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Properties

Label 79.10.a.a
Level $79$
Weight $10$
Character orbit 79.a
Self dual yes
Analytic conductor $40.688$
Analytic rank $1$
Dimension $27$
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] = [79,10,Mod(1,79)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(79, 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("79.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 79 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 79.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: \(40.6878310569\)
Analytic rank: \(1\)
Dimension: \(27\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 27 q - 16 q^{2} - 244 q^{3} + 6400 q^{4} - 5001 q^{5} - 11367 q^{6} - 2896 q^{7} - 8106 q^{8} + 104127 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 27 q - 16 q^{2} - 244 q^{3} + 6400 q^{4} - 5001 q^{5} - 11367 q^{6} - 2896 q^{7} - 8106 q^{8} + 104127 q^{9} - 60619 q^{10} - 137717 q^{11} - 155753 q^{12} - 85227 q^{13} - 349907 q^{14} - 349738 q^{15} + 1107652 q^{16} - 1419684 q^{17} - 612275 q^{18} - 325549 q^{19} - 5517369 q^{20} - 4651850 q^{21} - 2683326 q^{22} - 3385087 q^{23} + 501861 q^{24} + 10287792 q^{25} + 204309 q^{26} - 381832 q^{27} + 11235223 q^{28} - 7007352 q^{29} + 16454673 q^{30} + 899601 q^{31} + 385942 q^{32} - 14787978 q^{33} - 12750774 q^{34} - 40284552 q^{35} - 15423169 q^{36} - 9633690 q^{37} - 58991314 q^{38} - 37933566 q^{39} - 129802495 q^{40} - 109957222 q^{41} - 199668905 q^{42} - 44470738 q^{43} - 244775176 q^{44} - 197135823 q^{45} - 242198426 q^{46} - 157881674 q^{47} - 405321105 q^{48} - 116492405 q^{49} - 209399221 q^{50} - 174318072 q^{51} - 478228043 q^{52} - 222109360 q^{53} - 626917263 q^{54} - 360654156 q^{55} - 440859399 q^{56} - 310553708 q^{57} - 612114084 q^{58} - 516506940 q^{59} - 613774281 q^{60} - 252956136 q^{61} - 549247862 q^{62} - 143896826 q^{63} - 585537972 q^{64} - 356156586 q^{65} - 954543424 q^{66} - 258852261 q^{67} - 1049183286 q^{68} - 585944256 q^{69} - 935590425 q^{70} - 895357566 q^{71} - 987833265 q^{72} - 522779769 q^{73} - 882749602 q^{74} - 406592740 q^{75} - 1102820878 q^{76} - 1010994256 q^{77} - 1214530665 q^{78} - 1051652187 q^{79} - 3059696181 q^{80} - 1778257497 q^{81} - 1011523954 q^{82} - 2608668234 q^{83} - 3034832575 q^{84} - 1433169572 q^{85} - 507141622 q^{86} - 616045280 q^{87} - 54289552 q^{88} - 3824260645 q^{89} - 116732852 q^{90} + 814830578 q^{91} - 1393972874 q^{92} + 1884761084 q^{93} + 1369457621 q^{94} + 1965262761 q^{95} + 1983408045 q^{96} - 1394254241 q^{97} + 5027403777 q^{98} + 5036237593 q^{99}+O(q^{100}) \) 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 −42.2272 −129.181 1271.14 −1831.62 5454.94 4597.18 −32056.1 −2995.32 77344.2
1.2 −41.5001 −152.154 1210.26 2037.34 6314.41 3487.04 −28977.8 3467.85 −84550.0
1.3 −38.5966 207.660 977.698 −2101.65 −8014.96 6555.79 −17974.4 23439.5 81116.7
1.4 −33.3140 77.9128 597.824 1698.09 −2595.59 6014.15 −2859.13 −13612.6 −56570.3
1.5 −31.5111 −145.331 480.947 1175.63 4579.52 −8386.28 978.521 1438.01 −37045.4
1.6 −31.1549 229.587 458.628 −38.5807 −7152.76 −3239.75 1662.79 33027.1 1201.98
1.7 −28.1159 4.73625 278.505 740.374 −133.164 3204.70 6564.92 −19660.6 −20816.3
1.8 −27.6506 −50.9570 252.554 −2553.84 1408.99 −4852.61 7173.83 −17086.4 70615.1
1.9 −22.8025 211.363 7.95502 −1452.90 −4819.61 −5987.47 11493.5 24991.3 33129.9
1.10 −12.0694 −180.802 −366.330 −1765.89 2182.17 −4301.61 10600.9 13006.4 21313.3
1.11 −9.23697 13.7396 −426.678 57.6401 −126.912 1289.19 8670.54 −19494.2 −532.419
1.12 −5.50899 15.9254 −481.651 2489.36 −87.7332 1459.04 5474.02 −19429.4 −13713.9
1.13 −1.13671 219.845 −510.708 1253.38 −249.901 −6782.01 1162.52 28648.9 −1424.73
1.14 −0.378984 109.321 −511.856 −1233.24 −41.4308 4426.62 388.025 −7731.93 467.378
1.15 0.0369136 −215.740 −511.999 1111.38 −7.96374 −8674.31 −37.7995 26860.7 41.0250
1.16 2.25085 −130.082 −506.934 −1020.69 −292.796 10716.4 −2293.47 −2761.64 −2297.42
1.17 5.41461 −239.763 −482.682 −1469.43 −1298.22 1624.04 −5385.82 37803.2 −7956.42
1.18 14.7662 158.044 −293.960 −245.900 2333.71 5848.63 −11900.9 5294.99 −3631.00
1.19 22.0017 −143.457 −27.9251 1890.33 −3156.31 −1093.74 −11879.3 897.041 41590.4
1.20 25.3469 74.0991 130.464 −333.801 1878.18 4831.69 −9670.74 −14192.3 −8460.82
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(79\) \(1\)

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 79.10.a.a ✓ 27
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
79.10.a.a ✓ 27 1.a even 1 1 trivial