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Properties

Label 79.3.f.a
Level $79$
Weight $3$
Character orbit 79.f
Analytic conductor $2.153$
Analytic rank $0$
Dimension $156$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [79,3,Mod(12,79)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(79, base_ring=CyclotomicField(26))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("79.12");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 79 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 79.f (of order \(26\), degree \(12\), minimal)

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: no
Analytic conductor: \(2.15259408845\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(13\) over \(\Q(\zeta_{26})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{26}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 156 q - 9 q^{2} - 13 q^{3} - 41 q^{4} - 11 q^{5} - 13 q^{6} - 13 q^{7} - 57 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 156 q - 9 q^{2} - 13 q^{3} - 41 q^{4} - 11 q^{5} - 13 q^{6} - 13 q^{7} - 57 q^{8} + 24 q^{9} + 9 q^{10} + 63 q^{11} - 13 q^{12} + 17 q^{13} - 208 q^{14} - 143 q^{15} - 53 q^{16} - 13 q^{17} + 190 q^{18} + 19 q^{19} + 76 q^{20} + 171 q^{21} - 106 q^{22} - 86 q^{23} + 68 q^{25} + 60 q^{26} - 286 q^{27} - 13 q^{28} - 13 q^{29} - 13 q^{30} + 211 q^{31} - 7 q^{32} - 13 q^{33} + 182 q^{34} + 338 q^{35} + 129 q^{36} - 221 q^{37} - 297 q^{38} - 429 q^{39} - 424 q^{40} - 13 q^{41} + 61 q^{42} - 13 q^{43} + 419 q^{44} + 247 q^{45} - 557 q^{46} - 39 q^{47} + 39 q^{48} + 114 q^{49} - 276 q^{50} - 249 q^{51} + 633 q^{52} - 533 q^{53} + 923 q^{54} - 166 q^{55} + 299 q^{57} - 13 q^{58} + 507 q^{59} - 2106 q^{60} - 13 q^{61} + 150 q^{62} - 754 q^{63} + 1227 q^{64} + 131 q^{65} + 1885 q^{66} + 193 q^{67} + 507 q^{68} + 338 q^{69} + 143 q^{70} + 169 q^{71} + 562 q^{72} - 202 q^{73} + 1560 q^{74} + 143 q^{75} + 450 q^{76} + 65 q^{77} + 94 q^{79} + 748 q^{80} - 708 q^{81} - 221 q^{82} + 95 q^{83} - 1327 q^{84} - 377 q^{85} - 1612 q^{86} + 216 q^{87} - 381 q^{88} - 401 q^{89} - 609 q^{90} - 1274 q^{91} - 1406 q^{92} + 143 q^{93} - 1885 q^{94} + 187 q^{95} - 2561 q^{96} + 804 q^{97} - 1447 q^{98} - 152 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
12.1 −0.432972 − 3.56584i 0.830309 + 0.314895i −8.64401 + 2.13056i −2.03926 − 1.07029i 0.763365 − 3.09709i −9.60288 − 3.64189i 6.24483 + 16.4663i −6.14634 − 5.44518i −2.93353 + 7.73508i
12.2 −0.351449 − 2.89444i −5.07353 − 1.92414i −4.37050 + 1.07723i 2.11693 + 1.11105i −3.78621 + 15.3613i −2.93880 − 1.11454i 0.518301 + 1.36665i 15.3018 + 13.5563i 2.47188 − 6.51781i
12.3 −0.336641 − 2.77249i 2.66780 + 1.01176i −3.68961 + 0.909407i 7.04366 + 3.69680i 1.90701 − 7.73704i 2.17605 + 0.825267i −0.198043 − 0.522196i −0.643115 − 0.569750i 7.87815 − 20.7730i
12.4 −0.284855 − 2.34600i 4.88700 + 1.85340i −1.53879 + 0.379277i −7.15578 − 3.75564i 2.95597 − 11.9928i 7.54928 + 2.86307i −2.02393 − 5.33667i 13.7111 + 12.1470i −6.77235 + 17.8572i
12.5 −0.178469 − 1.46983i −1.96226 − 0.744188i 1.75523 − 0.432625i −5.73272 − 3.00877i −0.743624 + 3.01700i 1.00394 + 0.380745i −3.04928 − 8.04029i −3.43994 − 3.04752i −3.39925 + 8.96308i
