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Properties

Label 845.2.k.e
Level 845845
Weight 22
Character orbit 845.k
Analytic conductor 6.7476.747
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [845,2,Mod(268,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.268"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")
 
Level: N N == 845=5⋅132 845 = 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 845.k (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [20,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.747358970806.74735897080
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20+⋯ )\mathbb{Q}[x]/(x^{20} + \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6+⋯+1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,…,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content 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−β2q2+β9q3+(β8+β4−β3)q4−β17q5+(−β19−β18−β17+⋯+1)q6+(β11+β3)q7+(β19−β18−β17+⋯+1)q8+⋯+(−β19+2β18+⋯−4)q99+O(q100) q - \beta_{2} q^{2} + \beta_{9} q^{3} + (\beta_{8} + \beta_{4} - \beta_{3}) q^{4} - \beta_{17} q^{5} + ( - \beta_{19} - \beta_{18} - \beta_{17} + \cdots + 1) q^{6} + (\beta_{11} + \beta_{3}) q^{7} + (\beta_{19} - \beta_{18} - \beta_{17} + \cdots + 1) q^{8}+ \cdots + ( - \beta_{19} + 2 \beta_{18} + \cdots - 4) q^{99}+O(q^{100}) Copy content Toggle raw display
Tr⁡(f)(q)\operatorname{Tr}(f)(q) == 20q+8q2+4q3+12q4−6q5+4q6+12q8+8q10+8q11+24q12−24q15+4q16+14q17−4q19−22q20+4q21−32q22−8q23+4q24+⋯−60q99+O(q100) 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) Copy content Toggle raw display

Basis of coefficient ring in terms of a root ν\nu of x20+26x18+279x16+1604x14+5353x12+10466x10+11441x8+6176x6+⋯+1 x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 : Copy content Toggle raw display

