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Properties

Label 65.2.o.a
Level 6565
Weight 22
Character orbit 65.o
Analytic conductor 0.5190.519
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] = [65,2,Mod(2,65)] 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("65.2"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")
 
Level: N N == 65=5⋅13 65 = 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 65.o (of order 1212, degree 44, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.5190276131380.519027613138
Analytic rank: 00
Dimension: 2020
Relative dimension: 55 over Q(ζ12)\Q(\zeta_{12})
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,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

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+(β4−β3)q2+(−β19+β18+⋯+β2)q3+(−β18+2β12+⋯+2β1)q4+(β18−β17−β16+⋯−1)q5+⋯+(β19−2β18+2β15+⋯−4)q99+O(q100) q + (\beta_{4} - \beta_{3}) q^{2} + ( - \beta_{19} + \beta_{18} + \cdots + \beta_{2}) q^{3} + ( - \beta_{18} + 2 \beta_{12} + \cdots + 2 \beta_1) q^{4} + (\beta_{18} - \beta_{17} - \beta_{16} + \cdots - 1) q^{5}+ \cdots + (\beta_{19} - 2 \beta_{18} + 2 \beta_{15} + \cdots - 4) q^{99}+O(q^{100}) Copy content Toggle raw display
Tr⁡(f)(q)\operatorname{Tr}(f)(q) == 20q−4q2−2q3−6q4−6q5−8q6−6q7+12q8−12q9−10q10−16q11+24q12+2q13+12q15−2q16−10q17+20q19+14q20+4q21+⋯−60q99+O(q100) 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21}+ \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}== (−20ν18−389ν16−2695ν14−7125ν12+1214ν10+39860ν8+⋯−409)/5992 ( - 20 \nu^{18} - 389 \nu^{16} - 2695 \nu^{14} - 7125 \nu^{12} + 1214 \nu^{10} + 39860 \nu^{8} + \cdots - 409 ) / 5992 Copy content Toggle raw display
β2\beta_{2}== (20ν18+389ν16+2695ν14+7125ν12−1214ν10−39860ν8+⋯+409)/5992 ( 20 \nu^{18} + 389 \nu^{16} + 2695 \nu^{14} + 7125 \nu^{12} - 1214 \nu^{10} - 39860 \nu^{8} + \cdots + 409 ) / 5992 Copy content Toggle raw display
β3\beta_{3}== (−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
β4\beta_{4}== (321ν19−483ν18+9951ν17−11529ν16+127330ν15−110586ν14+⋯−3773)/23968 ( 321 \nu^{19} - 483 \nu^{18} + 9951 \nu^{17} - 11529 \nu^{16} + 127330 \nu^{15} - 110586 \nu^{14} + \cdots - 3773 ) / 23968 Copy content Toggle raw display
β5\beta_{5}== (700ν19+617ν18+17360ν17+16607ν16+174468ν15+185192ν14+⋯+26961)/11984 ( 700 \nu^{19} + 617 \nu^{18} + 17360 \nu^{17} + 16607 \nu^{16} + 174468 \nu^{15} + 185192 \nu^{14} + \cdots + 26961 ) / 11984 Copy content Toggle raw display
β6\beta_{6}== (−409ν19−10614ν17−113722ν15−653341ν13−2182252ν11−4281808ν9+⋯−2996)/5992 ( - 409 \nu^{19} - 10614 \nu^{17} - 113722 \nu^{15} - 653341 \nu^{13} - 2182252 \nu^{11} - 4281808 \nu^{9} + \cdots - 2996 ) / 5992 Copy content Toggle raw display
