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Properties

Label 51.5.c.c
Level 5151
Weight 55
Character orbit 51.c
Analytic conductor 5.2725.272
Analytic rank 00
Dimension 2020
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [51,5,Mod(50,51)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(51, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("51.50");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 51=3⋅17 51 = 3 \cdot 17
Weight: k k == 5 5
Character orbit: [χ][\chi] == 51.c (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.271868117285.27186811728
Analytic rank: 00
Dimension: 2020
Coefficient field: Q[x]/(x20+⋯ )\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+200x18+22051x16+1226808x14+5013252x12−3569195664x10+⋯+12 ⁣⋯ ⁣01 x^{20} + 200 x^{18} + 22051 x^{16} + 1226808 x^{14} + 5013252 x^{12} - 3569195664 x^{10} + \cdots + 12\!\cdots\!01 Copy content Toggle raw display
Coefficient ring: Z[a1,…,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 24⋅310 2^{4}\cdot 3^{10}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 

Coefficients of the qq-expansion are expressed in terms of a basis 1,β1,…,β191,\beta_1,\ldots,\beta_{19} for the coefficient ring described below. We also show the integral qq-expansion of the trace form.

f(q)f(q) == q+β1q2+β6q3+(−β4−8)q4−β14q5−β10q6+β15q7+(β9−7β1)q8+(β5−20)q9+(−β18+2β6)q10+⋯+(−31β19+⋯+243β6)q99+O(q100) q + \beta_1 q^{2} + \beta_{6} q^{3} + ( - \beta_{4} - 8) q^{4} - \beta_{14} q^{5} - \beta_{10} q^{6} + \beta_{15} q^{7} + (\beta_{9} - 7 \beta_1) q^{8} + (\beta_{5} - 20) q^{9} + ( - \beta_{18} + 2 \beta_{6}) q^{10}+ \cdots + ( - 31 \beta_{19} + \cdots + 243 \beta_{6}) q^{99}+O(q^{100}) Copy content Toggle raw display
Tr⁡(f)(q)\operatorname{Tr}(f)(q) == 20q−168q4−400q9−308q13−72q15+600q16−124q18−548q19+16q21+3200q25−2580q30+4088q33−2072q34+4588q36−464q42+9028q43+⋯−13736q94+O(q100) 20 q - 168 q^{4} - 400 q^{9} - 308 q^{13} - 72 q^{15} + 600 q^{16} - 124 q^{18} - 548 q^{19} + 16 q^{21} + 3200 q^{25} - 2580 q^{30} + 4088 q^{33} - 2072 q^{34} + 4588 q^{36} - 464 q^{42} + 9028 q^{43}+ \cdots - 13736 q^{94}+O(q^{100}) Copy content Toggle raw display

Basis of coefficient ring in terms of a root ν\nu of x20+200x18+22051x16+1226808x14+5013252x12−3569195664x10+⋯+12 ⁣⋯ ⁣01 x^{20} + 200 x^{18} + 22051 x^{16} + 1226808 x^{14} + 5013252 x^{12} - 3569195664 x^{10} + \cdots + 12\!\cdots\!01 : Copy content Toggle raw display

