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Properties

Label 83.14.a.a
Level $83$
Weight $14$
Character orbit 83.a
Self dual yes
Analytic conductor $89.002$
Analytic rank $1$
Dimension $42$
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] = [83,14,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, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("83.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 14 \)
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: \(89.0016710301\)
Analytic rank: \(1\)
Dimension: \(42\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 42 q - 193 q^{2} - 2057 q^{3} + 159925 q^{4} - 78072 q^{5} - 220839 q^{6} - 907547 q^{7} - 2367489 q^{8} + 21128599 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 42 q - 193 q^{2} - 2057 q^{3} + 159925 q^{4} - 78072 q^{5} - 220839 q^{6} - 907547 q^{7} - 2367489 q^{8} + 21128599 q^{9} - 3322219 q^{10} - 6613853 q^{11} - 34097993 q^{12} - 90924212 q^{13} - 65231028 q^{14} - 59381710 q^{15} + 550190485 q^{16} - 127487361 q^{17} - 472321352 q^{18} - 483420246 q^{19} - 597828353 q^{20} - 1907150309 q^{21} - 1800535919 q^{22} + 1159540876 q^{23} + 6106465677 q^{24} + 8057737922 q^{25} - 583937959 q^{26} - 6868049147 q^{27} - 14931049956 q^{28} - 15609919181 q^{29} - 50902696028 q^{30} - 12353998339 q^{31} - 72304994481 q^{32} - 43736653139 q^{33} - 54662415462 q^{34} - 16681157530 q^{35} + 70660329784 q^{36} - 89114280337 q^{37} + 35305273809 q^{38} - 35810441042 q^{39} - 2115410241 q^{40} + 18168056880 q^{41} + 195676622483 q^{42} - 70155296568 q^{43} + 291262583835 q^{44} - 35087610962 q^{45} + 70699700745 q^{46} + 91990904456 q^{47} + 167553864431 q^{48} + 641476123835 q^{49} + 621264516126 q^{50} + 75384511003 q^{51} - 274464049565 q^{52} - 519470005144 q^{53} + 1429521160197 q^{54} - 350602648902 q^{55} + 228289311570 q^{56} + 447379247974 q^{57} - 119824643939 q^{58} + 213671945573 q^{59} - 268102581580 q^{60} - 763612483985 q^{61} - 42621111550 q^{62} - 2513648267602 q^{63} + 1450675469757 q^{64} - 659331698888 q^{65} + 799487918921 q^{66} - 3754534972946 q^{67} - 3213958771678 q^{68} - 3961539592292 q^{69} - 327328800944 q^{70} - 3270010035646 q^{71} - 12131492000388 q^{72} - 6650117679694 q^{73} - 8846504075807 q^{74} - 2194836203583 q^{75} - 14688415395673 q^{76} - 8045133549737 q^{77} - 15836734082266 q^{78} - 6216673540866 q^{79} - 15278720197797 q^{80} + 4268560113418 q^{81} - 15620977385299 q^{82} - 13731495681498 q^{83} - 56946249044999 q^{84} - 32105826344090 q^{85} - 33659139253887 q^{86} - 31882394751581 q^{87} - 49146779358551 q^{88} - 3882887422926 q^{89} - 49216416148721 q^{90} - 1545866571122 q^{91} - 17483262874677 q^{92} - 25585828162397 q^{93} - 27821934949694 q^{94} + 5671233823420 q^{95} - 23362696882595 q^{96} - 40466741073806 q^{97} - 36273289449527 q^{98} + 5742810732070 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 −175.964 −2443.59 22771.5 −12795.4 429985. 307663. −2.56547e6 4.37682e6 2.25154e6
1.2 −173.375 406.222 21866.9 −32225.0 −70428.7 −318847. −2.37089e6 −1.42931e6 5.58701e6
1.3 −167.944 1014.35 20013.2 41561.3 −170354. −102386. −1.98530e6 −565418. −6.97997e6
1.4 −163.261 1948.11 18462.3 28443.7 −318051. −434274. −1.67675e6 2.20081e6 −4.64376e6
1.5 −157.578 −1211.15 16638.7 −39863.4 190850. −355581. −1.33101e6 −127448. 6.28159e6
1.6 −150.587 1075.37 14484.5 −6157.16 −161936. 219831. −947572. −437910. 927190.
1.7 −126.185 −1623.56 7730.54 −49459.9 204868. 489559. 58228.9 1.04163e6 6.24108e6
1.8 −120.672 −1250.71 6369.77 18437.3 150926. 197150. 219892. −30038.1 −2.22487e6
1.9 −112.845 −2238.42 4541.92 40419.9 252594. 189661. 411893. 3.41622e6 −4.56117e6
1.10 −110.627 −33.5967 4046.30 20300.3 3716.70 −564658. 458626. −1.59319e6 −2.24576e6
1.11 −105.820 1335.54 3005.84 −11010.4 −141327. 373585. 548799. 189357. 1.16512e6
1.12 −89.3889 322.475 −201.625 12180.6 −28825.7 601868. 750297. −1.49033e6 −1.08881e6
1.13 −82.5468 1774.29 −1378.03 57075.0 −146462. −137800. 789975. 1.55378e6 −4.71136e6
1.14 −77.8090 577.581 −2137.75 −50973.9 −44941.0 −397443. 803748. −1.26072e6 3.96623e6
1.15 −68.9178 −396.221 −3442.34 −46802.4 27306.7 −34987.8 801813. −1.43733e6 3.22551e6
1.16 −63.1139 −1854.62 −4208.63 23056.5 117053. −368906. 782653. 1.84531e6 −1.45518e6
1.17 −54.7651 1890.50 −5192.78 −54368.2 −103534. 348017. 733019. 1.97968e6 2.97748e6
1.18 −39.6666 1772.92 −6618.56 26028.3 −70325.7 −501026. 587484. 1.54893e6 −1.03245e6
1.19 −39.2692 2430.21 −6649.93 4719.25 −95432.5 67744.0 582831. 4.31160e6 −185321.
1.20 −34.8668 −1049.66 −6976.31 52381.8 36598.2 485449. 528870. −492543. −1.82638e6
See all 42 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.42
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 83.14.a.a ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.14.a.a ✓ 42 1.a even 1 1 trivial