[N,k,chi] = [175,10,Mod(1,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.1");
S:= CuspForms(chi, 10);
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
\(5\)
\(1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 21T_{2}^{2} - 1326T_{2} - 19080 \)
T2^3 + 21*T2^2 - 1326*T2 - 19080
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(175))\).
$p$
$F_p(T)$
$2$
\( T^{3} + 21 T^{2} - 1326 T - 19080 \)
T^3 + 21*T^2 - 1326*T - 19080
$3$
\( T^{3} + 84 T^{2} - 12996 T - 3024 \)
T^3 + 84*T^2 - 12996*T - 3024
$5$
\( T^{3} \)
T^3
$7$
\( (T + 2401)^{3} \)
(T + 2401)^3
$11$
\( T^{3} + \cdots + 108859759460352 \)
T^3 + 3444*T^2 - 6618499968*T + 108859759460352
$13$
\( T^{3} - 19782 T^{2} + \cdots + 41548412541440 \)
T^3 - 19782*T^2 - 12931283064*T + 41548412541440
$17$
\( T^{3} + 1016694 T^{2} + \cdots + 21\!\cdots\!32 \)
T^3 + 1016694*T^2 + 293494511292*T + 21973894921381032
$19$
\( T^{3} - 222852 T^{2} + \cdots - 43\!\cdots\!60 \)
T^3 - 222852*T^2 - 353981719620*T - 43011870587515760
$23$
\( T^{3} + 1885632 T^{2} + \cdots - 97\!\cdots\!36 \)
T^3 + 1885632*T^2 + 14194696128*T - 974648214470209536
$29$
\( T^{3} - 4081818 T^{2} + \cdots + 44\!\cdots\!00 \)
T^3 - 4081818*T^2 - 4782422143620*T + 4423213168251517800
$31$
\( T^{3} - 2869440 T^{2} + \cdots - 74\!\cdots\!84 \)
T^3 - 2869440*T^2 - 58176366315792*T - 74172820551747190784
$37$
\( T^{3} + 1395618 T^{2} + \cdots + 34\!\cdots\!28 \)
T^3 + 1395618*T^2 - 127209247191204*T + 345369799719000886328
$41$
\( T^{3} + 14420658 T^{2} + \cdots - 19\!\cdots\!12 \)
T^3 + 14420658*T^2 - 217166148381924*T - 1983508183225662258312
$43$
\( T^{3} - 61631172 T^{2} + \cdots - 68\!\cdots\!80 \)
T^3 - 61631172*T^2 + 1179825167354496*T - 6883868434203007924480
$47$
\( T^{3} - 10368960 T^{2} + \cdots + 43\!\cdots\!16 \)
T^3 - 10368960*T^2 - 410564457968592*T + 4382944923230012111616
$53$
\( T^{3} + 67502610 T^{2} + \cdots - 23\!\cdots\!28 \)
T^3 + 67502610*T^2 - 3604244065118868*T - 238763987118322051705128
$59$
\( T^{3} + 42590100 T^{2} + \cdots + 42\!\cdots\!00 \)
T^3 + 42590100*T^2 - 6912010951598820*T + 42255218866385698714800
$61$
\( T^{3} - 191746842 T^{2} + \cdots + 51\!\cdots\!08 \)
T^3 - 191746842*T^2 + 3514240390404936*T + 51129364193607680723008
$67$
\( T^{3} - 255175788 T^{2} + \cdots + 20\!\cdots\!64 \)
T^3 - 255175788*T^2 - 1447084483230480*T + 2046203321476325564406464
$71$
\( T^{3} - 296514504 T^{2} + \cdots + 16\!\cdots\!80 \)
T^3 - 296514504*T^2 + 10350223039033344*T + 1678437708012594690785280
$73$
\( T^{3} + 344213310 T^{2} + \cdots - 19\!\cdots\!48 \)
T^3 + 344213310*T^2 - 93316419822721428*T - 19666111377492988250804248
$79$
\( T^{3} + 960412656 T^{2} + \cdots - 11\!\cdots\!00 \)
T^3 + 960412656*T^2 + 207231646446206400*T - 11393072303017048698752000
$83$
\( T^{3} - 1100517180 T^{2} + \cdots - 18\!\cdots\!48 \)
T^3 - 1100517180*T^2 + 313075935079720092*T - 18999627411523605407800848
$89$
\( T^{3} - 506816478 T^{2} + \cdots + 19\!\cdots\!40 \)
T^3 - 506816478*T^2 - 94874685327766740*T + 199603832029143905001240
$97$
\( T^{3} - 647498250 T^{2} + \cdots + 49\!\cdots\!16 \)
T^3 - 647498250*T^2 - 1460996931372270852*T + 494596474576725271584703016
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