β1\beta_{1}== (9676288307ν18+2066932568335ν16+303759546502772ν14+⋯+16 ⁣⋯ ⁣61)/74 ⁣⋯ ⁣84 ( 9676288307 \nu^{18} + 2066932568335 \nu^{16} + 303759546502772 \nu^{14} + \cdots + 16\!\cdots\!61 ) / 74\!\cdots\!84 Copy content Toggle raw display
β2\beta_{2}== (−22296163853ν18−62252999998105ν16+⋯−14 ⁣⋯ ⁣07)/74 ⁣⋯ ⁣84 ( - 22296163853 \nu^{18} - 62252999998105 \nu^{16} + \cdots - 14\!\cdots\!07 ) / 74\!\cdots\!84 Copy content Toggle raw display
β3\beta_{3}== (10596916ν18−823861717ν16−222708163958ν14−20897213752134ν12+⋯−50 ⁣⋯ ⁣57)/53 ⁣⋯ ⁣48 ( 10596916 \nu^{18} - 823861717 \nu^{16} - 222708163958 \nu^{14} - 20897213752134 \nu^{12} + \cdots - 50\!\cdots\!57 ) / 53\!\cdots\!48 Copy content Toggle raw display
β4\beta_{4}== (47899676ν18+5914967161ν16+454247668586ν14+3196707526746ν12+⋯+33 ⁣⋯ ⁣13)/16 ⁣⋯ ⁣44 ( 47899676 \nu^{18} + 5914967161 \nu^{16} + 454247668586 \nu^{14} + 3196707526746 \nu^{12} + \cdots + 33\!\cdots\!13 ) / 16\!\cdots\!44 Copy content Toggle raw display
β5\beta_{5}== (−ν18−200ν16−22051ν14−1226808ν12−5013252ν10+⋯−33 ⁣⋯ ⁣80)/18 ⁣⋯ ⁣41 ( - \nu^{18} - 200 \nu^{16} - 22051 \nu^{14} - 1226808 \nu^{12} - 5013252 \nu^{10} + \cdots - 33\!\cdots\!80 ) / 18\!\cdots\!41 Copy content Toggle raw display
β6\beta_{6}== (ν19+200ν17+22051ν15+1226808ν13+5013252ν11+⋯+37 ⁣⋯ ⁣00ν)/15 ⁣⋯ ⁣21 ( \nu^{19} + 200 \nu^{17} + 22051 \nu^{15} + 1226808 \nu^{13} + 5013252 \nu^{11} + \cdots + 37\!\cdots\!00 \nu ) / 15\!\cdots\!21 Copy content Toggle raw display
β7\beta_{7}== (−ν19−200ν17−22051ν15−1226808ν13−5013252ν11+⋯+79 ⁣⋯ ⁣63ν)/15 ⁣⋯ ⁣21 ( - \nu^{19} - 200 \nu^{17} - 22051 \nu^{15} - 1226808 \nu^{13} - 5013252 \nu^{11} + \cdots + 79\!\cdots\!63 \nu ) / 15\!\cdots\!21 Copy content Toggle raw display
β8\beta_{8}== (158730996001ν19−122002712855335ν17+⋯−13 ⁣⋯ ⁣69ν)/20 ⁣⋯ ⁣68 ( 158730996001 \nu^{19} - 122002712855335 \nu^{17} + \cdots - 13\!\cdots\!69 \nu ) / 20\!\cdots\!68 Copy content Toggle raw display
β9\beta_{9}== (−174866532347ν18−6054603354571ν16−7355327030372ν14+⋯+23 ⁣⋯ ⁣07)/24 ⁣⋯ ⁣28 ( - 174866532347 \nu^{18} - 6054603354571 \nu^{16} - 7355327030372 \nu^{14} + \cdots + 23\!\cdots\!07 ) / 24\!\cdots\!28 Copy content Toggle raw display
