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Properties

Label 83.10.a.a
Level $83$
Weight $10$
Character orbit 83.a
Self dual yes
Analytic conductor $42.748$
Analytic rank $1$
Dimension $28$
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] = [83,10,Mod(1,83)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(83, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("83.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 83.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: \(42.7479744016\)
Analytic rank: \(1\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 49 q^{2} - 317 q^{3} + 6229 q^{4} - 3467 q^{5} - 3687 q^{6} - 13836 q^{7} - 37377 q^{8} + 140839 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 49 q^{2} - 317 q^{3} + 6229 q^{4} - 3467 q^{5} - 3687 q^{6} - 13836 q^{7} - 37377 q^{8} + 140839 q^{9} - 70619 q^{10} - 10173 q^{11} - 232553 q^{12} - 490487 q^{13} + 52908 q^{14} - 491800 q^{15} + 1233621 q^{16} - 469930 q^{17} - 2269304 q^{18} - 596711 q^{19} - 1747153 q^{20} - 3494933 q^{21} - 5961399 q^{22} - 3547195 q^{23} + 886389 q^{24} + 6359453 q^{25} + 5828985 q^{26} + 1486189 q^{27} + 3376012 q^{28} + 2068429 q^{29} + 34707316 q^{30} - 3908010 q^{31} + 2023847 q^{32} - 5625815 q^{33} - 19817758 q^{34} - 26431280 q^{35} + 614584 q^{36} - 72566059 q^{37} - 44944383 q^{38} - 24771554 q^{39} - 100168529 q^{40} - 40533527 q^{41} - 122737837 q^{42} - 73865327 q^{43} - 197745381 q^{44} - 203130941 q^{45} - 145008863 q^{46} - 122569318 q^{47} - 424615153 q^{48} - 13286584 q^{49} - 462776906 q^{50} - 112545191 q^{51} - 462144045 q^{52} - 301705683 q^{53} - 689730555 q^{54} - 349856082 q^{55} - 651119998 q^{56} - 481237934 q^{57} - 583145275 q^{58} - 176643831 q^{59} - 1389548452 q^{60} - 273536099 q^{61} - 380627358 q^{62} - 609998287 q^{63} - 663907987 q^{64} - 290588518 q^{65} - 812568463 q^{66} - 801279079 q^{67} - 773867342 q^{68} - 441252986 q^{69} - 1231202192 q^{70} - 590881986 q^{71} - 1790799396 q^{72} - 960852248 q^{73} - 477639791 q^{74} - 1122848271 q^{75} - 810958233 q^{76} - 1390618815 q^{77} - 1449936730 q^{78} - 760078872 q^{79} - 441202741 q^{80} - 612320180 q^{81} - 490092283 q^{82} - 1328832988 q^{83} - 1589396903 q^{84} - 3713079919 q^{85} - 2459663183 q^{86} - 4005425207 q^{87} - 3706822991 q^{88} - 784032234 q^{89} - 1113613985 q^{90} - 2928494941 q^{91} - 1853322453 q^{92} - 3419268179 q^{93} - 1661591790 q^{94} + 1546923940 q^{95} + 2056930957 q^{96} - 3313934280 q^{97} + 2731846201 q^{98} + 5414566804 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −43.6544 −209.554 1393.71 1968.79 9147.95 1485.01 −38490.4 24229.8 −85946.3
1.2 −39.7474 −67.9981 1067.85 −1642.00 2702.74 4077.81 −22093.7 −15059.3 65265.0
1.3 −37.3186 237.019 880.678 −2702.67 −8845.22 −2293.27 −13758.6 36495.0 100860.
1.4 −36.6004 −131.787 827.591 271.454 4823.44 2085.17 −11550.8 −2315.31 −9935.32
1.5 −35.5141 220.040 749.252 436.904 −7814.54 3126.51 −8425.78 28734.8 −15516.3
1.6 −33.6605 −10.5962 621.029 2112.16 356.675 6903.12 −3669.97 −19570.7 −71096.3
1.7 −28.7334 −161.881 313.611 1657.67 4651.41 −11166.2 5700.41 6522.54 −47630.6
1.8 −27.7664 143.437 258.973 −959.768 −3982.72 −1553.23 7025.64 891.071 26649.3
1.9 −24.9181 −125.556 108.911 −2461.22 3128.60 −8939.23 10044.2 −3918.79 61328.9
1.10 −16.2774 56.9446 −247.045 1653.91 −926.912 −84.2608 12355.3 −16440.3 −26921.4
1.11 −11.9537 238.345 −369.109 30.3673 −2849.10 −12533.6 10532.5 37125.4 −363.001
1.12 −8.15518 −18.0587 −445.493 −1571.47 147.272 1991.53 7808.53 −19356.9 12815.7
1.13 −7.06894 −159.442 −462.030 −973.674 1127.09 331.130 6885.36 5738.77 6882.85
1.14 0.276148 26.5296 −511.924 684.895 7.32609 8829.76 −282.755 −18979.2 189.132
1.15 1.44758 −263.173 −509.905 −1030.34 −380.963 −7422.83 −1479.29 49577.0 −1491.50
1.16 1.60247 −142.942 −509.432 2099.17 −229.061 −6862.07 −1636.81 749.502 3363.85
1.17 2.77166 172.611 −504.318 −558.105 478.419 3540.75 −2816.89 10111.5 −1546.88
1.18 9.87468 −230.290 −414.491 −2243.03 −2274.04 11738.8 −9148.80 33350.6 −22149.2
1.19 9.90930 208.538 −413.806 1442.04 2066.46 −5274.19 −9174.09 23805.0 14289.6
1.20 19.0953 110.351 −147.371 −754.066 2107.19 5649.15 −12590.9 −7505.56 −14399.1
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(83\) \(1\)

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 83.10.a.a ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.10.a.a ✓ 28 1.a even 1 1 trivial