β7\beta_{7}== (1635ν19−309ν18+41725ν17−7171ν16+436590ν15−66542ν14+⋯−30699)/23968 ( 1635 \nu^{19} - 309 \nu^{18} + 41725 \nu^{17} - 7171 \nu^{16} + 436590 \nu^{15} - 66542 \nu^{14} + \cdots - 30699 ) / 23968 Copy content Toggle raw display
β8\beta_{8}== (700ν19−617ν18+17360ν17−16607ν16+174468ν15−185192ν14+⋯−26961)/11984 ( 700 \nu^{19} - 617 \nu^{18} + 17360 \nu^{17} - 16607 \nu^{16} + 174468 \nu^{15} - 185192 \nu^{14} + \cdots - 26961 ) / 11984 Copy content Toggle raw display
β9\beta_{9}== (−419ν19+4593ν18−12681ν17+118807ν16−158886ν15+1266230ν14+⋯+83703)/23968 ( - 419 \nu^{19} + 4593 \nu^{18} - 12681 \nu^{17} + 118807 \nu^{16} - 158886 \nu^{15} + 1266230 \nu^{14} + \cdots + 83703 ) / 23968 Copy content Toggle raw display
β10\beta_{10}== (−3773ν19−565ν18−97615ν17−11551ν16−1041138ν15−83062ν14+⋯+81509)/23968 ( - 3773 \nu^{19} - 565 \nu^{18} - 97615 \nu^{17} - 11551 \nu^{16} - 1041138 \nu^{15} - 83062 \nu^{14} + \cdots + 81509 ) / 23968 Copy content Toggle raw display
β11\beta_{11}== (3773ν19+321ν18+97615ν17+9951ν16+1041138ν15+127330ν14+⋯+39483)/23968 ( 3773 \nu^{19} + 321 \nu^{18} + 97615 \nu^{17} + 9951 \nu^{16} + 1041138 \nu^{15} + 127330 \nu^{14} + \cdots + 39483 ) / 23968 Copy content Toggle raw display
β12\beta_{12}== (3773ν19−321ν18+97615ν17−9951ν16+1041138ν15−127330ν14+⋯−39483)/23968 ( 3773 \nu^{19} - 321 \nu^{18} + 97615 \nu^{17} - 9951 \nu^{16} + 1041138 \nu^{15} - 127330 \nu^{14} + \cdots - 39483 ) / 23968 Copy content Toggle raw display
β13\beta_{13}== (−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
β14\beta_{14}== (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
β15\beta_{15}== (−6965ν19+1863ν18−180971ν17+49605ν16−1940134ν15+545958ν14+⋯+1285)/23968 ( - 6965 \nu^{19} + 1863 \nu^{18} - 180971 \nu^{17} + 49605 \nu^{16} - 1940134 \nu^{15} + 545958 \nu^{14} + \cdots + 1285 ) / 23968 Copy content Toggle raw display
β16\beta_{16}== (8297ν19−175ν18+216915ν17−2093ν16+2342074ν15+9562ν14+⋯+23947)/23968 ( 8297 \nu^{19} - 175 \nu^{18} + 216915 \nu^{17} - 2093 \nu^{16} + 2342074 \nu^{15} + 9562 \nu^{14} + \cdots + 23947 ) / 23968 Copy content Toggle raw display
β17\beta_{17}== (−4979ν19−129835ν17−1398012ν15−8068552ν13−27041293ν11+⋯+11984)/11984 ( - 4979 \nu^{19} - 129835 \nu^{17} - 1398012 \nu^{15} - 8068552 \nu^{13} - 27041293 \nu^{11} + \cdots + 11984 ) / 11984 Copy content Toggle raw display
β18\beta_{18}== (10417ν19−483ν18+268635ν17−11529ν16+2853942ν15−110586ν14+⋯+20195)/23968 ( 10417 \nu^{19} - 483 \nu^{18} + 268635 \nu^{17} - 11529 \nu^{16} + 2853942 \nu^{15} - 110586 \nu^{14} + \cdots + 20195 ) / 23968 Copy content Toggle raw display
β19\beta_{19}== (−16083ν19−483ν18−419809ν17−11529ν16−4525598ν15+⋯−15757)/23968 ( - 16083 \nu^{19} - 483 \nu^{18} - 419809 \nu^{17} - 11529 \nu^{16} - 4525598 \nu^{15} + \cdots - 15757 ) / 23968 Copy content Toggle raw display