12.6 −0.133197 − 1.09697i −0.829828 − 0.314712i 2.69815 − 0.665035i 3.61480 + 1.89719i −0.234701 + 0.952219i 2.12388 + 0.805480i −2.65631 − 7.00412i −6.14703 − 5.44579i 1.59969 − 4.21804i
12.7 0.0265629 + 0.218765i 3.72120 + 1.41126i 3.83661 − 0.945641i −0.00511101 − 0.00268246i −0.209889 + 0.851555i −9.94598 − 3.77201i 0.621364 + 1.63840i 5.11905 + 4.53509i 0.000451066 − 0.00118936i
12.8 0.157500 + 1.29713i −4.34848 − 1.64916i 2.22603 − 0.548666i 4.71085 + 2.47244i 1.45429 − 5.90028i 5.14892 + 1.95273i 2.91568 + 7.68802i 9.45292 + 8.37456i −2.46512 + 6.50000i
12.9 0.172423 + 1.42003i 1.15657 + 0.438627i 1.89702 − 0.467573i −1.11782 − 0.586679i −0.423445 + 1.71799i 7.42238 + 2.81494i 3.02004 + 7.96320i −5.59135 − 4.95350i 0.640362 − 1.68850i
12.10 0.208646 + 1.71835i −3.48565 − 1.32193i 0.974564 − 0.240208i −6.48754 − 3.40492i 1.54428 − 6.26540i −10.0979 − 3.82962i 3.07135 + 8.09848i 3.66567 + 3.24750i 4.49726 − 11.8583i
12.11 0.358092 + 2.94916i 0.387113 + 0.146813i −4.68552 + 1.15488i 8.44459 + 4.43206i −0.294351 + 1.19423i −7.91141 − 3.00040i −0.869897 − 2.29373i −6.60829 − 5.85444i −10.0469 + 26.4915i
12.12 0.394320 + 3.24751i 3.77314 + 1.43096i −6.50709 + 1.60385i −3.64358 − 1.91230i −3.15925 + 12.8176i 1.51537 + 0.574703i −3.13424 − 8.26432i 5.45231 + 4.83032i 4.77347 − 12.5866i
12.13 0.456467 + 3.75935i −3.47188 − 1.31671i −10.0406 + 2.47478i −1.31708 − 0.691258i 3.36517 − 13.6530i 5.67329 + 2.15160i −8.51524 − 22.4528i 3.58363 + 3.17482i 1.99747 − 5.26691i
14.1 −3.82135 + 0.941879i −1.96753 + 2.22088i 10.1738 − 5.33961i 4.81175 + 6.97103i 5.42682 − 10.3399i 1.91184 − 2.15802i −22.0646 + 19.5476i 0.0236874 + 0.195083i −24.9533 − 22.1067i
14.2 −3.65816 + 0.901655i 3.76982 − 4.25524i 9.02732 − 4.73790i −2.75419 − 3.99013i −9.95383 + 18.9654i −2.83439 + 3.19936i −17.4709 + 15.4779i −2.81075 − 23.1486i 13.6730 + 12.1132i
14.3 −2.62316 + 0.646551i −0.613893 + 0.692942i 2.92111 − 1.53312i −2.29564 − 3.32581i 1.16232 − 2.21461i 1.22177 − 1.37910i 1.41760 − 1.25588i 0.981526 + 8.08359i 8.17214 + 7.23988i
14.4 −2.26399 + 0.558022i 0.542248 − 0.612071i 1.27242 − 0.667816i 0.711756 + 1.03116i −0.886091 + 1.68831i −4.11669 + 4.64679i 4.47326 − 3.96296i 1.00423 + 8.27059i −2.18681 − 1.93735i
14.5 −1.61741 + 0.398655i −3.60716 + 4.07164i −1.08475 + 0.569319i −0.618850 − 0.896559i 4.21106 − 8.02351i 3.49462 − 3.94462i 6.51503 − 5.77181i −2.48184 − 20.4398i 1.35835 + 1.20339i
14.6 −1.38370 + 0.341052i 2.99859 − 3.38471i −1.74351 + 0.915062i 4.14990 + 6.01217i −2.99480 + 5.70611i 4.05680 − 4.57918i 6.36727 − 5.64090i −1.37988 − 11.3643i −7.79270 − 6.90373i
14.7 −0.0875140 + 0.0215703i 1.99655 − 2.25364i −3.53463 + 1.85512i −5.01070 − 7.25925i −0.126115 + 0.240291i 7.43361 − 8.39081i 0.539177 − 0.477669i −0.00785065 − 0.0646559i 0.595090 + 0.527204i
See next 80 embeddings (of 156 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 12.13
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
79.f odd 26 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 79.3.f.a ✓ 156
79.f odd 26 1 inner 79.3.f.a ✓ 156
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
79.3.f.a ✓ 156 1.a even 1 1 trivial
79.3.f.a ✓ 156 79.f odd 26 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(79, [\chi])\).