[N,k,chi] = [3024,2,Mod(17,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.17");
S:= CuspForms(chi, 2);
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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\)
\(757\)
\(785\)
\(1135\)
\(2593\)
\(\chi(n)\)
\(1\)
\(\beta_{2}\)
\(1\)
\(1 - \beta_{2}\)
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
\( T_{5}^{8} - 24T_{5}^{6} - 12T_{5}^{5} + 171T_{5}^{4} + 135T_{5}^{3} - 324T_{5}^{2} - 261T_{5} - 18 \)
T5^8 - 24*T5^6 - 12*T5^5 + 171*T5^4 + 135*T5^3 - 324*T5^2 - 261*T5 - 18
acting on \(S_{2}^{\mathrm{new}}(3024, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{16} \)
T^16
$3$
\( T^{16} \)
T^16
$5$
\( (T^{8} - 24 T^{6} - 12 T^{5} + 171 T^{4} + \cdots - 18)^{2} \)
(T^8 - 24*T^6 - 12*T^5 + 171*T^4 + 135*T^3 - 324*T^2 - 261*T - 18)^2
$7$
\( T^{16} - T^{15} - 6 T^{14} + \cdots + 5764801 \)
T^16 - T^15 - 6*T^14 + 16*T^13 - 10*T^12 - 39*T^11 + 385*T^10 + 239*T^9 - 2880*T^8 + 1673*T^7 + 18865*T^6 - 13377*T^5 - 24010*T^4 + 268912*T^3 - 705894*T^2 - 823543*T + 5764801
$11$
\( T^{16} + 90 T^{14} + 3141 T^{12} + \cdots + 26244 \)
T^16 + 90*T^14 + 3141*T^12 + 53703*T^10 + 464616*T^8 + 1858950*T^6 + 2566080*T^4 + 544563*T^2 + 26244
$13$
\( T^{16} - 3 T^{15} - 51 T^{14} + \cdots + 3337929 \)
T^16 - 3*T^15 - 51*T^14 + 162*T^13 + 1980*T^12 - 4608*T^11 - 35379*T^10 + 66258*T^9 + 494064*T^8 - 321543*T^7 - 3499173*T^6 - 831303*T^5 + 18330786*T^4 + 40000230*T^3 + 38097783*T^2 + 17462466*T + 3337929
$17$
\( T^{16} - 9 T^{15} + 105 T^{14} + \cdots + 13549761 \)
T^16 - 9*T^15 + 105*T^14 - 420*T^13 + 3321*T^12 - 8910*T^11 + 73566*T^10 - 115920*T^9 + 912402*T^8 - 690741*T^7 + 8181405*T^6 - 1254096*T^5 + 32433372*T^4 + 25350003*T^3 + 94137876*T^2 + 35746191*T + 13549761
$19$
\( T^{16} - 93 T^{14} + 6156 T^{12} + \cdots + 2099601 \)
T^16 - 93*T^14 + 6156*T^12 - 7974*T^11 - 188478*T^10 + 316089*T^9 + 4276089*T^8 - 9517095*T^7 - 40684761*T^6 + 85622103*T^5 + 320108679*T^4 - 381649968*T^3 + 166640004*T^2 - 29655234*T + 2099601
$23$
\( T^{16} + 243 T^{14} + \cdots + 15198451524 \)
T^16 + 243*T^14 + 22446*T^12 + 1015092*T^10 + 24904827*T^8 + 342510444*T^6 + 2594476008*T^4 + 9992947563*T^2 + 15198451524
$29$
\( T^{16} + 6 T^{15} - 126 T^{14} + \cdots + 15752961 \)
T^16 + 6*T^15 - 126*T^14 - 828*T^13 + 12753*T^12 + 58239*T^11 - 577287*T^10 - 2348109*T^9 + 20028303*T^8 + 53675541*T^7 - 210471048*T^6 - 464916834*T^5 + 2135730888*T^4 - 105142212*T^3 - 182284263*T^2 + 9001692*T + 15752961
$31$
\( T^{16} + 6 T^{15} + \cdots + 3910251024 \)
T^16 + 6*T^15 - 120*T^14 - 792*T^13 + 11187*T^12 + 57834*T^11 - 490239*T^10 - 2259819*T^9 + 16995015*T^8 + 48203910*T^7 - 309231837*T^6 - 478336266*T^5 + 4449942117*T^4 - 4726500660*T^3 - 2625353532*T^2 + 4355979120*T + 3910251024
$37$
\( T^{16} - T^{15} + 108 T^{14} + \cdots + 52765696 \)
T^16 - T^15 + 108*T^14 - 167*T^13 + 8996*T^12 - 10395*T^11 + 263287*T^10 + 175166*T^9 + 5129568*T^8 + 1907864*T^7 + 40260736*T^6 + 12859776*T^5 + 232814336*T^4 + 5193472*T^3 + 115382016*T^2 + 3719168*T + 52765696
$41$
\( T^{16} + 6 T^{15} + \cdots + 91647269289 \)
T^16 + 6*T^15 + 186*T^14 + 330*T^13 + 18891*T^12 + 20637*T^11 + 1135899*T^10 - 430317*T^9 + 44578395*T^8 - 28504467*T^7 + 1038978252*T^6 - 1968463728*T^5 + 12508926552*T^4 - 8471239848*T^3 + 36627754095*T^2 - 3013404282*T + 91647269289
$43$
\( T^{16} - 2 T^{15} + \cdots + 28009034881 \)