β10\beta_{10}== (−907610110121ν19−118035894441973ν17+⋯+73 ⁣⋯ ⁣01ν)/60 ⁣⋯ ⁣04 ( - 907610110121 \nu^{19} - 118035894441973 \nu^{17} + \cdots + 73\!\cdots\!01 \nu ) / 60\!\cdots\!04 Copy content Toggle raw display
β11\beta_{11}== (−229167004ν18−46766958929ν16−2796425671090ν14+⋯−21 ⁣⋯ ⁣89)/16 ⁣⋯ ⁣44 ( - 229167004 \nu^{18} - 46766958929 \nu^{16} - 2796425671090 \nu^{14} + \cdots - 21\!\cdots\!89 ) / 16\!\cdots\!44 Copy content Toggle raw display
β12\beta_{12}== (−828988309543ν18−183250833369281ν16+⋯−16 ⁣⋯ ⁣75)/37 ⁣⋯ ⁣92 ( - 828988309543 \nu^{18} - 183250833369281 \nu^{16} + \cdots - 16\!\cdots\!75 ) / 37\!\cdots\!92 Copy content Toggle raw display
β13\beta_{13}== (−633534294115ν18−93776242199123ν16+⋯−26 ⁣⋯ ⁣57)/24 ⁣⋯ ⁣28 ( - 633534294115 \nu^{18} - 93776242199123 \nu^{16} + \cdots - 26\!\cdots\!57 ) / 24\!\cdots\!28 Copy content Toggle raw display
β14\beta_{14}== (−58464901223ν19−7551515335633ν17−434954518032500ν15+⋯−45 ⁣⋯ ⁣35ν)/15 ⁣⋯ ⁣08 ( - 58464901223 \nu^{19} - 7551515335633 \nu^{17} - 434954518032500 \nu^{15} + \cdots - 45\!\cdots\!35 \nu ) / 15\!\cdots\!08 Copy content Toggle raw display
β15\beta_{15}== (−18885109733ν19−3863813826733ν17−170035349894360ν15+⋯−15 ⁣⋯ ⁣11ν)/49 ⁣⋯ ⁣32 ( - 18885109733 \nu^{19} - 3863813826733 \nu^{17} - 170035349894360 \nu^{15} + \cdots - 15\!\cdots\!11 \nu ) / 49\!\cdots\!32 Copy content Toggle raw display
β16\beta_{16}== (347883676277ν19+69424256467225ν17+⋯+50 ⁣⋯ ⁣35ν)/66 ⁣⋯ ⁣56 ( 347883676277 \nu^{19} + 69424256467225 \nu^{17} + \cdots + 50\!\cdots\!35 \nu ) / 66\!\cdots\!56 Copy content Toggle raw display
β17\beta_{17}== (−7780409851645ν19+⋯−85 ⁣⋯ ⁣47ν)/60 ⁣⋯ ⁣04 ( - 7780409851645 \nu^{19} + \cdots - 85\!\cdots\!47 \nu ) / 60\!\cdots\!04 Copy content Toggle raw display
β18\beta_{18}== (−129290273341ν19−27416167122101ν17+⋯−30 ⁣⋯ ⁣55ν)/98 ⁣⋯ ⁣64 ( - 129290273341 \nu^{19} - 27416167122101 \nu^{17} + \cdots - 30\!\cdots\!55 \nu ) / 98\!\cdots\!64 Copy content Toggle raw display
β19\beta_{19}== (234547778099ν19+21510636793915ν17+⋯+21 ⁣⋯ ⁣69ν)/10 ⁣⋯ ⁣72 ( 234547778099 \nu^{19} + 21510636793915 \nu^{17} + \cdots + 21\!\cdots\!69 \nu ) / 10\!\cdots\!72 Copy content Toggle raw display