Display νj\nu^j in terms of βi\beta_i

ν\nu== β2+β1 \beta_{2} + \beta_1 Copy content Toggle raw display
ν2\nu^{2}== β12+β10−β3+β1−2 \beta_{12} + \beta_{10} - \beta_{3} + \beta _1 - 2 Copy content Toggle raw display
ν3\nu^{3}== β19+2β18−β13−3β12−2β11−2β10−β9+⋯−7β1 \beta_{19} + 2 \beta_{18} - \beta_{13} - 3 \beta_{12} - 2 \beta_{11} - 2 \beta_{10} - \beta_{9} + \cdots - 7 \beta_1 Copy content Toggle raw display
ν4\nu^{4}== β19−β18+β17+2β16−2β15+3β14−6β12+⋯+8 \beta_{19} - \beta_{18} + \beta_{17} + 2 \beta_{16} - 2 \beta_{15} + 3 \beta_{14} - 6 \beta_{12} + \cdots + 8 Copy content Toggle raw display
ν5\nu^{5}== −9β19−17β18−β17−3β14+11β13+26β12+17β11+⋯−2 - 9 \beta_{19} - 17 \beta_{18} - \beta_{17} - 3 \beta_{14} + 11 \beta_{13} + 26 \beta_{12} + 17 \beta_{11} + \cdots - 2 Copy content Toggle raw display
ν6\nu^{6}== −13β19+13β18−13β17−26β16+26β15−32β14+⋯−39 - 13 \beta_{19} + 13 \beta_{18} - 13 \beta_{17} - 26 \beta_{16} + 26 \beta_{15} - 32 \beta_{14} + \cdots - 39 Copy content Toggle raw display
ν7\nu^{7}== 66β19+122β18+14β17+37β14−89β13−189β12+⋯+21 66 \beta_{19} + 122 \beta_{18} + 14 \beta_{17} + 37 \beta_{14} - 89 \beta_{13} - 189 \beta_{12} + \cdots + 21 Copy content Toggle raw display
ν8\nu^{8}== 120β19−116β18+116β17+232β16−240β15+260β14+⋯+213 120 \beta_{19} - 116 \beta_{18} + 116 \beta_{17} + 232 \beta_{16} - 240 \beta_{15} + 260 \beta_{14} + \cdots + 213 Copy content Toggle raw display
ν9\nu^{9}== −462β19−840β18−136β17−332β14+657β13+1306β12+⋯−170 - 462 \beta_{19} - 840 \beta_{18} - 136 \beta_{17} - 332 \beta_{14} + 657 \beta_{13} + 1306 \beta_{12} + \cdots - 170 Copy content Toggle raw display
ν10\nu^{10}== −974β19+914β18−914β17−1828β16+1948β15−1941β14+⋯−1255 - 974 \beta_{19} + 914 \beta_{18} - 914 \beta_{17} - 1828 \beta_{16} + 1948 \beta_{15} - 1941 \beta_{14} + \cdots - 1255 Copy content Toggle raw display
ν11\nu^{11}== 3210β19+5733β18+1135β17+2648β14−4690β13−8890β12+⋯+1267 3210 \beta_{19} + 5733 \beta_{18} + 1135 \beta_{17} + 2648 \beta_{14} - 4690 \beta_{13} - 8890 \beta_{12} + \cdots + 1267 Copy content Toggle raw display
ν12\nu^{12}== 7438β19−6832β18+6832β17+13664β16−14876β15+14032β14+⋯+7797 7438 \beta_{19} - 6832 \beta_{18} + 6832 \beta_{17} + 13664 \beta_{16} - 14876 \beta_{15} + 14032 \beta_{14} + \cdots + 7797 Copy content Toggle raw display
ν13\nu^{13}== −22356β19−39188β18−8780β17−19984β14+33058β13+⋯−9130 - 22356 \beta_{19} - 39188 \beta_{18} - 8780 \beta_{17} - 19984 \beta_{14} + 33058 \beta_{13} + \cdots - 9130 Copy content Toggle raw display
ν14\nu^{14}== −54982β19+49778β18−49778β17−99556β16+109964β15+⋯−50290 - 54982 \beta_{19} + 49778 \beta_{18} - 49778 \beta_{17} - 99556 \beta_{16} + 109964 \beta_{15} + \cdots - 50290 Copy content Toggle raw display
ν15\nu^{15}== 156271β19+269080β18+65190β17+146494β14−231975β13+⋯+64782 156271 \beta_{19} + 269080 \beta_{18} + 65190 \beta_{17} + 146494 \beta_{14} - 231975 \beta_{13} + \cdots + 64782 Copy content Toggle raw display
ν16\nu^{16}== 398897β19−357747β18+357747β17+715494β16−797794β15+⋯+333034 398897 \beta_{19} - 357747 \beta_{18} + 357747 \beta_{17} + 715494 \beta_{16} - 797794 \beta_{15} + \cdots + 333034 Copy content Toggle raw display
ν17\nu^{17}== −1095413β19−1856511β18−472963β17−1056441β14+1625819β13+⋯−456258 - 1095413 \beta_{19} - 1856511 \beta_{18} - 472963 \beta_{17} - 1056441 \beta_{14} + 1625819 \beta_{13} + \cdots - 456258 Copy content Toggle raw display
ν18\nu^{18}== −2861437β19+2550751β18−2550751β17−5101502β16+5722874β15+⋯−2246355 - 2861437 \beta_{19} + 2550751 \beta_{18} - 2550751 \beta_{17} - 5101502 \beta_{16} + 5722874 \beta_{15} + \cdots - 2246355 Copy content Toggle raw display
ν19\nu^{19}== 7691530β19+12862874β18+3385870β17+7545155β14−11394317β13+⋯+3202109 7691530 \beta_{19} + 12862874 \beta_{18} + 3385870 \beta_{17} + 7545155 \beta_{14} - 11394317 \beta_{13} + \cdots + 3202109 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/65Z)×\left(\mathbb{Z}/65\mathbb{Z}\right)^\times.

