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Properties

Label 200.6.f.b
Level 200200
Weight 66
Character orbit 200.f
Analytic conductor 32.07732.077
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,6,Mod(149,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.149");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 200=23⋅52 200 = 2^{3} \cdot 5^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 200.f (of order 22, degree 11, not 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: 32.076763962632.0767639626
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: x20−2x19−17x18+78x17+253x16−884x15+2396x14+19376x13+⋯+1099511627776 x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 Copy content Toggle raw display
Coefficient ring: Z[a1,…,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 245⋅34⋅58 2^{45}\cdot 3^{4}\cdot 5^{8}
Twist minimal: no (minimal twist has level 40)
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+(−β7−2)q3+(β5+2)q4+(−β10+β2+2β1+10)q6+(−β6+β5+β2+⋯+1)q7+(β3+β2−2β1−12)q8+⋯+(−58β19+291β18+⋯+472)q99+O(q100) q - \beta_1 q^{2} + ( - \beta_{7} - 2) q^{3} + (\beta_{5} + 2) q^{4} + ( - \beta_{10} + \beta_{2} + 2 \beta_1 + 10) q^{6} + ( - \beta_{6} + \beta_{5} + \beta_{2} + \cdots + 1) q^{7} + (\beta_{3} + \beta_{2} - 2 \beta_1 - 12) q^{8}+ \cdots + ( - 58 \beta_{19} + 291 \beta_{18} + \cdots + 472) q^{99}+O(q^{100}) Copy content Toggle raw display
Tr⁡(f)(q)\operatorname{Tr}(f)(q) == 20q−2q2−36q3+32q4+204q6−248q8+1620q9−1252q12−2708q14+3080q16−2070q18−8244q22−1032q24−8084q26−11664q27−22924q28+⋯−663674q98+O(q100) 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28}+ \cdots - 663674 q^{98}+O(q^{100}) Copy content Toggle raw display

Basis of coefficient ring in terms of a root ν\nu of x20−2x19−17x18+78x17+253x16−884x15+2396x14+19376x13+⋯+1099511627776 x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 : Copy content Toggle raw display

β1\beta_{1}== (−67985ν19+62912ν18+1230021ν17−3396972ν16+⋯+11 ⁣⋯ ⁣16)/12 ⁣⋯ ⁣60 ( - 67985 \nu^{19} + 62912 \nu^{18} + 1230021 \nu^{17} - 3396972 \nu^{16} + \cdots + 11\!\cdots\!16 ) / 12\!\cdots\!60 Copy content Toggle raw display
β2\beta_{2}== (−1334623ν19−6032834ν18+30741327ν17+53342094ν16+⋯+31 ⁣⋯ ⁣84)/16 ⁣⋯ ⁣28 ( - 1334623 \nu^{19} - 6032834 \nu^{18} + 30741327 \nu^{17} + 53342094 \nu^{16} + \cdots + 31\!\cdots\!84 ) / 16\!\cdots\!28 Copy content Toggle raw display
β3\beta_{3}== (7166555ν19−46758710ν18−1326206475ν17+2375023674ν16+⋯−93 ⁣⋯ ⁣16)/82 ⁣⋯ ⁣40 ( 7166555 \nu^{19} - 46758710 \nu^{18} - 1326206475 \nu^{17} + 2375023674 \nu^{16} + \cdots - 93\!\cdots\!16 ) / 82\!\cdots\!40 Copy content Toggle raw display