Display νj\nu^j in terms of βi\beta_i

ν\nu== (β7+β6)/3 ( \beta_{7} + \beta_{6} ) / 3 Copy content Toggle raw display
ν2\nu^{2}== (−β5−β4−β3+β2−β1−60)/3 ( -\beta_{5} - \beta_{4} - \beta_{3} + \beta_{2} - \beta _1 - 60 ) / 3 Copy content Toggle raw display
ν3\nu^{3}== (−3β19+9β18−15β17+9β16−3β15+18β14+⋯+5β6)/3 ( - 3 \beta_{19} + 9 \beta_{18} - 15 \beta_{17} + 9 \beta_{16} - 3 \beta_{15} + 18 \beta_{14} + \cdots + 5 \beta_{6} ) / 3 Copy content Toggle raw display
ν4\nu^{4}== (45β12−9β11+63β9+28β5+523β4−80β3−28β2+⋯−1425)/3 ( 45 \beta_{12} - 9 \beta_{11} + 63 \beta_{9} + 28 \beta_{5} + 523 \beta_{4} - 80 \beta_{3} - 28 \beta_{2} + \cdots - 1425 ) / 3 Copy content Toggle raw display
ν5\nu^{5}== (651β19−171β18−102β17−486β16−321β15+⋯−5306β6)/3 ( 651 \beta_{19} - 171 \beta_{18} - 102 \beta_{17} - 486 \beta_{16} - 321 \beta_{15} + \cdots - 5306 \beta_{6} ) / 3 Copy content Toggle raw display
ν6\nu^{6}== (−4482β13+1764β12−540β11−4950β9−667β5−47458β4+⋯+483618)/3 ( - 4482 \beta_{13} + 1764 \beta_{12} - 540 \beta_{11} - 4950 \beta_{9} - 667 \beta_{5} - 47458 \beta_{4} + \cdots + 483618 ) / 3 Copy content Toggle raw display
ν7\nu^{7}== (−42474β19−10116β18−48030β17−193680β16−113592β15+⋯+112559β6)/3 ( - 42474 \beta_{19} - 10116 \beta_{18} - 48030 \beta_{17} - 193680 \beta_{16} - 113592 \beta_{15} + \cdots + 112559 \beta_{6} ) / 3 Copy content Toggle raw display
ν8\nu^{8}== (−85320β13+117360β12+196056β11+937692β9−713276β5+⋯+753171)/3 ( - 85320 \beta_{13} + 117360 \beta_{12} + 196056 \beta_{11} + 937692 \beta_{9} - 713276 \beta_{5} + \cdots + 753171 ) / 3 Copy content Toggle raw display
ν9\nu^{9}== (1025922β19+6022260β18−1097454β17+2422242β16+⋯+41402443β6)/3 ( 1025922 \beta_{19} + 6022260 \beta_{18} - 1097454 \beta_{17} + 2422242 \beta_{16} + \cdots + 41402443 \beta_{6} ) / 3 Copy content Toggle raw display
ν10\nu^{10}== (19939770β13+16676316β12−32255190β11−29438298β9−28540027β5+⋯−3412104702)/3 ( 19939770 \beta_{13} + 16676316 \beta_{12} - 32255190 \beta_{11} - 29438298 \beta_{9} - 28540027 \beta_{5} + \cdots - 3412104702 ) / 3 Copy content Toggle raw display
ν11\nu^{11}== (207475341β19+96119307β18−17584647β17−560202507β16+⋯+2135081579β6)/3 ( 207475341 \beta_{19} + 96119307 \beta_{18} - 17584647 \beta_{17} - 560202507 \beta_{16} + \cdots + 2135081579 \beta_{6} ) / 3 Copy content Toggle raw display
ν12\nu^{12}== (−3049074144β13+1282313043β12+1412735175β11−261088263β9+⋯−183613046097)/3 ( - 3049074144 \beta_{13} + 1282313043 \beta_{12} + 1412735175 \beta_{11} - 261088263 \beta_{9} + \cdots - 183613046097 ) / 3 Copy content Toggle raw display
ν13\nu^{13}== (−14516668581β19−24712389801β18+35536646076β17+⋯+41511557974β6)/3 ( - 14516668581 \beta_{19} - 24712389801 \beta_{18} + 35536646076 \beta_{17} + \cdots + 41511557974 \beta_{6} ) / 3 Copy content Toggle raw display
ν14\nu^{14}== (104328211032β13−153044906400β12+195191011512β11+129975854544β9+⋯−4524796184604)/3 ( 104328211032 \beta_{13} - 153044906400 \beta_{12} + 195191011512 \beta_{11} + 129975854544 \beta_{9} + \cdots - 4524796184604 ) / 3 Copy content Toggle raw display
ν15\nu^{15}== (−117333258888β19+259120246032β18−1101385341240β17+⋯+12750738869741β6)/3 ( - 117333258888 \beta_{19} + 259120246032 \beta_{18} - 1101385341240 \beta_{17} + \cdots + 12750738869741 \beta_{6} ) / 3 Copy content Toggle raw display
ν16\nu^{16}== (6337818083376β13−1189044059040β12−30691850959800β11+9229689217080β9+⋯−814310579928765)/3 ( 6337818083376 \beta_{13} - 1189044059040 \beta_{12} - 30691850959800 \beta_{11} + 9229689217080 \beta_{9} + \cdots - 814310579928765 ) / 3 Copy content Toggle raw display
ν17\nu^{17}== (687231001272β19+45116932842000β18+362332230399384β17+⋯+282679244400001β6)/3 ( 687231001272 \beta_{19} + 45116932842000 \beta_{18} + 362332230399384 \beta_{17} + \cdots + 282679244400001 \beta_{6} ) / 3 Copy content Toggle raw display
ν18\nu^{18}== (−84541607934696β13−59745797980704β12+⋯−59 ⁣⋯ ⁣48)/3 ( - 84541607934696 \beta_{13} - 59745797980704 \beta_{12} + \cdots - 59\!\cdots\!48 ) / 3 Copy content Toggle raw display
ν19\nu^{19}== (85 ⁣⋯ ⁣65β19+⋯+73 ⁣⋯ ⁣29β6)/3 ( 85\!\cdots\!65 \beta_{19} + \cdots + 73\!\cdots\!29 \beta_{6} ) / 3 Copy content Toggle raw display