β1\beta_{1}== ν \nu Copy content Toggle raw display
β2\beta_{2}== (69ν18+1647ν16+15798ν14+78322ν12+214723ν10+324081ν8+⋯+539)/1712 ( 69 \nu^{18} + 1647 \nu^{16} + 15798 \nu^{14} + 78322 \nu^{12} + 214723 \nu^{10} + 324081 \nu^{8} + \cdots + 539 ) / 1712 Copy content Toggle raw display
β3\beta_{3}== (−2051ν19−1625ν18−52213ν17−40407ν16−546574ν15−409402ν14+⋯−11323)/23968 ( - 2051 \nu^{19} - 1625 \nu^{18} - 52213 \nu^{17} - 40407 \nu^{16} - 546574 \nu^{15} - 409402 \nu^{14} + \cdots - 11323 ) / 23968 Copy content Toggle raw display
β4\beta_{4}== (−1625ν18−40407ν16−409402ν14−2186822ν12−6647231ν10+⋯−35291)/11984 ( - 1625 \nu^{18} - 40407 \nu^{16} - 409402 \nu^{14} - 2186822 \nu^{12} - 6647231 \nu^{10} + \cdots - 35291 ) / 11984 Copy content Toggle raw display
β5\beta_{5}== (2137ν19+321ν18+55159ν17+9951ν16+586250ν15+127330ν14+⋯+27499)/23968 ( 2137 \nu^{19} + 321 \nu^{18} + 55159 \nu^{17} + 9951 \nu^{16} + 586250 \nu^{15} + 127330 \nu^{14} + \cdots + 27499 ) / 23968 Copy content Toggle raw display
β6\beta_{6}== (−908ν19−41ν18−22604ν17−11ν16−229460ν15+13762ν14+⋯+12681)/11984 ( - 908 \nu^{19} - 41 \nu^{18} - 22604 \nu^{17} - 11 \nu^{16} - 229460 \nu^{15} + 13762 \nu^{14} + \cdots + 12681 ) / 11984 Copy content Toggle raw display
β7\beta_{7}== (−2137ν19+321ν18−55159ν17+9951ν16−586250ν15+127330ν14+⋯+51467)/23968 ( - 2137 \nu^{19} + 321 \nu^{18} - 55159 \nu^{17} + 9951 \nu^{16} - 586250 \nu^{15} + 127330 \nu^{14} + \cdots + 51467 ) / 23968 Copy content Toggle raw display
β8\beta_{8}== (−2051ν19+1625ν18−52213ν17+40407ν16−546574ν15+409402ν14+⋯+11323)/23968 ( - 2051 \nu^{19} + 1625 \nu^{18} - 52213 \nu^{17} + 40407 \nu^{16} - 546574 \nu^{15} + 409402 \nu^{14} + \cdots + 11323 ) / 23968 Copy content Toggle raw display
β9\beta_{9}== (−2753ν19−867ν18−71035ν17−22593ν16−754642ν15−243222ν14+⋯−15221)/11984 ( - 2753 \nu^{19} - 867 \nu^{18} - 71035 \nu^{17} - 22593 \nu^{16} - 754642 \nu^{15} - 243222 \nu^{14} + \cdots - 15221 ) / 11984 Copy content Toggle raw display
β10\beta_{10}== (−2753ν19+867ν18−71035ν17+22593ν16−754642ν15+243222ν14+⋯+15221)/11984 ( - 2753 \nu^{19} + 867 \nu^{18} - 71035 \nu^{17} + 22593 \nu^{16} - 754642 \nu^{15} + 243222 \nu^{14} + \cdots + 15221 ) / 11984 Copy content Toggle raw display
β11\beta_{11}== (−6161ν19+1625ν18−162487ν17+40407ν16−1774122ν15+⋯+11323)/23968 ( - 6161 \nu^{19} + 1625 \nu^{18} - 162487 \nu^{17} + 40407 \nu^{16} - 1774122 \nu^{15} + \cdots + 11323 ) / 23968 Copy content Toggle raw display
β12\beta_{12}== (−5315ν19+3731ν18−137269ν17+93877ν16−1459766ν15+⋯+89369)/23968 ( - 5315 \nu^{19} + 3731 \nu^{18} - 137269 \nu^{17} + 93877 \nu^{16} - 1459766 \nu^{15} + \cdots + 89369 ) / 23968 Copy content Toggle raw display
β13\beta_{13}== (539ν19+13945ν17+148734ν15+848758ν13+2806945ν11+⋯+22081ν)/1712 ( 539 \nu^{19} + 13945 \nu^{17} + 148734 \nu^{15} + 848758 \nu^{13} + 2806945 \nu^{11} + \cdots + 22081 \nu ) / 1712 Copy content Toggle raw display
β14\beta_{14}== (−10681ν19−2701ν18−278863ν17−65979ν16−3007858ν15+⋯−76919)/23968 ( - 10681 \nu^{19} - 2701 \nu^{18} - 278863 \nu^{17} - 65979 \nu^{16} - 3007858 \nu^{15} + \cdots - 76919 ) / 23968 Copy content Toggle raw display
β15\beta_{15}== (11655ν19−191ν18+301777ν17−4801ν16+3219622ν15−49518ν14+⋯+54179)/23968 ( 11655 \nu^{19} - 191 \nu^{18} + 301777 \nu^{17} - 4801 \nu^{16} + 3219622 \nu^{15} - 49518 \nu^{14} + \cdots + 54179 ) / 23968 Copy content Toggle raw display
β16\beta_{16}== (−5223ν19+1330ν18−135929ν17+34482ν16−1460102ν15+⋯+34314)/11984 ( - 5223 \nu^{19} + 1330 \nu^{18} - 135929 \nu^{17} + 34482 \nu^{16} - 1460102 \nu^{15} + \cdots + 34314 ) / 11984 Copy content Toggle raw display
β17\beta_{17}== (1767ν19+203ν18+46090ν17+5334ν16+496321ν15+57876ν14+⋯−455)/2996 ( 1767 \nu^{19} + 203 \nu^{18} + 46090 \nu^{17} + 5334 \nu^{16} + 496321 \nu^{15} + 57876 \nu^{14} + \cdots - 455 ) / 2996 Copy content Toggle raw display
β18\beta_{18}== (−14121ν19+1997ν18−366743ν17+48691ν16−3929786ν15+⋯+34959)/23968 ( - 14121 \nu^{19} + 1997 \nu^{18} - 366743 \nu^{17} + 48691 \nu^{16} - 3929786 \nu^{15} + \cdots + 34959 ) / 23968 Copy content Toggle raw display
β19\beta_{19}== (−17385ν19−3359ν18−451799ν17−85593ν16−4842978ν15+⋯−41765)/23968 ( - 17385 \nu^{19} - 3359 \nu^{18} - 451799 \nu^{17} - 85593 \nu^{16} - 4842978 \nu^{15} + \cdots - 41765 ) / 23968 Copy content Toggle raw display