β4\beta_{4}== (−192881341ν19+14688393370ν18+34351336269ν17−97539248310ν16+⋯+53 ⁣⋯ ⁣36)/21 ⁣⋯ ⁣40 ( - 192881341 \nu^{19} + 14688393370 \nu^{18} + 34351336269 \nu^{17} - 97539248310 \nu^{16} + \cdots + 53\!\cdots\!36 ) / 21\!\cdots\!40 Copy content Toggle raw display
β5\beta_{5}== (−36529ν19+37138ν18+952929ν17+2345826ν16+⋯+36 ⁣⋯ ⁣00)/321582991933440 ( - 36529 \nu^{19} + 37138 \nu^{18} + 952929 \nu^{17} + 2345826 \nu^{16} + \cdots + 36\!\cdots\!00 ) / 321582991933440 Copy content Toggle raw display
β6\beta_{6}== (−299251771ν19+3783277174ν18+21114888939ν17+1756737030ν16+⋯+30 ⁣⋯ ⁣00)/21 ⁣⋯ ⁣40 ( - 299251771 \nu^{19} + 3783277174 \nu^{18} + 21114888939 \nu^{17} + 1756737030 \nu^{16} + \cdots + 30\!\cdots\!00 ) / 21\!\cdots\!40 Copy content Toggle raw display
β7\beta_{7}== (−1159161ν19−876270ν18+12454985ν17−11755262ν16+⋯+12 ⁣⋯ ⁣68)/46 ⁣⋯ ⁣60 ( - 1159161 \nu^{19} - 876270 \nu^{18} + 12454985 \nu^{17} - 11755262 \nu^{16} + \cdots + 12\!\cdots\!68 ) / 46\!\cdots\!60 Copy content Toggle raw display
β8\beta_{8}== (156457ν19+977582ν18+2983239ν17−17626242ν16+⋯+28 ⁣⋯ ⁣24)/605332690698240 ( 156457 \nu^{19} + 977582 \nu^{18} + 2983239 \nu^{17} - 17626242 \nu^{16} + \cdots + 28\!\cdots\!24 ) / 605332690698240 Copy content Toggle raw display
β9\beta_{9}== (−213569915ν19−3356881930ν18−18244966869ν17−19203947130ν16+⋯−22 ⁣⋯ ⁣76)/53 ⁣⋯ ⁣60 ( - 213569915 \nu^{19} - 3356881930 \nu^{18} - 18244966869 \nu^{17} - 19203947130 \nu^{16} + \cdots - 22\!\cdots\!76 ) / 53\!\cdots\!60 Copy content Toggle raw display
β10\beta_{10}== (180646075ν19+1159891466ν18−400600683ν17−3359147142ν16+⋯−37 ⁣⋯ ⁣20)/35 ⁣⋯ ⁣40 ( 180646075 \nu^{19} + 1159891466 \nu^{18} - 400600683 \nu^{17} - 3359147142 \nu^{16} + \cdots - 37\!\cdots\!20 ) / 35\!\cdots\!40 Copy content Toggle raw display
β11\beta_{11}== (1103951461ν19−10117315594ν18−26494398261ν17+135432087558ν16+⋯−70 ⁣⋯ ⁣68)/21 ⁣⋯ ⁣40 ( 1103951461 \nu^{19} - 10117315594 \nu^{18} - 26494398261 \nu^{17} + 135432087558 \nu^{16} + \cdots - 70\!\cdots\!68 ) / 21\!\cdots\!40 Copy content Toggle raw display
β12\beta_{12}== (−93706979ν19−141114154ν18+1115274483ν17+149641926ν16+⋯+78 ⁣⋯ ⁣80)/17 ⁣⋯ ⁣20 ( - 93706979 \nu^{19} - 141114154 \nu^{18} + 1115274483 \nu^{17} + 149641926 \nu^{16} + \cdots + 78\!\cdots\!80 ) / 17\!\cdots\!20 Copy content Toggle raw display
β13\beta_{13}== (67985ν19−62912ν18−1230021ν17+3396972ν16+⋯−11 ⁣⋯ ⁣92)/128633196773376 ( 67985 \nu^{19} - 62912 \nu^{18} - 1230021 \nu^{17} + 3396972 \nu^{16} + \cdots - 11\!\cdots\!92 ) / 128633196773376 Copy content Toggle raw display
β14\beta_{14}== (1346839351ν19−1644923758ν18−43011703719ν17−15233921598ν16+⋯−41 ⁣⋯ ⁣68)/21 ⁣⋯ ⁣40 ( 1346839351 \nu^{19} - 1644923758 \nu^{18} - 43011703719 \nu^{17} - 15233921598 \nu^{16} + \cdots - 41\!\cdots\!68 ) / 21\!\cdots\!40 Copy content Toggle raw display