Display βi\beta_i in terms of νj\nu^j

Character values

We give the values of χ\chi on generators for (Z/51Z)×\left(\mathbb{Z}/51\mathbb{Z}\right)^\times.

nn 3535 3737
χ(n)\chi(n) −1-1 −1-1

Embeddings

For each embedding ιm\iota_m of the coefficient field, the values ιm(an)\iota_m(a_n) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   ιm(ν)\iota_m(\nu) a2 a_{2} a3 a_{3} a4 a_{4} a5 a_{5} a6 a_{6} a7 a_{7} a8 a_{8} a9 a_{9} a10 a_{10}
50.1
1.27725 − 8.90891i
−1.27725 + 8.90891i
8.75115 − 2.10174i
−8.75115 + 2.10174i
6.04116 + 6.67116i
−6.04116 − 6.67116i
3.53470 + 8.27683i
−3.53470 − 8.27683i
5.02953 − 7.46350i
−5.02953 + 7.46350i
5.02953 + 7.46350i
−5.02953 − 7.46350i
3.53470 − 8.27683i
−3.53470 + 8.27683i
6.04116 − 6.67116i
−6.04116 + 6.67116i
8.75115 + 2.10174i
−8.75115 − 2.10174i
1.27725 + 8.90891i
−1.27725 − 8.90891i
− 7.45221i −1.27725 − 8.90891i −39.5354 18.0441 −66.3910 + 9.51836i − 41.9203i 175.391i −77.7372 + 22.7579i − 134.468i
50.2 − 7.45221i 1.27725 + 8.90891i −39.5354 −18.0441 66.3910 − 9.51836i 41.9203i 175.391i −77.7372 + 22.7579i 134.468i
50.3 − 5.60864i −8.75115 − 2.10174i −15.4569 −14.8672 −11.7879 + 49.0821i 42.9260i − 3.04611i 72.1654 + 36.7853i 83.3848i
50.4 − 5.60864i 8.75115 + 2.10174i −15.4569 14.8672 11.7879 − 49.0821i − 42.9260i − 3.04611i 72.1654 + 36.7853i − 83.3848i
50.5 − 4.92716i −6.04116 + 6.67116i −8.27693 40.8754 32.8699 + 29.7658i − 9.63955i − 38.0528i −8.00871 − 80.6031i − 201.400i
50.6 − 4.92716i 6.04116 − 6.67116i −8.27693 −40.8754 −32.8699 − 29.7658i 9.63955i − 38.0528i −8.00871 − 80.6031i 201.400i
50.7 − 2.64556i −3.53470 + 8.27683i 9.00101 −41.0631 21.8968 + 9.35126i − 79.2595i − 66.1417i −56.0118 − 58.5122i 108.635i
50.8 − 2.64556i 3.53470 − 8.27683i 9.00101 41.0631 −21.8968 − 9.35126i 79.2595i − 66.1417i −56.0118 − 58.5122i − 108.635i
50.9 − 1.93178i −5.02953 − 7.46350i 12.2682 4.62649 −14.4178 + 9.71595i − 58.0263i − 54.6080i −30.4076 + 75.0758i − 8.93735i
50.10 − 1.93178i 5.02953 + 7.46350i 12.2682 −4.62649 14.4178 − 9.71595i 58.0263i − 54.6080i −30.4076 + 75.0758i 8.93735i