Display νj\nu^j in terms of βi\beta_i

ν\nu== β1 \beta_1 Copy content Toggle raw display
ν2\nu^{2}== −β8−β4+β3−2 -\beta_{8} - \beta_{4} + \beta_{3} - 2 Copy content Toggle raw display
ν3\nu^{3}== β19+β18+β17−β14+2β13−β12+β11+⋯−3β1 \beta_{19} + \beta_{18} + \beta_{17} - \beta_{14} + 2 \beta_{13} - \beta_{12} + \beta_{11} + \cdots - 3 \beta_1 Copy content Toggle raw display
ν4\nu^{4}== 3β19−β18+2β15+2β13−β12+2β10−2β9+⋯+9 3 \beta_{19} - \beta_{18} + 2 \beta_{15} + 2 \beta_{13} - \beta_{12} + 2 \beta_{10} - 2 \beta_{9} + \cdots + 9 Copy content Toggle raw display
ν5\nu^{5}== −8β19−9β18−8β17+β15+8β14−15β13+9β12+⋯−3 - 8 \beta_{19} - 9 \beta_{18} - 8 \beta_{17} + \beta_{15} + 8 \beta_{14} - 15 \beta_{13} + 9 \beta_{12} + \cdots - 3 Copy content Toggle raw display
ν6\nu^{6}== −32β19+13β18+2β17+2β16−19β15−19β13+⋯−50 - 32 \beta_{19} + 13 \beta_{18} + 2 \beta_{17} + 2 \beta_{16} - 19 \beta_{15} - 19 \beta_{13} + \cdots - 50 Copy content Toggle raw display
ν7\nu^{7}== 51β19+68β18+54β17−15β15−54β14+99β13+⋯+36 51 \beta_{19} + 68 \beta_{18} + 54 \beta_{17} - 15 \beta_{15} - 54 \beta_{14} + 99 \beta_{13} + \cdots + 36 Copy content Toggle raw display
ν8\nu^{8}== 267β19−120β18−28β17−24β16+147β15−4β14+⋯+304 267 \beta_{19} - 120 \beta_{18} - 28 \beta_{17} - 24 \beta_{16} + 147 \beta_{15} - 4 \beta_{14} + \cdots + 304 Copy content Toggle raw display
ν9\nu^{9}== −308β19−488β18−352β17+154β15+352β14−648β13+⋯−323 - 308 \beta_{19} - 488 \beta_{18} - 352 \beta_{17} + 154 \beta_{15} + 352 \beta_{14} - 648 \beta_{13} + \cdots - 323 Copy content Toggle raw display
ν10\nu^{10}== −2044β19+974β18+274β17+214β16−1070β15+60β14+⋯−1940 - 2044 \beta_{19} + 974 \beta_{18} + 274 \beta_{17} + 214 \beta_{16} - 1070 \beta_{15} + 60 \beta_{14} + \cdots - 1940 Copy content Toggle raw display
ν11\nu^{11}== 1854β19+3434β18+2299β17−1356β15−2299β14+4298β13+⋯+2590 1854 \beta_{19} + 3434 \beta_{18} + 2299 \beta_{17} - 1356 \beta_{15} - 2299 \beta_{14} + 4298 \beta_{13} + \cdots + 2590 Copy content Toggle raw display
ν12\nu^{12}== 15044β19−7438β18−2330β17−1724β16+7606β15−606β14+⋯+12755 15044 \beta_{19} - 7438 \beta_{18} - 2330 \beta_{17} - 1724 \beta_{16} + 7606 \beta_{15} - 606 \beta_{14} + \cdots + 12755 Copy content Toggle raw display
ν13\nu^{13}== −11342β19−23984β18−15204β17+11014β15+15204β14+⋯−19642 - 11342 \beta_{19} - 23984 \beta_{18} - 15204 \beta_{17} + 11014 \beta_{15} + 15204 \beta_{14} + \cdots - 19642 Copy content Toggle raw display
ν14\nu^{14}== −108504β19+54982β18+18452β17+13248β16−53522β15+⋯−85534 - 108504 \beta_{19} + 54982 \beta_{18} + 18452 \beta_{17} + 13248 \beta_{16} - 53522 \beta_{15} + \cdots - 85534 Copy content Toggle raw display
ν15\nu^{15}== 71003β19+167135β18+101945β17−85268β15−101945β14+⋯+144450 71003 \beta_{19} + 167135 \beta_{18} + 101945 \beta_{17} - 85268 \beta_{15} - 101945 \beta_{14} + \cdots + 144450 Copy content Toggle raw display
ν16\nu^{16}== 773909β19−398897β18−140250β17−99100β16+375012β15+⋯+581415 773909 \beta_{19} - 398897 \beta_{18} - 140250 \beta_{17} - 99100 \beta_{16} + 375012 \beta_{15} + \cdots + 581415 Copy content Toggle raw display
ν17\nu^{17}== −455154β19−1164737β18−691774β17+640259β15+691774β14+⋯−1043445 - 455154 \beta_{19} - 1164737 \beta_{18} - 691774 \beta_{17} + 640259 \beta_{15} + 691774 \beta_{14} + \cdots - 1043445 Copy content Toggle raw display
ν18\nu^{18}== −5484892β19+2861437β18+1039156β17+728470β16−2623455β15+⋯−3989746 - 5484892 \beta_{19} + 2861437 \beta_{18} + 1039156 \beta_{17} + 728470 \beta_{16} - 2623455 \beta_{15} + \cdots - 3989746 Copy content Toggle raw display
ν19\nu^{19}== 2980455β19+8124372β18+4738502β17−4711075β15−4738502β14+⋯+7456686 2980455 \beta_{19} + 8124372 \beta_{18} + 4738502 \beta_{17} - 4711075 \beta_{15} - 4738502 \beta_{14} + \cdots + 7456686 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/845Z)×\left(\mathbb{Z}/845\mathbb{Z}\right)^\times.