β15\beta_{15}== (505812019ν19+4224516506ν18−6123990627ν17−35257502838ν16+⋯−12 ⁣⋯ ⁣12)/71 ⁣⋯ ⁣80 ( 505812019 \nu^{19} + 4224516506 \nu^{18} - 6123990627 \nu^{17} - 35257502838 \nu^{16} + \cdots - 12\!\cdots\!12 ) / 71\!\cdots\!80 Copy content Toggle raw display
β16\beta_{16}== (1853756651ν19+1747045642ν18+9318978981ν17−49450238790ν16+⋯−49 ⁣⋯ ⁣44)/10 ⁣⋯ ⁣20 ( 1853756651 \nu^{19} + 1747045642 \nu^{18} + 9318978981 \nu^{17} - 49450238790 \nu^{16} + \cdots - 49\!\cdots\!44 ) / 10\!\cdots\!20 Copy content Toggle raw display
β17\beta_{17}== (−3850944367ν19−1017879362ν18+45482103711ν17+174754088526ν16+⋯+85 ⁣⋯ ⁣76)/21 ⁣⋯ ⁣40 ( - 3850944367 \nu^{19} - 1017879362 \nu^{18} + 45482103711 \nu^{17} + 174754088526 \nu^{16} + \cdots + 85\!\cdots\!76 ) / 21\!\cdots\!40 Copy content Toggle raw display
β18\beta_{18}== (130011995ν19−169747150ν18−3380145243ν17+415414866ν16+⋯−57 ⁣⋯ ⁣04)/59 ⁣⋯ ⁣40 ( 130011995 \nu^{19} - 169747150 \nu^{18} - 3380145243 \nu^{17} + 415414866 \nu^{16} + \cdots - 57\!\cdots\!04 ) / 59\!\cdots\!40 Copy content Toggle raw display
β19\beta_{19}== (−1224412387ν19−847266530ν18+17618041827ν17−19790632194ν16+⋯+13 ⁣⋯ ⁣48)/53 ⁣⋯ ⁣60 ( - 1224412387 \nu^{19} - 847266530 \nu^{18} + 17618041827 \nu^{17} - 19790632194 \nu^{16} + \cdots + 13\!\cdots\!48 ) / 53\!\cdots\!60 Copy content Toggle raw display

Display νj\nu^j in terms of βi\beta_i

ν\nu== (β13+10β1+1)/20 ( \beta_{13} + 10\beta _1 + 1 ) / 20 Copy content Toggle raw display
ν2\nu^{2}== (β12−2β7−β2+β1+19)/10 ( \beta_{12} - 2\beta_{7} - \beta_{2} + \beta _1 + 19 ) / 10 Copy content Toggle raw display
ν3\nu^{3}== (β19+β18−β17+β16−3β15+β12+β10+3β8+⋯−123)/20 ( \beta_{19} + \beta_{18} - \beta_{17} + \beta_{16} - 3 \beta_{15} + \beta_{12} + \beta_{10} + 3 \beta_{8} + \cdots - 123 ) / 20 Copy content Toggle raw display
ν4\nu^{4}== (−3β19−β18+β16+β15−2β14−3β13+β12+⋯−147)/4 ( - 3 \beta_{19} - \beta_{18} + \beta_{16} + \beta_{15} - 2 \beta_{14} - 3 \beta_{13} + \beta_{12} + \cdots - 147 ) / 4 Copy content Toggle raw display
ν5\nu^{5}== (10β19−40β18−31β17+10β16+10β15+122β14+⋯−2530)/20 ( 10 \beta_{19} - 40 \beta_{18} - 31 \beta_{17} + 10 \beta_{16} + 10 \beta_{15} + 122 \beta_{14} + \cdots - 2530 ) / 20 Copy content Toggle raw display
ν6\nu^{6}== (5β19−11β18−45β17−7β16+145β15−248β14+⋯−31087)/20 ( 5 \beta_{19} - 11 \beta_{18} - 45 \beta_{17} - 7 \beta_{16} + 145 \beta_{15} - 248 \beta_{14} + \cdots - 31087 ) / 20 Copy content Toggle raw display
ν7\nu^{7}== (257β19−413β18−188β17−403β16−491β15+958β14+⋯−122399)/20 ( 257 \beta_{19} - 413 \beta_{18} - 188 \beta_{17} - 403 \beta_{16} - 491 \beta_{15} + 958 \beta_{14} + \cdots - 122399 ) / 20 Copy content Toggle raw display
ν8\nu^{8}== (−126β19+344β18+189β17−110β16+2β15−558β14+⋯+52990)/4 ( - 126 \beta_{19} + 344 \beta_{18} + 189 \beta_{17} - 110 \beta_{16} + 2 \beta_{15} - 558 \beta_{14} + \cdots + 52990 ) / 4 Copy content Toggle raw display
