Properties

Label 1849.2.a.n
Level $1849$
Weight $2$
Character orbit 1849.a
Self dual yes
Analytic conductor $14.764$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1849,2,Mod(1,1849)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1849.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

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: yes
Analytic conductor: \(14.7643393337\)
Analytic rank: \(1\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} - 3223 x^{10} - 8851 x^{9} + 9909 x^{8} + 10400 x^{7} - 14483 x^{6} - 5118 x^{5} + \cdots - 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{17}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q - \beta_1 q^{2} - \beta_{14} q^{3} + (\beta_{7} - \beta_{5} + \beta_{3} + 1) q^{4} + ( - \beta_{13} - \beta_{10} - \beta_{5} - \beta_{4} - 1) q^{5} + (\beta_{14} - \beta_{12} + \beta_{9} - \beta_{3} - 1) q^{6} + (\beta_{16} + \beta_{15} - \beta_{11} - \beta_{9} - \beta_{8} + \beta_{7} - 2 \beta_{6} - \beta_{4} + \beta_{2} + \beta_1 - 2) q^{7} + ( - \beta_{17} - \beta_{16} - \beta_{15} + \beta_{11} + \beta_{9} + \beta_{8} - 2 \beta_{7} + 2 \beta_{6} + \cdots + 1) q^{8}+ \cdots + ( - \beta_{16} - \beta_{6} + \beta_{3} + 1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - \beta_1 q^{2} - \beta_{14} q^{3} + (\beta_{7} - \beta_{5} + \beta_{3} + 1) q^{4} + ( - \beta_{13} - \beta_{10} - \beta_{5} - \beta_{4} - 1) q^{5} + (\beta_{14} - \beta_{12} + \beta_{9} - \beta_{3} - 1) q^{6} + (\beta_{16} + \beta_{15} - \beta_{11} - \beta_{9} - \beta_{8} + \beta_{7} - 2 \beta_{6} - \beta_{4} + \beta_{2} + \beta_1 - 2) q^{7} + ( - \beta_{17} - \beta_{16} - \beta_{15} + \beta_{11} + \beta_{9} + \beta_{8} - 2 \beta_{7} + 2 \beta_{6} + \cdots + 1) q^{8}+ \cdots + (2 \beta_{17} - \beta_{14} - \beta_{13} + 2 \beta_{12} - \beta_{9} + 2 \beta_{7} - 2 \beta_{5} + 3 \beta_{3} + \cdots + 5) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} - 3223 x^{10} - 8851 x^{9} + 9909 x^{8} + 10400 x^{7} - 14483 x^{6} - 5118 x^{5} + \cdots - 27 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( 13275 \nu^{17} + 49216 \nu^{16} - 638270 \nu^{15} - 817698 \nu^{14} + 10040797 \nu^{13} + 4293380 \nu^{12} - 76161915 \nu^{11} - 2151884 \nu^{10} + \cdots - 16390890 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( 20710 \nu^{17} - 38599 \nu^{16} - 543260 \nu^{15} + 949666 \nu^{14} + 5791002 \nu^{13} - 9559915 \nu^{12} - 31639730 \nu^{11} + 50308357 \nu^{10} + 90932936 \nu^{9} + \cdots - 7389 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( - 44003 \nu^{17} + 173548 \nu^{16} + 771312 \nu^{15} - 3533264 \nu^{14} - 4677973 \nu^{13} + 28270866 \nu^{12} + 8945071 \nu^{11} - 112470798 \nu^{10} + \cdots + 401490 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( - 55583 \nu^{17} + 218229 \nu^{16} + 1056380 \nu^{15} - 4620818 \nu^{14} - 7782617 \nu^{13} + 39149731 \nu^{12} + 28825423 \nu^{11} - 169440829 \nu^{10} + \cdots + 9437373 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( 69430 \nu^{17} - 284265 \nu^{16} - 1359184 \nu^{15} + 6326890 \nu^{14} + 10180162 \nu^{13} - 57120029 \nu^{12} - 35687486 \nu^{11} + 268538099 \nu^{10} + \cdots - 4659615 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( - 76293 \nu^{17} + 256828 \nu^{16} + 1599640 \nu^{15} - 5570484 \nu^{14} - 13573619 \nu^{13} + 48709646 \nu^{12} + 60465153 \nu^{11} - 219749186 \nu^{10} + \cdots + 5508270 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( 59046 \nu^{17} - 244357 \nu^{16} - 1095040 \nu^{15} + 5288955 \nu^{14} + 7351847 \nu^{13} - 46037891 \nu^{12} - 18893697 \nu^{11} + 206093975 \nu^{10} + \cdots + 4297068 ) / 656082 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( 124637 \nu^{17} - 455245 \nu^{16} - 2516574 \nu^{15} + 9987848 \nu^{14} + 19725175 \nu^{13} - 88235805 \nu^{12} - 74360329 \nu^{11} + 401793495 \nu^{10} + \cdots + 2059911 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( 141246 \nu^{17} - 576685 \nu^{16} - 2561026 \nu^{15} + 12268074 \nu^{14} + 16443476 \nu^{13} - 104501855 \nu^{12} - 36379716 \nu^{11} + 454974713 \nu^{10} + \cdots + 8750907 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( 167003 \nu^{17} - 649353 \nu^{16} - 3148820 \nu^{15} + 13928240 \nu^{14} + 21852299 \nu^{13} - 119904103 \nu^{12} - 61900753 \nu^{11} + 529610989 \nu^{10} + \cdots + 6009885 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( 94434 \nu^{17} - 367211 \nu^{16} - 1822472 \nu^{15} + 8017242 \nu^{14} + 13158388 \nu^{13} - 70696261 \nu^{12} - 40633854 \nu^{11} + 322516021 \nu^{10} + \cdots + 9088893 ) / 656082 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 204816 \nu^{17} - 823249 \nu^{16} - 3821242 \nu^{15} + 17751510 \nu^{14} + 25899626 \nu^{13} - 153706883 \nu^{12} - 68256762 \nu^{11} + 683247641 \nu^{10} + \cdots + 11305827 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( 245597 \nu^{17} - 1067329 \nu^{16} - 4433508 \nu^{15} + 23271404 \nu^{14} + 27818161 \nu^{13} - 204864951 \nu^{12} - 52751011 \nu^{11} + 932572533 \nu^{10} + \cdots + 24053769 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 253199 \nu^{17} + 944792 \nu^{16} + 4923820 \nu^{15} - 20322290 \nu^{14} - 36421791 \nu^{13} + 175651034 \nu^{12} + 122991985 \nu^{11} - 780467606 \nu^{10} + \cdots - 2620152 ) / 1312164 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( 160886 \nu^{17} - 603273 \nu^{16} - 3199685 \nu^{15} + 13198295 \nu^{14} + 24565100 \nu^{13} - 116487784 \nu^{12} - 89543356 \nu^{11} + 531312130 \nu^{10} + \cdots - 572175 ) / 656082 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( 249517 \nu^{17} - 1016292 \nu^{16} - 4644175 \nu^{15} + 21964198 \nu^{14} + 31393966 \nu^{13} - 190931687 \nu^{12} - 82343444 \nu^{11} + 853971125 \nu^{10} + \cdots + 13820985 ) / 656082 \) Copy content Toggle raw display