T^16 - 2*T^15 + 207*T^14 + 104*T^13 + 30590*T^12 + 18162*T^11 + 2048842*T^10 + 3925843*T^9 + 97936317*T^8 + 87622111*T^7 + 1058091937*T^6 - 324910827*T^5 + 8330008163*T^4 - 953140042*T^3 + 16892706132*T^2 - 1271593682*T + 28009034881
$47$
\( T^{16} + 18 T^{15} + \cdots + 1971620372736 \)
T^16 + 18*T^15 + 438*T^14 + 4884*T^13 + 84231*T^12 + 846819*T^11 + 10379754*T^10 + 79062246*T^9 + 712315611*T^8 + 4775169699*T^7 + 32201307486*T^6 + 148161520953*T^5 + 540676969353*T^4 + 1330775271864*T^3 + 2461461067440*T^2 + 2703471458688*T + 1971620372736
$53$
\( T^{16} - 153 T^{14} + 19764 T^{12} + \cdots + 531441 \)
T^16 - 153*T^14 + 19764*T^12 - 56376*T^11 - 466074*T^10 + 1451439*T^9 + 9705177*T^8 - 16579647*T^7 - 60026589*T^6 + 102922407*T^5 + 292233501*T^4 - 457747848*T^3 + 191318760*T^2 + 18068994*T + 531441
$59$
\( T^{16} + 15 T^{15} + \cdots + 165574120464 \)
T^16 + 15*T^15 + 393*T^14 + 3882*T^13 + 79218*T^12 + 720099*T^11 + 8617212*T^10 + 42107274*T^9 + 309484062*T^8 + 677695707*T^7 + 7073934444*T^6 + 9743030109*T^5 + 77431736565*T^4 - 11513862288*T^3 + 484571771388*T^2 + 266986987488*T + 165574120464
$61$
\( T^{16} - 3 T^{15} + \cdots + 1475481744 \)
T^16 - 3*T^15 - 111*T^14 + 342*T^13 + 8784*T^12 - 19287*T^11 - 366912*T^10 + 569754*T^9 + 11523348*T^8 - 1463967*T^7 - 176063652*T^6 - 166075839*T^5 + 1891535733*T^4 + 6644786400*T^3 + 9308572164*T^2 + 5807894400*T + 1475481744
$67$
\( T^{16} - 7 T^{15} + \cdots + 2114953586944 \)
T^16 - 7*T^15 + 270*T^14 - 1859*T^13 + 50012*T^12 - 318924*T^11 + 4411018*T^10 - 20606821*T^9 + 231304086*T^8 - 951833224*T^7 + 7944661591*T^6 - 24180967287*T^5 + 163978476161*T^4 - 427777738280*T^3 + 2010327590448*T^2 - 2140118586496*T + 2114953586944
$71$
\( T^{16} + \cdots + 780959242139904 \)
T^16 + 747*T^14 + 233316*T^12 + 39561129*T^10 + 3949834995*T^8 + 234856231407*T^6 + 7956570857364*T^4 + 134744717006208*T^2 + 780959242139904
$73$
\( T^{16} - 306 T^{14} + \cdots + 7523023152969 \)
T^16 - 306*T^14 + 71235*T^12 + 432909*T^11 - 5521941*T^10 - 59680611*T^9 + 317278665*T^8 + 8564672457*T^7 + 62170270956*T^6 + 213060248478*T^5 + 238887968904*T^4 - 558789791238*T^3 - 1191205799235*T^2 + 2752955922474*T + 7523023152969
$79$
\( T^{16} - T^{15} + 144 T^{14} + \cdots + 10549504 \)
T^16 - T^15 + 144*T^14 - 779*T^13 + 18914*T^12 - 68454*T^11 + 497152*T^10 - 943669*T^9 + 7394544*T^8 - 16316434*T^7 + 35635933*T^6 - 38599749*T^5 + 44789945*T^4 - 29157800*T^3 + 30606480*T^2 - 14992768*T + 10549504
$83$
\( T^{16} + 330 T^{14} + \cdots + 669184533369 \)
T^16 + 330*T^14 + 1272*T^13 + 80712*T^12 + 290448*T^11 + 8300268*T^10 + 32727636*T^9 + 614588409*T^8 + 2208157416*T^7 + 25248534300*T^6 + 85919425596*T^5 + 720461504880*T^4 + 1903485074616*T^3 + 5773577517018*T^2 + 2061188196012*T + 669184533369
$89$
\( T^{16} - 21 T^{15} + \cdots + 7161826993281 \)
T^16 - 21*T^15 + 459*T^14 - 5130*T^13 + 69741*T^12 - 611550*T^11 + 6642648*T^10 - 43169922*T^9 + 335911536*T^8 - 1422741915*T^7 + 9647366571*T^6 - 30425509008*T^5 + 180123305796*T^4 - 236676836007*T^3 + 1294382305422*T^2 - 1051545832029*T + 7161826993281
$97$
\( T^{16} - 3 T^{15} + \cdots + 22864161681 \)
T^16 - 3*T^15 - 384*T^14 + 1161*T^13 + 109872*T^12 - 394884*T^11 - 12357171*T^10 + 41968233*T^9 + 1044816804*T^8 - 2243025486*T^7 - 41675283648*T^6 + 71751605004*T^5 + 1208668941423*T^4 - 766864072890*T^3 - 8224102287*T^2 + 104576900445*T + 22864161681
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