ν9\nu^{9}== (−1659β19+2021β18−2349β17−8039β16−2703β15+⋯+1453393)/20 ( - 1659 \beta_{19} + 2021 \beta_{18} - 2349 \beta_{17} - 8039 \beta_{16} - 2703 \beta_{15} + \cdots + 1453393 ) / 20 Copy content Toggle raw display
ν10\nu^{10}== (113β19+26739β18+14572β17−14739β16+7525β15+⋯−4767607)/20 ( 113 \beta_{19} + 26739 \beta_{18} + 14572 \beta_{17} - 14739 \beta_{16} + 7525 \beta_{15} + \cdots - 4767607 ) / 20 Copy content Toggle raw display
ν11\nu^{11}== (147162β19+238392β18−9527β17−37158β16−196966β15+⋯+20624462)/20 ( 147162 \beta_{19} + 238392 \beta_{18} - 9527 \beta_{17} - 37158 \beta_{16} - 196966 \beta_{15} + \cdots + 20624462 ) / 20 Copy content Toggle raw display
ν12\nu^{12}== (−86847β19+50961β18+52727β17+31301β16−78563β15+⋯−19463843)/4 ( - 86847 \beta_{19} + 50961 \beta_{18} + 52727 \beta_{17} + 31301 \beta_{16} - 78563 \beta_{15} + \cdots - 19463843 ) / 4 Copy content Toggle raw display
ν13\nu^{13}== (−969663β19−189853β18+974964β17+1126797β16+139669β15+⋯+435249937)/20 ( - 969663 \beta_{19} - 189853 \beta_{18} + 974964 \beta_{17} + 1126797 \beta_{16} + 139669 \beta_{15} + \cdots + 435249937 ) / 20 Copy content Toggle raw display
ν14\nu^{14}== (7200106β19−2130120β18−6637631β17−378214β16+2461290β15+⋯−528732762)/20 ( 7200106 \beta_{19} - 2130120 \beta_{18} - 6637631 \beta_{17} - 378214 \beta_{16} + 2461290 \beta_{15} + \cdots - 528732762 ) / 20 Copy content Toggle raw display
ν15\nu^{15}== (3690981β19−30470619β18+5305331β17+5479801β16+8408337β15+⋯−5009602511)/20 ( 3690981 \beta_{19} - 30470619 \beta_{18} + 5305331 \beta_{17} + 5479801 \beta_{16} + 8408337 \beta_{15} + \cdots - 5009602511 ) / 20 Copy content Toggle raw display
ν16\nu^{16}== (30094205β19−17270761β18−540148β17−2613911β16−11151071β15+⋯+2735351589)/4 ( 30094205 \beta_{19} - 17270761 \beta_{18} - 540148 \beta_{17} - 2613911 \beta_{16} - 11151071 \beta_{15} + \cdots + 2735351589 ) / 4 Copy content Toggle raw display
ν17\nu^{17}== (−532611398β19−437359688β18+226848345β17+283715482β16+⋯+83066270718)/20 ( - 532611398 \beta_{19} - 437359688 \beta_{18} + 226848345 \beta_{17} + 283715482 \beta_{16} + \cdots + 83066270718 ) / 20 Copy content Toggle raw display
ν18\nu^{18}== (−300117019β19−2853763499β18+592592179β17−524067847β16+⋯+91076734833)/20 ( - 300117019 \beta_{19} - 2853763499 \beta_{18} + 592592179 \beta_{17} - 524067847 \beta_{16} + \cdots + 91076734833 ) / 20 Copy content Toggle raw display
ν19\nu^{19}== (2877301505β19+5664859555β18−333178812β17+7928989165β16+⋯+375256454785)/20 ( 2877301505 \beta_{19} + 5664859555 \beta_{18} - 333178812 \beta_{17} + 7928989165 \beta_{16} + \cdots + 375256454785 ) / 20 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/200Z)×\left(\mathbb{Z}/200\mathbb{Z}\right)^\times.