nn 2727 4141
χ(n)\chi(n) −β11−β12-\beta_{11} - \beta_{12} −β11-\beta_{11}

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}
2.1
2.64975i
1.83163i
0.493902i
0.274809i
− 1.51805i
2.08794i
1.58474i
− 0.131303i
− 1.02262i
− 2.25081i
− 2.64975i
− 1.83163i
− 0.493902i
− 0.274809i
1.51805i
− 2.08794i
− 1.58474i
0.131303i
1.02262i
2.25081i
−1.32488 − 2.29475i −1.25278 − 0.335680i −2.51060 + 4.34849i −1.30391 − 1.81654i 0.889471 + 3.31955i 0.0972962 + 0.0561740i 8.00544 −1.14131 − 0.658935i −2.44100 + 5.39885i
2.2 −0.915816 − 1.58624i 1.91432 + 0.512942i −0.677439 + 1.17336i 1.45480 + 1.69810i −0.939520 − 3.50634i −3.06478 − 1.76945i −1.18163 0.803451 + 0.463873i 1.36126 − 3.86282i
2.3 −0.246951 − 0.427732i 0.908353 + 0.243392i 0.878030 − 1.52079i −2.21791 + 0.284413i −0.120212 − 0.448637i 3.18307 + 1.83775i −1.85513 −1.83221 − 1.05783i 0.669366 + 0.878433i
2.4 −0.137404 − 0.237991i −2.28256 − 0.611610i 0.962240 − 1.66665i 1.69883 − 1.45395i 0.168076 + 0.627267i −0.334376 − 0.193052i −1.07848 2.23793 + 1.29207i −0.579454 − 0.204528i
2.5 0.759023 + 1.31467i −0.653367 − 0.175069i −0.152233 + 0.263675i 0.600231 + 2.15400i −0.265763 − 0.991842i −2.24723 − 1.29744i 2.57390 −2.20184 − 1.27123i −2.37621 + 2.42404i
32.1 −1.04397 + 1.80821i 0.713171 + 2.66159i −1.17974 − 2.04338i −0.194361 − 2.22760i −5.55724 − 1.48906i 2.52122 − 1.45563i 0.750585 −3.97738 + 2.29634i 4.23088 + 1.97411i
32.2 −0.792369 + 1.37242i −0.0510678 − 0.190588i −0.255697 − 0.442881i 0.0672627 + 2.23506i 0.302032 + 0.0809291i −0.474866 + 0.274164i −2.35905 2.56436 − 1.48053i −3.12074 − 1.67868i
32.3 0.0656513 − 0.113711i −0.0890070 − 0.332179i 0.991380 + 1.71712i 0.813169 − 2.08297i −0.0436159 − 0.0116869i −2.40874 + 1.39069i 0.522947 2.49566 − 1.44087i −0.183472 − 0.229216i
32.4 0.511309 − 0.885613i −0.721300 − 2.69193i 0.477126 + 0.826407i −1.69584 + 1.45744i −2.75281 − 0.737614i 0.834479 − 0.481787i 3.02107 −4.12812 + 2.38337i 0.423625 + 2.24706i
32.5 1.12540 − 1.94926i 0.514229 + 1.91913i −1.53307 − 2.65535i −2.22228 − 0.247944i 4.31958 + 1.15743i −1.10607 + 0.638592i −2.39966 −0.820542 + 0.473740i −2.98427 + 4.05275i
33.1 −1.32488 + 2.29475i −1.25278 + 0.335680i −2.51060 − 4.34849i −1.30391 + 1.81654i 0.889471 − 3.31955i 0.0972962 − 0.0561740i 8.00544 −1.14131 + 0.658935i −2.44100 − 5.39885i
33.2 −0.915816 + 1.58624i 1.91432 − 0.512942i −0.677439 − 1.17336i 1.45480 − 1.69810i −0.939520 + 3.50634i −3.06478 + 1.76945i −1.18163 0.803451 − 0.463873i 1.36126 + 3.86282i
33.3 −0.246951 + 0.427732i 0.908353 − 0.243392i 0.878030 + 1.52079i −2.21791 − 0.284413i −0.120212 + 0.448637i 3.18307 − 1.83775i −1.85513 −1.83221 + 1.05783i 0.669366 − 0.878433i
33.4 −0.137404 + 0.237991i −2.28256 + 0.611610i 0.962240 + 1.66665i 1.69883 + 1.45395i 0.168076 − 0.627267i −0.334376 + 0.193052i −1.07848 2.23793 − 1.29207i −0.579454 + 0.204528i