nn 171171 677677
χ(n)\chi(n) −β13-\beta_{13} β13\beta_{13}

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.

Copy content comment:embeddings in the coefficient field
 
Copy content 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}
268.1
− 2.25081i
− 1.51805i
− 1.02262i
− 0.131303i
0.274809i
0.493902i
1.58474i
1.83163i
2.08794i
2.64975i
2.25081i
1.51805i
1.02262i
0.131303i
− 0.274809i
− 0.493902i
− 1.58474i
− 1.83163i
− 2.08794i
− 2.64975i
−2.25081 1.40490 + 1.40490i 3.06613 −2.22228 + 0.247944i −3.16216 − 3.16216i 1.27718i −2.39966 0.947480i 5.00192 − 0.558075i
268.2 −1.51805 0.478298 + 0.478298i 0.304465 0.600231 − 2.15400i −0.726078 − 0.726078i − 2.59488i 2.57390 − 2.54246i −0.911178 + 3.26987i
268.3 −1.02262 −1.97063 − 1.97063i −0.954253 −1.69584 − 1.45744i 2.01520 + 2.01520i − 0.963574i 3.02107 4.76674i 1.73420 + 1.49040i
268.4 −0.131303 −0.243172 − 0.243172i −1.98276 0.813169 + 2.08297i 0.0319291 + 0.0319291i 2.78137i 0.522947 − 2.88174i −0.106771 − 0.273499i
268.5 0.274809 1.67095 + 1.67095i −1.92448 1.69883 + 1.45395i 0.459191 + 0.459191i − 0.386104i −1.07848 2.58414i 0.466854 + 0.399558i
268.6 0.493902 −0.664960 − 0.664960i −1.75606 −2.21791 − 0.284413i −0.328425 − 0.328425i 3.67549i −1.85513 − 2.11566i −1.09543 − 0.140472i
268.7 1.58474 −0.139520 − 0.139520i 0.511395 0.0672627 − 2.23506i −0.221103 − 0.221103i 0.548328i −2.35905 − 2.96107i 0.106594 − 3.54198i
268.8 1.83163 −1.40138 − 1.40138i 1.35488 1.45480 − 1.69810i −2.56682 − 2.56682i − 3.53890i −1.18163 0.927746i 2.66466 − 3.11030i
268.9 2.08794 1.94842 + 1.94842i 2.35949 −0.194361 + 2.22760i 4.06818 + 4.06818i − 2.91126i 0.750585 4.59268i −0.405815 + 4.65110i
268.10 2.64975 0.917096 + 0.917096i 5.02120 −1.30391 + 1.81654i 2.43008 + 2.43008i 0.112348i 8.00544 − 1.31787i −3.45504 + 4.81339i
577.1 −2.25081 1.40490 − 1.40490i 3.06613 −2.22228 − 0.247944i −3.16216 + 3.16216i − 1.27718i −2.39966 − 0.947480i 5.00192 + 0.558075i
577.2 −1.51805 0.478298 − 0.478298i 0.304465 0.600231 + 2.15400i −0.726078 + 0.726078i 2.59488i 2.57390 2.54246i −0.911178 − 3.26987i
577.3 −1.02262 −1.97063 + 1.97063i −0.954253 −1.69584 + 1.45744i 2.01520 − 2.01520i 0.963574i 3.02107 − 4.76674i 1.73420 − 1.49040i
577.4 −0.131303 −0.243172 + 0.243172i −1.98276 0.813169 − 2.08297i 0.0319291 − 0.0319291i − 2.78137i 0.522947 2.88174i −0.106771 + 0.273499i
577.5 0.274809 1.67095 − 1.67095i −1.92448 1.69883 − 1.45395i 0.459191 − 0.459191i 0.386104i −1.07848 − 2.58414i 0.466854 − 0.399558i
577.6 0.493902 −0.664960 + 0.664960i −1.75606 −2.21791 + 0.284413i −0.328425 + 0.328425i − 3.67549i −1.85513 2.11566i −1.09543 + 0.140472i
577.7 1.58474 −0.139520 + 0.139520i 0.511395 0.0672627 + 2.23506i −0.221103 + 0.221103i − 0.548328i −2.35905 2.96107i 0.106594 + 3.54198i