nn 101101 151151 177177
χ(n)\chi(n) −1-1 11 −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}
149.1
3.18502 − 2.41984i
3.18502 + 2.41984i
3.46430 − 1.99965i
3.46430 + 1.99965i
0.593959 + 3.95566i
0.593959 − 3.95566i
3.72553 + 1.45618i
3.72553 − 1.45618i
−2.63430 + 3.01006i
−2.63430 − 3.01006i
2.93366 + 2.71913i
2.93366 − 2.71913i
−3.90102 + 0.884346i
−3.90102 − 0.884346i
0.236693 + 3.99299i
0.236693 − 3.99299i
−3.80026 − 1.24819i
−3.80026 + 1.24819i
−2.80358 + 2.85306i
−2.80358 − 2.85306i
−5.60486 − 0.765181i 17.3148 30.8290 + 8.57748i 0 −97.0471 − 13.2490i 9.19080i −166.229 − 71.6654i 56.8021 0
149.2 −5.60486 + 0.765181i 17.3148 30.8290 − 8.57748i 0 −97.0471 + 13.2490i − 9.19080i −166.229 + 71.6654i 56.8021 0
149.3 −5.46395 − 1.46465i −29.2080 27.7096 + 16.0056i 0 159.591 + 42.7797i 168.173i −127.961 − 128.039i 610.110 0
149.4 −5.46395 + 1.46465i −29.2080 27.7096 − 16.0056i 0 159.591 − 42.7797i − 168.173i −127.961 + 128.039i 610.110 0
149.5 −4.54962 − 3.36170i −6.93089 9.39799 + 30.5888i 0 31.5329 + 23.2996i 47.1406i 60.0732 − 170.761i −194.963 0
149.6 −4.54962 + 3.36170i −6.93089 9.39799 − 30.5888i 0 31.5329 − 23.2996i − 47.1406i 60.0732 + 170.761i −194.963 0
149.7 −2.26935 − 5.18171i −10.8240 −21.7001 + 23.5182i 0 24.5634 + 56.0868i − 163.706i 171.109 + 59.0729i −125.841 0
149.8 −2.26935 + 5.18171i −10.8240 −21.7001 − 23.5182i 0 24.5634 − 56.0868i 163.706i 171.109 − 59.0729i −125.841 0
149.9 −0.375761 − 5.64436i −6.67450 −31.7176 + 4.24186i 0 2.50801 + 37.6733i − 38.2812i 35.8608 + 177.432i −198.451 0
149.10 −0.375761 + 5.64436i −6.67450 −31.7176 − 4.24186i 0 2.50801 − 37.6733i 38.2812i 35.8608 − 177.432i −198.451 0
149.11 −0.214529 − 5.65278i 18.7876 −31.9080 + 2.42537i 0 −4.03048 − 106.202i 107.536i 20.5552 + 179.848i 109.975 0
149.12 −0.214529 + 5.65278i 18.7876 −31.9080 − 2.42537i 0 −4.03048 + 106.202i − 107.536i 20.5552 − 179.848i 109.975 0
149.13 3.01667 − 4.78536i 25.4343 −13.7994 − 28.8717i 0 76.7270 − 121.712i − 56.4938i −179.790 − 21.0614i 403.904 0
149.14 3.01667 + 4.78536i 25.4343 −13.7994 + 28.8717i 0 76.7270 + 121.712i 56.4938i −179.790 + 21.0614i 403.904 0
149.15 3.75630 − 4.22968i −25.0521 −3.78045 − 31.7759i 0 −94.1031 + 105.962i − 103.624i −148.603 − 103.370i 384.607 0