33.5 0.759023 − 1.31467i −0.653367 + 0.175069i −0.152233 − 0.263675i 0.600231 − 2.15400i −0.265763 + 0.991842i −2.24723 + 1.29744i 2.57390 −2.20184 + 1.27123i −2.37621 − 2.42404i
63.1 −1.04397 − 1.80821i 0.713171 − 2.66159i −1.17974 + 2.04338i −0.194361 + 2.22760i −5.55724 + 1.48906i 2.52122 + 1.45563i 0.750585 −3.97738 − 2.29634i 4.23088 − 1.97411i
63.2 −0.792369 − 1.37242i −0.0510678 + 0.190588i −0.255697 + 0.442881i 0.0672627 − 2.23506i 0.302032 − 0.0809291i −0.474866 − 0.274164i −2.35905 2.56436 + 1.48053i −3.12074 + 1.67868i
63.3 0.0656513 + 0.113711i −0.0890070 + 0.332179i 0.991380 − 1.71712i 0.813169 + 2.08297i −0.0436159 + 0.0116869i −2.40874 − 1.39069i 0.522947 2.49566 + 1.44087i −0.183472 + 0.229216i
63.4 0.511309 + 0.885613i −0.721300 + 2.69193i 0.477126 − 0.826407i −1.69584 − 1.45744i −2.75281 + 0.737614i 0.834479 + 0.481787i 3.02107 −4.12812 − 2.38337i 0.423625 − 2.24706i
63.5 1.12540 + 1.94926i 0.514229 − 1.91913i −1.53307 + 2.65535i −2.22228 + 0.247944i 4.31958 − 1.15743i −1.10607 − 0.638592i −2.39966 −0.820542 − 0.473740i −2.98427 − 4.05275i
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.5
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
65.o even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 65.2.o.a ✓ 20
3.b odd 2 1 585.2.cf.a 20
5.b even 2 1 325.2.s.b 20
5.c odd 4 1 65.2.t.a yes 20
5.c odd 4 1 325.2.x.b 20
13.b even 2 1 845.2.o.g 20
13.c even 3 1 845.2.k.e 20
13.c even 3 1 845.2.o.e 20
13.d odd 4 1 845.2.t.e 20
13.d odd 4 1 845.2.t.f 20
13.e even 6 1 845.2.k.d 20
13.e even 6 1 845.2.o.f 20
13.f odd 12 1 65.2.t.a yes 20
13.f odd 12 1 845.2.f.d 20
13.f odd 12 1 845.2.f.e 20
13.f odd 12 1 845.2.t.g 20
15.e even 4 1 585.2.dp.a 20
39.k even 12 1 585.2.dp.a 20
65.f even 4 1 845.2.o.f 20
65.h odd 4 1 845.2.t.g 20
65.k even 4 1 845.2.o.e 20
65.o even 12 1 inner 65.2.o.a ✓ 20
65.o even 12 1 845.2.k.e 20
65.q odd 12 1 845.2.f.e 20
65.q odd 12 1 845.2.t.f 20
65.r odd 12 1 845.2.f.d 20
65.r odd 12 1 845.2.t.e 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.k.d 20
65.t even 12 1 845.2.o.g 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 1.a even 1 1 trivial
65.2.o.a ✓ 20 65.o even 12 1 inner
65.2.t.a yes 20 5.c odd 4 1
65.2.t.a yes 20 13.f odd 12 1
325.2.s.b 20 5.b even 2 1
325.2.s.b 20 65.t even 12 1
325.2.x.b 20 5.c odd 4 1
325.2.x.b 20 65.s odd 12 1
585.2.cf.a 20 3.b odd 2 1
585.2.cf.a 20 195.bn odd 12 1
585.2.dp.a 20 15.e even 4 1
585.2.dp.a 20 39.k even 12 1
845.2.f.d 20 13.f odd 12 1
845.2.f.d 20 65.r odd 12 1
845.2.f.e 20 13.f odd 12 1
845.2.f.e 20 65.q odd 12 1
845.2.k.d 20 13.e even 6 1
845.2.k.d 20 65.t even 12 1
845.2.k.e 20 13.c even 3 1
845.2.k.e 20 65.o even 12 1
845.2.o.e 20 13.c even 3 1
845.2.o.e 20 65.k even 4 1
845.2.o.f 20 13.e even 6 1
845.2.o.f 20 65.f even 4 1
845.2.o.g 20 13.b even 2 1
845.2.o.g 20 65.t even 12 1
845.2.t.e 20 13.d odd 4 1
845.2.t.e 20 65.r odd 12 1
845.2.t.f 20 13.d odd 4 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.h odd 4 1

