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Properties

Label 83.14.a.b
Level $83$
Weight $14$
Character orbit 83.a
Self dual yes
Analytic conductor $89.002$
Analytic rank $0$
Dimension $48$
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: \(0\)
Dimension: \(48\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 127 q^{2} + 2317 q^{3} + 221365 q^{4} + 78178 q^{5} - 34215 q^{6} + 739539 q^{7} + 1564671 q^{8} + 30694537 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 127 q^{2} + 2317 q^{3} + 221365 q^{4} + 78178 q^{5} - 34215 q^{6} + 739539 q^{7} + 1564671 q^{8} + 30694537 q^{9} + 6677781 q^{10} + 4015513 q^{11} + 19649719 q^{12} + 73187294 q^{13} - 20053812 q^{14} + 122868290 q^{15} + 1103838613 q^{16} + 65613191 q^{17} + 377984248 q^{18} + 175222088 q^{19} + 682171647 q^{20} + 2483093398 q^{21} + 1434595063 q^{22} - 338134917 q^{23} - 8950472465 q^{24} + 16682792848 q^{25} - 1168940895 q^{26} + 6482539786 q^{27} + 16873765792 q^{28} + 11586862903 q^{29} + 58531175576 q^{30} + 19443751771 q^{31} + 48780524209 q^{32} + 32677356418 q^{33} + 58304697472 q^{34} + 29334463750 q^{35} + 193898401900 q^{36} + 106210983591 q^{37} + 50447009513 q^{38} - 27679174392 q^{39} - 25333468689 q^{40} - 24248633477 q^{41} - 211904210777 q^{42} + 70251091188 q^{43} - 454740345093 q^{44} + 10411945394 q^{45} + 26106034351 q^{46} + 76859912108 q^{47} - 740431860729 q^{48} + 795238127933 q^{49} - 962765997536 q^{50} - 257240039384 q^{51} - 245516706993 q^{52} + 314507554294 q^{53} - 1179564255355 q^{54} - 399145852032 q^{55} - 1297011837014 q^{56} + 1081108347438 q^{57} + 748713978463 q^{58} + 566093824891 q^{59} - 234591376922 q^{60} + 848715312387 q^{61} - 31454730582 q^{62} - 204856918819 q^{63} + 6086311667481 q^{64} + 1327138046072 q^{65} + 3114238962043 q^{66} + 2609149873748 q^{67} + 1534402993666 q^{68} + 2705449367488 q^{69} + 10247004497848 q^{70} + 1071035334478 q^{71} + 8828200206724 q^{72} + 2700207330998 q^{73} + 5681975415985 q^{74} + 9251748374079 q^{75} + 3969241466831 q^{76} + 12524841932326 q^{77} + 15517032876218 q^{78} + 6046590701508 q^{79} + 15366045202639 q^{80} + 28073454662304 q^{81} + 24420401924587 q^{82} + 15693137921712 q^{83} + 72857728250633 q^{84} + 38304156255526 q^{85} + 37323136756349 q^{86} + 24325330152665 q^{87} + 15668582890395 q^{88} + 23822081266262 q^{89} + 43508186008735 q^{90} - 4665859084270 q^{91} + 9441568975171 q^{92} + 36923108414106 q^{93} + 41754873188586 q^{94} - 905604444380 q^{95} - 26875115518143 q^{96} + 21541135250578 q^{97} + 7267184821581 q^{98} - 36983723704562 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 −176.918 1973.04 23107.9 −53354.5 −349066. 430025. −2.63890e6 2.29857e6 9.43937e6
1.2 −166.164 −1766.71 19418.3 62891.3 293563. −482911. −1.86541e6 1.52694e6 −1.04502e7
1.3 −165.885 −86.0897 19325.7 47652.7 14281.0 529191. −1.84691e6 −1.58691e6 −7.90485e6
1.4 −165.555 −947.542 19216.4 −5959.99 156870. 213001. −1.82515e6 −696488. 986705.
1.5 −150.757 −1099.71 14535.7 31293.4 165789. −156732. −956355. −384961. −4.71770e6
1.6 −145.076 2331.16 12855.0 42247.2 −338195. 452789. −676493. 3.83999e6 −6.12906e6
1.7 −134.393 425.261 9869.56 −35193.0 −57152.2 −64415.8 −225453. −1.41348e6 4.72971e6
1.8 −133.335 −288.769 9586.33 −69034.0 38503.2 407619. −185914. −1.51094e6 9.20467e6
1.9 −128.310 −2160.72 8271.55 −35742.7 277243. −336276. −10207.4 3.07440e6 4.58617e6
1.10 −127.962 2022.23 8182.20 −60840.6 −258768. −409433. 1253.58 2.49509e6 7.78526e6
1.11 −127.497 861.267 8063.42 36518.0 −109809. −193441. 16393.8 −852542. −4.65592e6
1.12 −123.104 2103.31 6962.72 −15806.3 −258927. −148440. 151330. 2.82958e6 1.94583e6
1.13 −104.640 142.999 2757.44 67945.4 −14963.4 112974. 568670. −1.57387e6 −7.10977e6
1.14 −84.9041 −1684.54 −983.288 −25915.5 143024. −372910. 779020. 1.24335e6 2.20034e6
1.15 −76.7579 −357.777 −2300.23 7515.39 27462.2 −75846.1 805361. −1.46632e6 −576865.
1.16 −64.4993 1706.01 −4031.84 38981.1 −110036. 195394. 788429. 1.31614e6 −2.51425e6
1.17 −58.9076 −950.606 −4721.89 −16426.5 55998.0 163160. 760727. −690671. 967647.
1.18 −49.4491 1337.25 −5746.79 −18376.4 −66125.7 −279997. 689260. 193912. 908698.
1.19 −45.3819 −2227.58 −6132.48 −48340.2 101092. 109291. 650072. 3.36781e6 2.19377e6
1.20 −36.1093 589.974 −6888.12 −21444.8 −21303.6 301985. 544533. −1.24625e6 774359.
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.48
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.b ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.14.a.b ✓ 48 1.a even 1 1 trivial