577.8 1.83163 −1.40138 + 1.40138i 1.35488 1.45480 + 1.69810i −2.56682 + 2.56682i 3.53890i −1.18163 − 0.927746i 2.66466 + 3.11030i
577.9 2.08794 1.94842 − 1.94842i 2.35949 −0.194361 − 2.22760i 4.06818 − 4.06818i 2.91126i 0.750585 − 4.59268i −0.405815 − 4.65110i
577.10 2.64975 0.917096 − 0.917096i 5.02120 −1.30391 − 1.81654i 2.43008 − 2.43008i − 0.112348i 8.00544 1.31787i −3.45504 − 4.81339i
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 268.10
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
65.k even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 845.2.k.e 20
5.c odd 4 1 845.2.f.e 20
13.b even 2 1 845.2.k.d 20
13.c even 3 1 65.2.o.a ✓ 20
13.c even 3 1 845.2.o.e 20
13.d odd 4 1 845.2.f.d 20
13.d odd 4 1 845.2.f.e 20
13.e even 6 1 845.2.o.f 20
13.e even 6 1 845.2.o.g 20
13.f odd 12 1 65.2.t.a yes 20
13.f odd 12 1 845.2.t.e 20
13.f odd 12 1 845.2.t.f 20
13.f odd 12 1 845.2.t.g 20
39.i odd 6 1 585.2.cf.a 20
39.k even 12 1 585.2.dp.a 20
65.f even 4 1 845.2.k.d 20
65.h odd 4 1 845.2.f.d 20
65.k even 4 1 inner 845.2.k.e 20
65.n even 6 1 325.2.s.b 20
65.o even 12 1 65.2.o.a ✓ 20
65.o even 12 1 845.2.o.e 20
65.q odd 12 1 65.2.t.a yes 20
65.q odd 12 1 325.2.x.b 20
65.q odd 12 1 845.2.t.f 20
65.r odd 12 1 845.2.t.e 20
65.r odd 12 1 845.2.t.g 20
65.s odd 12 1 325.2.x.b 20
65.t even 12 1 325.2.s.b 20
65.t even 12 1 845.2.o.f 20
65.t even 12 1 845.2.o.g 20
195.bl even 12 1 585.2.dp.a 20
195.bn odd 12 1 585.2.cf.a 20
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
65.2.o.a ✓ 20 13.c even 3 1
65.2.o.a ✓ 20 65.o even 12 1
65.2.t.a yes 20 13.f odd 12 1
65.2.t.a yes 20 65.q odd 12 1
325.2.s.b 20 65.n even 6 1
325.2.s.b 20 65.t even 12 1
325.2.x.b 20 65.q odd 12 1
325.2.x.b 20 65.s odd 12 1
585.2.cf.a 20 39.i odd 6 1
585.2.cf.a 20 195.bn odd 12 1
585.2.dp.a 20 39.k even 12 1
585.2.dp.a 20 195.bl even 12 1
845.2.f.d 20 13.d odd 4 1
845.2.f.d 20 65.h odd 4 1
845.2.f.e 20 5.c odd 4 1
845.2.f.e 20 13.d odd 4 1
845.2.k.d 20 13.b even 2 1
845.2.k.d 20 65.f even 4 1
845.2.k.e 20 1.a even 1 1 trivial
845.2.k.e 20 65.k even 4 1 inner
845.2.o.e 20 13.c even 3 1
845.2.o.e 20 65.o even 12 1
845.2.o.f 20 13.e even 6 1
845.2.o.f 20 65.t even 12 1
845.2.o.g 20 13.e even 6 1
845.2.o.g 20 65.t even 12 1
845.2.t.e 20 13.f odd 12 1
845.2.t.e 20 65.r odd 12 1
845.2.t.f 20 13.f odd 12 1
845.2.t.f 20 65.q odd 12 1
845.2.t.g 20 13.f odd 12 1
845.2.t.g 20 65.r odd 12 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T210−4T29−5T28+34T27−9T26−80T25+51T24+52T23−37T22+2T2+1 T_{2}^{10} - 4T_{2}^{9} - 5T_{2}^{8} + 34T_{2}^{7} - 9T_{2}^{6} - 80T_{2}^{5} + 51T_{2}^{4} + 52T_{2}^{3} - 37T_{2}^{2} + 2T_{2} + 1 acting on S2new(845,[χ])S_{2}^{\mathrm{new}}(845, [\chi]). Copy content Toggle raw display