Hecke kernels

This newform subspace is the entire newspace S2new(65,[χ])S_{2}^{\mathrm{new}}(65, [\chi]).

Hecke characteristic polynomials

pp Fp(T)F_p(T)
22 T20+4T19+⋯+1 T^{20} + 4 T^{19} + \cdots + 1 Copy content Toggle raw display
33 T20+2T19+⋯+16 T^{20} + 2 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+6T19+⋯+64 T^{20} + 6 T^{19} + \cdots + 64 Copy content Toggle raw display
1111 T20+16T19+⋯+256 T^{20} + 16 T^{19} + \cdots + 256 Copy content Toggle raw display
1313 T20+⋯+137858491849 T^{20} + \cdots + 137858491849 Copy content Toggle raw display
1717 T20+10T19+⋯+1168561 T^{20} + 10 T^{19} + \cdots + 1168561 Copy content Toggle raw display
1919 T20+⋯+1583721616 T^{20} + \cdots + 1583721616 Copy content Toggle raw display
2323 T20+2T19+⋯+144 T^{20} + 2 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 T20−16T19+⋯+33856 T^{20} - 16 T^{19} + \cdots + 33856 Copy content Toggle raw display
6161 T20+⋯+826457355409 T^{20} + \cdots + 826457355409 Copy content Toggle raw display
6767 T20+⋯+15478905336976 T^{20} + \cdots + 15478905336976 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 T20+⋯+28 ⁣⋯ ⁣36 T^{20} + \cdots + 28\!\cdots\!36 Copy content Toggle raw display
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