\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta_{7} - \beta_{5} + \beta_{3} + 3 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( \beta_{17} + \beta_{16} + \beta_{15} - \beta_{11} - \beta_{9} - \beta_{8} + 2 \beta_{7} - 2 \beta_{6} - \beta_{5} - \beta_{4} + \beta_{3} + \beta_{2} + 5 \beta _1 - 1 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( \beta_{16} + \beta_{13} + \beta_{12} - 2 \beta_{11} - \beta_{10} - \beta_{9} + 8 \beta_{7} - 2 \beta_{6} - 8 \beta_{5} - \beta_{4} + 7 \beta_{3} + \beta _1 + 13 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( 7 \beta_{17} + 10 \beta_{16} + 7 \beta_{15} + \beta_{12} - 9 \beta_{11} - 2 \beta_{10} - 9 \beta_{9} - 7 \beta_{8} + 18 \beta_{7} - 18 \beta_{6} - 11 \beta_{5} - 8 \beta_{4} + 9 \beta_{3} + 6 \beta_{2} + 28 \beta _1 - 7 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( 2 \beta_{17} + 15 \beta_{16} + \beta_{15} + 7 \beta_{13} + 9 \beta_{12} - 23 \beta_{11} - 9 \beta_{10} - 12 \beta_{9} - 4 \beta_{8} + 58 \beta_{7} - 25 \beta_{6} - 56 \beta_{5} - 11 \beta_{4} + 46 \beta_{3} - \beta_{2} + 16 \beta _1 + 60 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( 45 \beta_{17} + 82 \beta_{16} + 42 \beta_{15} - \beta_{14} - 3 \beta_{13} + 14 \beta_{12} - 73 \beta_{11} - 24 \beta_{10} - 67 \beta_{9} - 46 \beta_{8} + 142 \beta_{7} - 138 \beta_{6} - 98 \beta_{5} - 56 \beta_{4} + 72 \beta_{3} + 29 \beta_{2} + 167 \beta _1 - 43 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( 30 \beta_{17} + 152 \beta_{16} + 10 \beta_{15} + 33 \beta_{13} + 69 \beta_{12} - 206 \beta_{11} - 73 \beta_{10} - 108 \beta_{9} - 52 \beta_{8} + 424 \beta_{7} - 240 \beta_{6} - 394 \beta_{5} - 94 \beta_{4} + 306 \beta_{3} - 14 \beta_{2} + \cdots + 278 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( 296 \beta_{17} + 635 \beta_{16} + 240 \beta_{15} - 10 \beta_{14} - 55 \beta_{13} + 136 \beta_{12} - 579 \beta_{11} - 221 \beta_{10} - 472 \beta_{9} - 315 \beta_{8} + 1085 \beta_{7} - 1031 \beta_{6} - 808 \beta_{5} - 387 \beta_{4} + \cdots - 271 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( 316 \beta_{17} + 1342 \beta_{16} + 69 \beta_{15} + 10 \beta_{14} + 78 \beta_{13} + 510 \beta_{12} - 1692 \beta_{11} - 590 \beta_{10} - 868 \beta_{9} - 503 \beta_{8} + 3135 \beta_{7} - 2093 \beta_{6} - 2827 \beta_{5} - 749 \beta_{4} + \cdots + 1229 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( 2009 \beta_{17} + 4827 \beta_{16} + 1330 \beta_{15} - 40 \beta_{14} - 677 \beta_{13} + 1147 \beta_{12} - 4541 \beta_{11} - 1862 \beta_{10} - 3259 \beta_{9} - 2253 \beta_{8} + 8199 \beta_{7} - 7724 \beta_{6} - 6419 \beta_{5} + \cdots - 1846 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( 2884 \beta_{17} + 11118 \beta_{16} + 381 \beta_{15} + 236 \beta_{14} - 629 \beta_{13} + 3722 \beta_{12} - 13363 \beta_{11} - 4774 \beta_{10} - 6582 \beta_{9} - 4401 \beta_{8} + 23307 \beta_{7} - 17419 \beta_{6} + \cdots + 4724 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( 13986 \beta_{17} + 36498 \beta_{16} + 7132 \beta_{15} + 284 \beta_{14} - 7029 \beta_{13} + 9034 \beta_{12} - 35326 \beta_{11} - 15080 \beta_{10} - 22338 \beta_{9} - 16633 \beta_{8} + 61687 \beta_{7} + \cdots - 13667 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( 24429 \beta_{17} + 89053 \beta_{16} + 1512 \beta_{15} + 3507 \beta_{14} - 12885 \beta_{13} + 27005 \beta_{12} - 103453 \beta_{11} - 38486 \beta_{10} - 48265 \beta_{9} - 36816 \beta_{8} + 173685 \beta_{7} + \cdots + 10825 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( 99222 \beta_{17} + 275782 \beta_{16} + 36415 \beta_{15} + 8100 \beta_{14} - 66561 \beta_{13} + 68573 \beta_{12} - 273052 \beta_{11} - 119674 \beta_{10} - 152784 \beta_{9} - 125404 \beta_{8} + \cdots - 107636 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( 198097 \beta_{17} + 699601 \beta_{16} + 156 \beta_{15} + 42115 \beta_{14} - 150414 \beta_{13} + 195355 \beta_{12} - 792366 \beta_{11} - 308182 \beta_{10} - 346727 \beta_{9} - 300668 \beta_{8} + \cdots - 58659 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( 713751 \beta_{17} + 2085523 \beta_{16} + 170041 \beta_{15} + 112366 \beta_{14} - 595897 \beta_{13} + 509658 \beta_{12} - 2099810 \beta_{11} - 938905 \beta_{10} - 1045038 \beta_{9} + \cdots - 877416 \) Copy content Toggle raw display

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) 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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
2.75930
2.61223
2.31259
2.16300
1.78421
1.69598
1.10272
1.04477
0.847401
0.131407
0.0953887
−0.800597
−1.09100
−1.18520
−1.70036
−2.17399
−2.27976
−2.31808
−2.75930 −1.44592 5.61371 0.916508 3.98973 1.94308 −9.97129 −0.909309 −2.52892
1.2 −2.61223 1.92275 4.82373 −2.98756 −5.02267 0.679767 −7.37622 0.696981 7.80417
1.3 −2.31259 −2.69989 3.34809 −2.53973 6.24374 2.18729 −3.11758 4.28939 5.87337
1.4 −2.16300 −2.91800 2.67858 2.73005 6.31164 −2.02167 −1.46776 5.51474 −5.90511
1.5 −1.78421 2.96672 1.18339 −0.596316 −5.29325 −4.36308 1.45700 5.80145 1.06395
1.6 −1.69598 −1.71311 0.876333 0.385406 2.90540 −3.49171 1.90571 −0.0652397 −0.653640
1.7 −1.10272 −0.645986 −0.784019 −3.32240 0.712338 −2.46546 3.06998 −2.58270 3.66366
1.8 −1.04477 2.52412 −0.908449 −0.499809 −2.63714 3.30668 3.03867 3.37119 0.522187
1.9 −0.847401 0.0176385 −1.28191 3.43657 −0.0149469 0.269043 2.78110 −2.99969 −2.91216
1.10 −0.131407 1.32082 −1.98273 1.78074 −0.173564 0.0149856 0.523357 −1.25544 −0.234000
1.11 −0.0953887 −2.36384 −1.99090 −3.81314 0.225484 −2.61962 0.380687 2.58774 0.363731
1.12 0.800597 −0.744601 −1.35904 1.40135 −0.596125 4.75856 −2.68924 −2.44557 1.12192
1.13 1.09100 1.45952 −0.809726 1.35087 1.59233 0.216325 −3.06540 −0.869803 1.47379
1.14 1.18520 −2.30227 −0.595300 −3.24275 −2.72866 2.76837 −3.07595 2.30047 −3.84331
1.15 1.70036 1.15587 0.891224 −1.76341 1.96539 0.594565 −1.88532 −1.66397 −2.99843
1.16 2.17399 0.327650 2.72622 −0.0263127 0.712306 −3.12927 1.57880 −2.89265 −0.0572034
1.17 2.27976 −3.20997 3.19730 −0.137674 −7.31797 −1.86944 2.72957 7.30393 −0.313864
1.18 2.31808 1.34851 3.37350 −4.07240 3.12595 −2.77841 3.18389 −1.18153 −9.44015
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.18
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(43\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1849.2.a.n 18