149.16 3.75630 + 4.22968i −25.0521 −3.78045 + 31.7759i 0 −94.1031 − 105.962i 103.624i −148.603 + 103.370i 384.607 0
149.17 5.04846 − 2.55207i −11.5927 18.9739 − 25.7680i 0 −58.5253 + 29.5854i − 231.529i 30.0270 − 178.512i −108.609 0
149.18 5.04846 + 2.55207i −11.5927 18.9739 + 25.7680i 0 −58.5253 − 29.5854i 231.529i 30.0270 + 178.512i −108.609 0
149.19 5.65664 − 0.0494789i 10.7455 31.9951 − 0.559768i 0 60.7833 − 0.531674i − 198.733i 180.957 − 4.74949i −127.535 0
149.20 5.65664 + 0.0494789i 10.7455 31.9951 + 0.559768i 0 60.7833 + 0.531674i 198.733i 180.957 + 4.74949i −127.535 0
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 149.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
40.f even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 200.6.f.b 20
4.b odd 2 1 800.6.f.c 20
5.b even 2 1 200.6.f.c 20
5.c odd 4 1 40.6.d.a ✓ 20
5.c odd 4 1 200.6.d.b 20
8.b even 2 1 200.6.f.c 20
8.d odd 2 1 800.6.f.b 20
15.e even 4 1 360.6.k.b 20
20.d odd 2 1 800.6.f.b 20
20.e even 4 1 160.6.d.a 20
20.e even 4 1 800.6.d.c 20
40.e odd 2 1 800.6.f.c 20
40.f even 2 1 inner 200.6.f.b 20
40.i odd 4 1 40.6.d.a ✓ 20
40.i odd 4 1 200.6.d.b 20
40.k even 4 1 160.6.d.a 20
40.k even 4 1 800.6.d.c 20
120.w even 4 1 360.6.k.b 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
40.6.d.a ✓ 20 5.c odd 4 1
40.6.d.a ✓ 20 40.i odd 4 1
160.6.d.a 20 20.e even 4 1
160.6.d.a 20 40.k even 4 1
200.6.d.b 20 5.c odd 4 1
200.6.d.b 20 40.i odd 4 1
200.6.f.b 20 1.a even 1 1 trivial
200.6.f.b 20 40.f even 2 1 inner
200.6.f.c 20 5.b even 2 1
200.6.f.c 20 8.b even 2 1
360.6.k.b 20 15.e even 4 1
360.6.k.b 20 120.w even 4 1
800.6.d.c 20 20.e even 4 1
800.6.d.c 20 40.k even 4 1
800.6.f.b 20 8.d odd 2 1
800.6.f.b 20 20.d odd 2 1
800.6.f.c 20 4.b odd 2 1
800.6.f.c 20 40.e odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T310+18T39−1458T38−23328T37+690600T36+10222224T35+⋯+377626901472 T_{3}^{10} + 18 T_{3}^{9} - 1458 T_{3}^{8} - 23328 T_{3}^{7} + 690600 T_{3}^{6} + 10222224 T_{3}^{5} + \cdots + 377626901472 acting on S6new(200,[χ])S_{6}^{\mathrm{new}}(200, [\chi]). Copy content Toggle raw display

Hecke characteristic polynomials

pp Fp(T)F_p(T)
22 T20+⋯+11 ⁣⋯ ⁣24 T^{20} + \cdots + 11\!\cdots\!24 Copy content Toggle raw display
