Properties

Label 83.12.a.a
Level $83$
Weight $12$
Character orbit 83.a
Self dual yes
Analytic conductor $63.772$
Analytic rank $1$
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] = [83,12,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, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("83.1");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 12 \)
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: \(63.7724839864\)
Analytic rank: \(1\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 41 q^{2} - 719 q^{3} + 30213 q^{4} - 19862 q^{5} - 375 q^{6} - 97477 q^{7} - 283137 q^{8} + 1552225 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q - 41 q^{2} - 719 q^{3} + 30213 q^{4} - 19862 q^{5} - 375 q^{6} - 97477 q^{7} - 283137 q^{8} + 1552225 q^{9} - 643995 q^{10} - 746555 q^{11} - 1033817 q^{12} - 5359938 q^{13} - 3588060 q^{14} - 10990846 q^{15} + 18923829 q^{16} + 9437 q^{17} - 2177456 q^{18} - 25692936 q^{19} - 28861257 q^{20} - 11277422 q^{21} - 48221899 q^{22} - 96468141 q^{23} - 306383607 q^{24} + 90423942 q^{25} - 317805135 q^{26} - 235513934 q^{27} - 584880284 q^{28} - 300777167 q^{29} + 77884300 q^{30} - 205240949 q^{31} + 584169763 q^{32} + 162322654 q^{33} + 1033437326 q^{34} + 902133790 q^{35} + 1598747944 q^{36} - 2126309575 q^{37} + 233196209 q^{38} + 1061630296 q^{39} + 892882839 q^{40} + 1217371681 q^{41} + 2988950819 q^{42} - 3039986236 q^{43} + 4701567003 q^{44} - 4207462262 q^{45} - 1732176379 q^{46} - 5366747620 q^{47} - 2706601057 q^{48} + 1240245445 q^{49} - 8500688582 q^{50} - 4351634600 q^{51} - 10702365301 q^{52} - 7942102538 q^{53} - 18994896603 q^{54} - 3896228256 q^{55} - 22435175318 q^{56} - 22724117006 q^{57} - 36326346631 q^{58} - 12314409905 q^{59} - 62250169552 q^{60} - 30353025547 q^{61} - 61850134902 q^{62} - 25015189987 q^{63} - 36790810619 q^{64} - 40543327264 q^{65} - 82218834907 q^{66} - 28921303644 q^{67} - 92351155382 q^{68} - 113409515600 q^{69} - 149316033232 q^{70} - 57119188034 q^{71} - 193241701428 q^{72} - 56498127426 q^{73} - 140196465095 q^{74} - 102892719501 q^{75} - 151647036633 q^{76} - 145466440286 q^{77} - 230842740586 q^{78} - 60451794172 q^{79} - 233243524253 q^{80} - 67593763310 q^{81} - 267797006311 q^{82} + 133927381862 q^{83} - 360464353559 q^{84} - 140465813182 q^{85} - 49523190463 q^{86} + 20579124553 q^{87} - 262277395275 q^{88} - 141356345986 q^{89} - 457066025057 q^{90} - 229116843550 q^{91} - 456832900901 q^{92} - 514029589202 q^{93} - 390171995430 q^{94} - 619714100348 q^{95} - 863659669883 q^{96} - 424406592446 q^{97} - 601083344295 q^{98} - 1097993066018 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −84.6320 725.642 5114.57 −138.417 −61412.5 −14766.5 −259530. 349410. 11714.5
1.2 −80.2968 299.624 4399.57 −9801.24 −24058.9 −79629.7 −188824. −87372.4 787008.
1.3 −76.8174 −698.255 3852.92 −1497.23 53638.2 −37606.2 −138649. 310413. 115013.
1.4 −75.1515 310.620 3599.76 −3331.75 −23343.6 22846.3 −116617. −80662.3 250387.
1.5 −74.8322 −175.191 3551.87 481.582 13109.9 71848.6 −112538. −146455. −36037.9
1.6 −72.0004 −662.974 3136.06 7943.35 47734.4 65761.4 −78341.0 262387. −571924.
1.7 −61.6711 −219.979 1755.33 −9872.64 13566.4 −39761.8 18049.5 −128756. 608857.
1.8 −56.1374 −353.575 1103.41 13945.8 19848.8 −19965.2 53026.9 −52131.4 −782881.
1.9 −55.4460 550.444 1026.26 6117.02 −30519.9 −54173.9 56651.6 125842. −339164.
1.10 −49.6278 −218.214 414.923 −1461.75 10829.5 41649.1 81046.1 −129530. 72543.5
1.11 −38.6686 427.650 −552.737 6694.69 −16536.6 66374.6 100567. 5737.36 −258874.
1.12 −36.2955 −411.095 −730.638 9845.98 14920.9 −576.671 100852. −8148.14 −357365.
1.13 −27.3201 389.394 −1301.61 −8154.66 −10638.3 −30368.3 91511.7 −25519.7 222786.
1.14 −17.6153 −304.962 −1737.70 −3502.17 5372.00 −76614.1 66686.3 −84145.3 61691.8
1.15 −10.3628 −25.0784 −1940.61 −11152.5 259.883 62955.9 41333.2 −176518. 115571.
1.16 −10.3472 −687.970 −1940.93 −11758.9 7118.59 −46300.0 41274.4 296156. 121672.
1.17 −3.34813 588.225 −2036.79 −2172.37 −1969.45 32142.0 13676.4 168862. 7273.36
1.18 5.69141 560.569 −2015.61 −1354.87 3190.43 2723.03 −23127.7 137091. −7711.12
1.19 11.0295 −323.150 −1926.35 7514.61 −3564.17 45.2205 −43835.0 −72721.2 82882.2
1.20 16.6341 −475.219 −1771.31 −9331.09 −7904.85 535.476 −63530.9 48685.8 −155215.
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 83.12.a.a 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.12.a.a 34 1.a even 1 1 trivial