[N,k,chi] = [102,14,Mod(1,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.1");
S:= CuspForms(chi, 14);
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 ι m \iota_m ι m of the coefficient field, the values ι m ( a n ) \iota_m(a_n) ι m ( a n ) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
p p p
Sign
2 2 2
− 1 -1 − 1
3 3 3
+ 1 +1 + 1
17 17 1 7
− 1 -1 − 1
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
T 5 4 + 36750 T 5 3 − 2162286135 T 5 2 − 40701412457500 T 5 + 1389219666096442500 T_{5}^{4} + 36750T_{5}^{3} - 2162286135T_{5}^{2} - 40701412457500T_{5} + 1389219666096442500 T 5 4 + 3 6 7 5 0 T 5 3 − 2 1 6 2 2 8 6 1 3 5 T 5 2 − 4 0 7 0 1 4 1 2 4 5 7 5 0 0 T 5 + 1 3 8 9 2 1 9 6 6 6 0 9 6 4 4 2 5 0 0
T5^4 + 36750*T5^3 - 2162286135*T5^2 - 40701412457500*T5 + 1389219666096442500
acting on S 14 n e w ( Γ 0 ( 102 ) ) S_{14}^{\mathrm{new}}(\Gamma_0(102)) S 1 4 n e w ( Γ 0 ( 1 0 2 ) ) .
p p p
F p ( T ) F_p(T) F p ( T )
2 2 2
( T − 64 ) 4 (T - 64)^{4} ( T − 6 4 ) 4
(T - 64)^4
3 3 3
( T + 729 ) 4 (T + 729)^{4} ( T + 7 2 9 ) 4
(T + 729)^4
5 5 5
T 4 + ⋯ + 13 ⋯ 00 T^{4} + \cdots + 13\!\cdots\!00 T 4 + ⋯ + 1 3 ⋯ 0 0
T^4 + 36750*T^3 - 2162286135*T^2 - 40701412457500*T + 1389219666096442500
7 7 7
T 4 + ⋯ + 61 ⋯ 44 T^{4} + \cdots + 61\!\cdots\!44 T 4 + ⋯ + 6 1 ⋯ 4 4
T^4 - 176212*T^3 - 232243601248*T^2 - 2019980325249536*T + 6139355474263868473344
11 11 1 1
T 4 + ⋯ − 77 ⋯ 00 T^{4} + \cdots - 77\!\cdots\!00 T 4 + ⋯ − 7 7 ⋯ 0 0
T^4 + 3922006*T^3 - 92372702135571*T^2 - 594050980799160201240*T - 770981966072491929127772400
13 13 1 3
T 4 + ⋯ + 97 ⋯ 56 T^{4} + \cdots + 97\!\cdots\!56 T 4 + ⋯ + 9 7 ⋯ 5 6
T^4 + 10375302*T^3 - 256810192359331*T^2 - 374990092375148952132*T + 9742178899001281021224261156
17 17 1 7
( T − 24137569 ) 4 (T - 24137569)^{4} ( T − 2 4 1 3 7 5 6 9 ) 4
(T - 24137569)^4
19 19 1 9
T 4 + ⋯ + 63 ⋯ 64 T^{4} + \cdots + 63\!\cdots\!64 T 4 + ⋯ + 6 3 ⋯ 6 4
T^4 + 567072802*T^3 + 8851123332515097*T^2 - 21981147441383374829086264*T + 639885285237544868285024982912464
23 23 2 3
T 4 + ⋯ + 13 ⋯ 96 T^{4} + \cdots + 13\!\cdots\!96 T 4 + ⋯ + 1 3 ⋯ 9 6
T^4 - 452201610*T^3 - 866725572288127347*T^2 + 226596073089733401678807960*T + 137563792167579911092523885244708096
29 29 2 9
T 4 + ⋯ − 10 ⋯ 00 T^{4} + \cdots - 10\!\cdots\!00 T 4 + ⋯ − 1 0 ⋯ 0 0
T^4 - 7466949832*T^3 - 7674742763521692664*T^2 + 120934279986963623764666911520*T - 104152961538489306694526632666105700400
31 31 3 1
T 4 + ⋯ − 14 ⋯ 00 T^{4} + \cdots - 14\!\cdots\!00 T 4 + ⋯ − 1 4 ⋯ 0 0
T^4 - 5866788796*T^3 - 28370199743917756076*T^2 + 182730222863927384672298602400*T - 147386121417837225283321973963113344000
37 37 3 7
T 4 + ⋯ − 37 ⋯ 64 T^{4} + \cdots - 37\!\cdots\!64 T 4 + ⋯ − 3 7 ⋯ 6 4
T^4 + 30080445548*T^3 - 175656837409534811436*T^2 - 7625263956495864944012411324288*T - 37750723677931625945671520006066965598464
41 41 4 1
T 4 + ⋯ − 21 ⋯ 04 T^{4} + \cdots - 21\!\cdots\!04 T 4 + ⋯ − 2 1 ⋯ 0 4