Hecke characteristic polynomials

pp Fp(T)F_p(T)
22 (T10−4T9−5T8+⋯+1)2 (T^{10} - 4 T^{9} - 5 T^{8} + \cdots + 1)^{2} Copy content Toggle raw display
33 T20−4T19+⋯+16 T^{20} - 4 T^{19} + \cdots + 16 Copy content Toggle raw display
55 T20+6T19+⋯+9765625 T^{20} + 6 T^{19} + \cdots + 9765625 Copy content Toggle raw display
77 T20+52T18+⋯+64 T^{20} + 52 T^{18} + \cdots + 64 Copy content Toggle raw display
1111 T20−8T19+⋯+256 T^{20} - 8 T^{19} + \cdots + 256 Copy content Toggle raw display
1313 T20 T^{20} Copy content Toggle raw display
1717 T20−14T19+⋯+1168561 T^{20} - 14 T^{19} + \cdots + 1168561 Copy content Toggle raw display
1919 T20+⋯+1583721616 T^{20} + \cdots + 1583721616 Copy content Toggle raw display
2323 T20+8T19+⋯+144 T^{20} + 8 T^{19} + \cdots + 144 Copy content Toggle raw display
2929 T20+⋯+206213167449 T^{20} + \cdots + 206213167449 Copy content Toggle raw display
3131 T20−104T17+⋯+2166784 T^{20} - 104 T^{17} + \cdots + 2166784 Copy content Toggle raw display
3737 T20+⋯+4508182449 T^{20} + \cdots + 4508182449 Copy content Toggle raw display
4141 T20+⋯+3748255729 T^{20} + \cdots + 3748255729 Copy content Toggle raw display
4343 T20+⋯+1370772640000 T^{20} + \cdots + 1370772640000 Copy content Toggle raw display
4747 T20+⋯+807469056 T^{20} + \cdots + 807469056 Copy content Toggle raw display
5353 T20+⋯+2978634160384 T^{20} + \cdots + 2978634160384 Copy content Toggle raw display
5959 T20+8T19+⋯+33856 T^{20} + 8 T^{19} + \cdots + 33856 Copy content Toggle raw display
6161 (T10−16T9+⋯+909097)2 (T^{10} - 16 T^{9} + \cdots + 909097)^{2} Copy content Toggle raw display
6767 (T10−58T9+⋯+3934324)2 (T^{10} - 58 T^{9} + \cdots + 3934324)^{2} Copy content Toggle raw display
7171 T20+⋯+11 ⁣⋯ ⁣44 T^{20} + \cdots + 11\!\cdots\!44 Copy content Toggle raw display
7373 (T10−36T9+⋯+253113232)2 (T^{10} - 36 T^{9} + \cdots + 253113232)^{2} Copy content Toggle raw display
7979 T20+⋯+75 ⁣⋯ ⁣36 T^{20} + \cdots + 75\!\cdots\!36 Copy content Toggle raw display
8383 T20+⋯+11512611864576 T^{20} + \cdots + 11512611864576 Copy content Toggle raw display
8989 T20+⋯+329648222500 T^{20} + \cdots + 329648222500 Copy content Toggle raw display
9797 (T10−22T9+⋯+169592356)2 (T^{10} - 22 T^{9} + \cdots + 169592356)^{2} Copy content Toggle raw display
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