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Properties

Label 83.10.a.b
Level $83$
Weight $10$
Character orbit 83.a
Self dual yes
Analytic conductor $42.748$
Analytic rank $0$
Dimension $34$
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: \(0\)
Dimension: \(34\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q + 31 q^{2} + 169 q^{3} + 10069 q^{4} + 2783 q^{5} + 1497 q^{6} + 19778 q^{7} + 24063 q^{8} + 258937 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q + 31 q^{2} + 169 q^{3} + 10069 q^{4} + 2783 q^{5} + 1497 q^{6} + 19778 q^{7} + 24063 q^{8} + 258937 q^{9} + 29381 q^{10} + 77673 q^{11} + 140695 q^{12} + 480587 q^{13} + 283404 q^{14} + 318200 q^{15} + 3396309 q^{16} + 198238 q^{17} + 355096 q^{18} + 1227783 q^{19} + 1452847 q^{20} + 5625265 q^{21} + 8734559 q^{22} + 2585119 q^{23} - 2716985 q^{24} + 20373087 q^{25} - 10806623 q^{26} - 8516003 q^{27} + 5135664 q^{28} - 3710655 q^{29} - 44706808 q^{30} + 7469196 q^{31} - 9065543 q^{32} + 16900207 q^{33} - 10631144 q^{34} - 11018660 q^{35} + 85027852 q^{36} + 77829465 q^{37} + 33221593 q^{38} + 54147078 q^{39} + 79061599 q^{40} + 77117435 q^{41} + 251360455 q^{42} + 80822307 q^{43} + 296907003 q^{44} + 174132953 q^{45} + 137211735 q^{46} + 76048366 q^{47} + 408951399 q^{48} + 410247362 q^{49} + 526850936 q^{50} + 312154573 q^{51} + 596205983 q^{52} + 211809527 q^{53} + 784639109 q^{54} + 198801198 q^{55} + 533465114 q^{56} + 321691194 q^{57} + 692430359 q^{58} + 294912987 q^{59} + 817772830 q^{60} + 437176865 q^{61} + 1072167402 q^{62} + 665912975 q^{63} + 1319055977 q^{64} + 689725922 q^{65} + 675509011 q^{66} + 802272187 q^{67} + 950870418 q^{68} + 1261499014 q^{69} + 1156406616 q^{70} + 269747718 q^{71} + 1862768548 q^{72} + 699240444 q^{73} + 1150178625 q^{74} + 307037487 q^{75} + 1248527055 q^{76} + 811373775 q^{77} + 1092468698 q^{78} + 351769752 q^{79} + 1583731743 q^{80} + 1814177730 q^{81} + 1648090771 q^{82} + 1613582914 q^{83} + 4990108649 q^{84} + 4309294395 q^{85} + 1989407117 q^{86} + 4649715299 q^{87} + 4987231763 q^{88} + 1321982690 q^{89} + 1884905359 q^{90} + 1981050853 q^{91} + 1591337571 q^{92} + 3159048087 q^{93} - 1230260870 q^{94} + 175533180 q^{95} - 3915587631 q^{96} + 506287336 q^{97} - 637321971 q^{98} - 2544701180 q^{99}+O(q^{100}) \) 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 −44.5543 145.199 1473.08 433.848 −6469.25 12004.9 −42820.3 1399.83 −19329.8
1.2 −42.3196 84.7329 1278.94 −794.506 −3585.86 −7076.89 −32456.8 −12503.3 33623.1
1.3 −40.4343 −108.744 1122.93 −514.214 4396.97 −6586.69 −24702.6 −7857.83 20791.9
1.4 −39.8778 160.355 1078.24 2515.39 −6394.58 −10503.9 −22580.3 6030.60 −100308.
1.5 −37.1394 −266.926 867.336 −1980.45 9913.48 5464.36 −13197.0 51566.6 73552.7
1.6 −31.8146 43.9372 500.169 389.987 −1397.84 −2325.92 376.403 −17752.5 −12407.3
1.7 −27.4900 −253.242 243.702 70.0924 6961.63 −4630.57 7375.53 44448.4 −1926.84
1.8 −26.7159 25.6540 201.737 −1954.16 −685.367 10981.5 8288.93 −19024.9 52207.1
1.9 −25.0389 254.386 114.947 1395.31 −6369.54 840.963 9941.77 45029.1 −34936.9
1.10 −22.2146 −179.513 −18.5128 1080.66 3987.79 8011.74 11785.1 12541.7 −24006.5
1.11 −17.8811 −168.783 −192.267 −523.245 3018.03 5874.76 12593.1 8804.83 9356.19
1.12 −17.2599 79.1797 −214.095 −973.594 −1366.64 −7964.64 12532.3 −13413.6 16804.2
1.13 −14.0839 202.311 −313.643 −290.525 −2849.33 10797.1 11628.3 21246.7 4091.73
1.14 −13.2927 −46.4253 −335.304 1476.24 617.118 −7136.60 11263.0 −17527.7 −19623.2
1.15 −7.15670 175.018 −460.782 2486.60 −1252.55 4054.08 6961.90 10948.3 −17795.9
1.16 −3.95811 210.804 −496.333 −2500.74 −834.384 609.954 3991.09 24755.3 9898.18
1.17 −3.24605 −257.657 −501.463 2574.06 836.368 3850.40 3289.76 46704.1 −8355.53
1.18 3.49074 −67.9257 −499.815 218.639 −237.111 −3318.62 −3531.99 −15069.1 763.212
1.19 10.2929 64.7565 −406.057 −1987.73 666.529 −5791.22 −9449.43 −15489.6 −20459.4
1.20 10.3921 76.5253 −404.004 645.392 795.260 −8931.90 −9519.22 −13826.9 6706.99
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.34
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.b ✓ 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.10.a.b ✓ 34 1.a even 1 1 trivial