T^4 + 61925267970*T^3 + 675240151914333838593*T^2 - 13933111079943450935520271082860*T - 213694511215382012820927447614720474510604
43 43 4 3
T 4 + ⋯ − 32 ⋯ 84 T^{4} + \cdots - 32\!\cdots\!84 T 4 + ⋯ − 3 2 ⋯ 8 4
T^4 + 46365502830*T^3 - 3647128612772385678567*T^2 - 233947987472751345590467292358680*T - 3277209148522704771336114296679821117699184
47 47 4 7
T 4 + ⋯ − 79 ⋯ 36 T^{4} + \cdots - 79\!\cdots\!36 T 4 + ⋯ − 7 9 ⋯ 3 6
T^4 + 78528307448*T^3 - 11470977886021867580948*T^2 - 642177393351423593087532080540736*T - 7954665643095352243109084471738345400231936
53 53 5 3
T 4 + ⋯ − 12 ⋯ 76 T^{4} + \cdots - 12\!\cdots\!76 T 4 + ⋯ − 1 2 ⋯ 7 6
T^4 - 372296114716*T^3 - 15097466218610583597632*T^2 + 16143220572868847467546921775227248*T - 1260184183919647056691410653460024793384367376
59 59 5 9
T 4 + ⋯ + 96 ⋯ 80 T^{4} + \cdots + 96\!\cdots\!80 T 4 + ⋯ + 9 6 ⋯ 8 0
T^4 + 543053500884*T^3 + 1514206188561268857204*T^2 - 19610358151335792212436165699101280*T + 961860450848415522024313022771883162787894080
61 61 6 1
T 4 + ⋯ + 87 ⋯ 80 T^{4} + \cdots + 87\!\cdots\!80 T 4 + ⋯ + 8 7 ⋯ 8 0
T^4 + 26421432784*T^3 - 20230784889035763542556*T^2 + 819519971889307469060474987414800*T + 8774313454125766527834266332738182672206080
67 67 6 7
T 4 + ⋯ − 97 ⋯ 80 T^{4} + \cdots - 97\!\cdots\!80 T 4 + ⋯ − 9 7 ⋯ 8 0
T^4 + 43428239608*T^3 - 1047110649895967506038144*T^2 - 605948384629998160487722222205477760*T - 97686404307636315490829449286372798888992692480
71 71 7 1
T 4 + ⋯ + 32 ⋯ 36 T^{4} + \cdots + 32\!\cdots\!36 T 4 + ⋯ + 3 2 ⋯ 3 6
T^4 + 1081258312680*T^3 - 4087978425051362552711952*T^2 - 3054389267866065196782749046448026240*T + 3268261616860804461242523374035715665331464667136
73 73 7 3
T 4 + ⋯ + 59 ⋯ 44 T^{4} + \cdots + 59\!\cdots\!44 T 4 + ⋯ + 5 9 ⋯ 4 4
T^4 + 3636861272948*T^3 + 2665343932276384929416592*T^2 - 878473566040310190153815768754907856*T + 59352657879620233232970807730446559101655604144
79 79 7 9
T 4 + ⋯ + 17 ⋯ 00 T^{4} + \cdots + 17\!\cdots\!00 T 4 + ⋯ + 1 7 ⋯ 0 0
T^4 - 187742689364*T^3 - 14861917454657460090800796*T^2 - 4500623359631403322053714798261676000*T + 1714559650971134244600489497355113048077387136000
83 83 8 3
T 4 + ⋯ + 62 ⋯ 24 T^{4} + \cdots + 62\!\cdots\!24 T 4 + ⋯ + 6 2 ⋯ 2 4
T^4 + 10027298590208*T^3 + 33176893034100005818318812*T^2 + 38475449209323645736141710181057859424*T + 6259559793626068799974720090428964659343646860224
89 89 8 9
T 4 + ⋯ − 67 ⋯ 84 T^{4} + \cdots - 67\!\cdots\!84 T 4 + ⋯ − 6 7 ⋯ 8 4
T^4 + 13835123617760*T^3 + 39215590137075015538440532*T^2 - 158699026267595879737888254173589439920*T - 672240802026121674791517458767888820876085978345984
97 97 9 7
T 4 + ⋯ − 13 ⋯ 80 T^{4} + \cdots - 13\!\cdots\!80 T 4 + ⋯ − 1 3 ⋯ 8 0
T^4 + 14912805328152*T^3 + 24750048206291492118640436*T^2 - 413490712397726804389997962200087082320*T - 1394576775603370189584257395539094819567317196174080
show more
show less