50.11 1.93178i −5.02953 + 7.46350i 12.2682 4.62649 −14.4178 − 9.71595i 58.0263i 54.6080i −30.4076 − 75.0758i 8.93735i
50.12 1.93178i 5.02953 − 7.46350i 12.2682 −4.62649 14.4178 + 9.71595i − 58.0263i 54.6080i −30.4076 − 75.0758i − 8.93735i
50.13 2.64556i −3.53470 − 8.27683i 9.00101 −41.0631 21.8968 − 9.35126i 79.2595i 66.1417i −56.0118 + 58.5122i − 108.635i
50.14 2.64556i 3.53470 + 8.27683i 9.00101 41.0631 −21.8968 + 9.35126i − 79.2595i 66.1417i −56.0118 + 58.5122i 108.635i
50.15 4.92716i −6.04116 − 6.67116i −8.27693 40.8754 32.8699 − 29.7658i 9.63955i 38.0528i −8.00871 + 80.6031i 201.400i
50.16 4.92716i 6.04116 + 6.67116i −8.27693 −40.8754 −32.8699 + 29.7658i − 9.63955i 38.0528i −8.00871 + 80.6031i − 201.400i
50.17 5.60864i −8.75115 + 2.10174i −15.4569 −14.8672 −11.7879 − 49.0821i − 42.9260i 3.04611i 72.1654 − 36.7853i − 83.3848i
50.18 5.60864i 8.75115 − 2.10174i −15.4569 14.8672 11.7879 + 49.0821i 42.9260i 3.04611i 72.1654 − 36.7853i 83.3848i
50.19 7.45221i −1.27725 + 8.90891i −39.5354 18.0441 −66.3910 − 9.51836i 41.9203i − 175.391i −77.7372 − 22.7579i 134.468i
50.20 7.45221i 1.27725 − 8.90891i −39.5354 −18.0441 66.3910 + 9.51836i − 41.9203i − 175.391i −77.7372 − 22.7579i − 134.468i
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 50.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
17.b even 2 1 inner
51.c odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 51.5.c.c ✓ 20
3.b odd 2 1 inner 51.5.c.c ✓ 20
17.b even 2 1 inner 51.5.c.c ✓ 20
51.c odd 2 1 inner 51.5.c.c ✓ 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
51.5.c.c ✓ 20 1.a even 1 1 trivial
51.5.c.c ✓ 20 3.b odd 2 1 inner
51.5.c.c ✓ 20 17.b even 2 1 inner
51.5.c.c ✓ 20 51.c odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on S5new(51,[χ])S_{5}^{\mathrm{new}}(51, [\chi]):

T210+122T28+5079T26+86726T24+555892T22+1107720 T_{2}^{10} + 122T_{2}^{8} + 5079T_{2}^{6} + 86726T_{2}^{4} + 555892T_{2}^{2} + 1107720 Copy content Toggle raw display
T510−3925T58+4807776T56−1882685412T54+240880604544T52−4339677233664 T_{5}^{10} - 3925T_{5}^{8} + 4807776T_{5}^{6} - 1882685412T_{5}^{4} + 240880604544T_{5}^{2} - 4339677233664 Copy content Toggle raw display

