303620*T^3 - 433811593216*T^2 - 137322402965760*T + 19915394051665920
$83$
\( T^{6} - 1050 T^{5} + \cdots + 85\!\cdots\!80 \)
T^6 - 1050*T^5 - 652392*T^4 + 1247618240*T^3 - 509652870144*T^2 + 41554043850240*T + 8599636203182080
$89$
\( T^{6} + \cdots + 257876154228240 \)
T^6 - 10*T^5 - 484211*T^4 - 126035568*T^3 + 16602487704*T^2 + 6617306443680*T + 257876154228240
$97$
\( T^{6} - 1496 T^{5} + \cdots + 55\!\cdots\!20 \)
T^6 - 1496*T^5 - 2819131*T^4 + 3946770910*T^3 + 925823194844*T^2 - 1364373536795000*T + 55526046718309120
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