33 (T10+⋯+377626901472)2 (T^{10} + \cdots + 377626901472)^{2} Copy content Toggle raw display
55 T20 T^{20} Copy content Toggle raw display
77 T20+⋯+17 ⁣⋯ ⁣64 T^{20} + \cdots + 17\!\cdots\!64 Copy content Toggle raw display
1111 T20+⋯+70 ⁣⋯ ⁣00 T^{20} + \cdots + 70\!\cdots\!00 Copy content Toggle raw display
1313 (T10+⋯+12 ⁣⋯ ⁣00)2 (T^{10} + \cdots + 12\!\cdots\!00)^{2} Copy content Toggle raw display
1717 T20+⋯+86 ⁣⋯ ⁣24 T^{20} + \cdots + 86\!\cdots\!24 Copy content Toggle raw display
1919 T20+⋯+23 ⁣⋯ ⁣56 T^{20} + \cdots + 23\!\cdots\!56 Copy content Toggle raw display
2323 T20+⋯+78 ⁣⋯ ⁣56 T^{20} + \cdots + 78\!\cdots\!56 Copy content Toggle raw display
2929 T20+⋯+42 ⁣⋯ ⁣00 T^{20} + \cdots + 42\!\cdots\!00 Copy content Toggle raw display
3131 (T10+⋯−42 ⁣⋯ ⁣88)2 (T^{10} + \cdots - 42\!\cdots\!88)^{2} Copy content Toggle raw display
3737 (T10+⋯+42 ⁣⋯ ⁣56)2 (T^{10} + \cdots + 42\!\cdots\!56)^{2} Copy content Toggle raw display
4141 (T10+⋯−21 ⁣⋯ ⁣00)2 (T^{10} + \cdots - 21\!\cdots\!00)^{2} Copy content Toggle raw display
4343 (T10+⋯−49 ⁣⋯ ⁣76)2 (T^{10} + \cdots - 49\!\cdots\!76)^{2} Copy content Toggle raw display
4747 T20+⋯+26 ⁣⋯ ⁣64 T^{20} + \cdots + 26\!\cdots\!64 Copy content Toggle raw display
5353 (T10+⋯+90 ⁣⋯ ⁣88)2 (T^{10} + \cdots + 90\!\cdots\!88)^{2} Copy content Toggle raw display
5959 T20+⋯+40 ⁣⋯ ⁣76 T^{20} + \cdots + 40\!\cdots\!76 Copy content Toggle raw display
6161 T20+⋯+29 ⁣⋯ ⁣00 T^{20} + \cdots + 29\!\cdots\!00 Copy content Toggle raw display
6767 (T10+⋯+71 ⁣⋯ ⁣52)2 (T^{10} + \cdots + 71\!\cdots\!52)^{2} Copy content Toggle raw display
7171 (T10+⋯+19 ⁣⋯ ⁣32)2 (T^{10} + \cdots + 19\!\cdots\!32)^{2} Copy content Toggle raw display
7373 T20+⋯+61 ⁣⋯ ⁣56 T^{20} + \cdots + 61\!\cdots\!56 Copy content Toggle raw display
7979 (T10+⋯+28 ⁣⋯ ⁣00)2 (T^{10} + \cdots + 28\!\cdots\!00)^{2} Copy content Toggle raw display
8383 (T10+⋯+15 ⁣⋯ ⁣44)2 (T^{10} + \cdots + 15\!\cdots\!44)^{2} Copy content Toggle raw display
8989 (T10+⋯+21 ⁣⋯ ⁣00)2 (T^{10} + \cdots + 21\!\cdots\!00)^{2} Copy content Toggle raw display
9797 T20+⋯+49 ⁣⋯ ⁣04 T^{20} + \cdots + 49\!\cdots\!04 Copy content Toggle raw display
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