Hecke characteristic polynomials

pp Fp(T)F_p(T)
22 (T10+122T8+⋯+1107720)2 (T^{10} + 122 T^{8} + \cdots + 1107720)^{2} Copy content Toggle raw display
33 T20+⋯+12 ⁣⋯ ⁣01 T^{20} + \cdots + 12\!\cdots\!01 Copy content Toggle raw display
55 (T10+⋯−4339677233664)2 (T^{10} + \cdots - 4339677233664)^{2} Copy content Toggle raw display
77 (T10+⋯+63 ⁣⋯ ⁣00)2 (T^{10} + \cdots + 63\!\cdots\!00)^{2} Copy content Toggle raw display
1111 (T10+⋯−5675378866696)2 (T^{10} + \cdots - 5675378866696)^{2} Copy content Toggle raw display
1313 (T5+77T4+⋯+29775471712)4 (T^{5} + 77 T^{4} + \cdots + 29775471712)^{4} Copy content Toggle raw display
1717 T20+⋯+16 ⁣⋯ ⁣01 T^{20} + \cdots + 16\!\cdots\!01 Copy content Toggle raw display
1919 (T5+⋯−2581305358016)4 (T^{5} + \cdots - 2581305358016)^{4} Copy content Toggle raw display
2323 (T10+⋯−91 ⁣⋯ ⁣96)2 (T^{10} + \cdots - 91\!\cdots\!96)^{2} Copy content Toggle raw display
2929 (T10+⋯−22 ⁣⋯ ⁣76)2 (T^{10} + \cdots - 22\!\cdots\!76)^{2} Copy content Toggle raw display
3131 (T10+⋯+20 ⁣⋯ ⁣20)2 (T^{10} + \cdots + 20\!\cdots\!20)^{2} Copy content Toggle raw display
3737 (T10+⋯+13 ⁣⋯ ⁣00)2 (T^{10} + \cdots + 13\!\cdots\!00)^{2} Copy content Toggle raw display
4141 (T10+⋯−26 ⁣⋯ ⁣16)2 (T^{10} + \cdots - 26\!\cdots\!16)^{2} Copy content Toggle raw display
4343 (T5+⋯−14 ⁣⋯ ⁣44)4 (T^{5} + \cdots - 14\!\cdots\!44)^{4} Copy content Toggle raw display
4747 (T10+⋯+86 ⁣⋯ ⁣00)2 (T^{10} + \cdots + 86\!\cdots\!00)^{2} Copy content Toggle raw display
5353 (T10+⋯+19 ⁣⋯ ⁣80)2 (T^{10} + \cdots + 19\!\cdots\!80)^{2} Copy content Toggle raw display
5959 (T10+⋯+13 ⁣⋯ ⁣80)2 (T^{10} + \cdots + 13\!\cdots\!80)^{2} Copy content Toggle raw display
6161 (T10+⋯+35 ⁣⋯ ⁣00)2 (T^{10} + \cdots + 35\!\cdots\!00)^{2} Copy content Toggle raw display
6767 (T5+⋯+11 ⁣⋯ ⁣48)4 (T^{5} + \cdots + 11\!\cdots\!48)^{4} Copy content Toggle raw display
7171 (T10+⋯−51 ⁣⋯ ⁣04)2 (T^{10} + \cdots - 51\!\cdots\!04)^{2} Copy content Toggle raw display
7373 (T10+⋯+98 ⁣⋯ ⁣20)2 (T^{10} + \cdots + 98\!\cdots\!20)^{2} Copy content Toggle raw display
7979 (T10+⋯+20 ⁣⋯ ⁣80)2 (T^{10} + \cdots + 20\!\cdots\!80)^{2} Copy content Toggle raw display
8383 (T10+⋯+11 ⁣⋯ ⁣80)2 (T^{10} + \cdots + 11\!\cdots\!80)^{2} Copy content Toggle raw display
8989 (T10+⋯+56 ⁣⋯ ⁣20)2 (T^{10} + \cdots + 56\!\cdots\!20)^{2} Copy content Toggle raw display
9797 (T10+⋯+23 ⁣⋯ ⁣80)2 (T^{10} + \cdots + 23\!\cdots\!80)^{2} Copy content Toggle raw display
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