43.b odd 2 1 1849.2.a.o 18
43.g even 21 2 43.2.g.a 36
129.o odd 42 2 387.2.y.c 36
172.o odd 42 2 688.2.bg.c 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.2.g.a 36 43.g even 21 2
387.2.y.c 36 129.o odd 42 2
688.2.bg.c 36 172.o odd 42 2
1849.2.a.n 18 1.a even 1 1 trivial
1849.2.a.o 18 43.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{18} + 5 T_{2}^{17} - 15 T_{2}^{16} - 106 T_{2}^{15} + 47 T_{2}^{14} + 897 T_{2}^{13} + 364 T_{2}^{12} - 3855 T_{2}^{11} - 3223 T_{2}^{10} + 8851 T_{2}^{9} + 9909 T_{2}^{8} - 10400 T_{2}^{7} - 14483 T_{2}^{6} + 5118 T_{2}^{5} + \cdots - 27 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1849))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{18} + 5 T^{17} - 15 T^{16} - 106 T^{15} + \cdots - 27 \) Copy content Toggle raw display
$3$ \( T^{18} + 5 T^{17} - 22 T^{16} - 134 T^{15} + \cdots - 41 \) Copy content Toggle raw display
$5$ \( T^{18} + 11 T^{17} + 11 T^{16} - 266 T^{15} + \cdots - 27 \) Copy content Toggle raw display
$7$ \( T^{18} + 6 T^{17} - 42 T^{16} - 310 T^{15} + \cdots + 211 \) Copy content Toggle raw display
$11$ \( T^{18} + 2 T^{17} - 92 T^{16} + \cdots + 4079943 \) Copy content Toggle raw display
$13$ \( T^{18} + 7 T^{17} - 57 T^{16} + \cdots + 5432407 \) Copy content Toggle raw display
$17$ \( T^{18} + 11 T^{17} - 75 T^{16} + \cdots + 6460371 \) Copy content Toggle raw display
$19$ \( T^{18} + 31 T^{17} + 333 T^{16} + \cdots + 6136831 \) Copy content Toggle raw display
$23$ \( T^{18} + 11 T^{17} - 69 T^{16} + \cdots - 189 \) Copy content Toggle raw display
$29$ \( T^{18} + 37 T^{17} + \cdots + 505748853 \) Copy content Toggle raw display
$31$ \( T^{18} + 12 T^{17} + \cdots + 765689239 \) Copy content Toggle raw display
$37$ \( T^{18} - 19 T^{17} - 77 T^{16} + \cdots + 21918373 \) Copy content Toggle raw display
$41$ \( T^{18} + 7 T^{17} + \cdots - 40423514319 \) Copy content Toggle raw display
$43$ \( T^{18} \) Copy content Toggle raw display
$47$ \( T^{18} + T^{17} - 405 T^{16} + \cdots + 7697721249 \) Copy content Toggle raw display
$53$ \( T^{18} - 3 T^{17} + \cdots - 85602704687163 \) Copy content Toggle raw display
$59$ \( T^{18} - 17 T^{17} + \cdots + 3722978673 \) Copy content Toggle raw display
$61$ \( T^{18} + 28 T^{17} + \cdots - 78208816261967 \) Copy content Toggle raw display
$67$ \( T^{18} - 18 T^{17} + \cdots + 3811996587673 \) Copy content Toggle raw display
$71$ \( T^{18} + 86 T^{17} + \cdots - 6746599476063 \) Copy content Toggle raw display
$73$ \( T^{18} - 27 T^{17} + \cdots + 41464581495793 \) Copy content Toggle raw display
$79$ \( T^{18} - 17 T^{17} + \cdots + 6058161830533 \) Copy content Toggle raw display
$83$ \( T^{18} + 12 T^{17} + \cdots + 36277283457297 \) Copy content Toggle raw display
$89$ \( T^{18} + 51 T^{17} + \cdots - 1411268878683 \) Copy content Toggle raw display
$97$ \( T^{18} + 19 T^{17} + \cdots + 77389866919 \) Copy content Toggle raw display
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