↑

Properties

Label 799.6.a.d
Level $799$
Weight $6$
Character orbit 799.a
Self dual yes
Analytic conductor $128.147$
Analytic rank $0$
Dimension $82$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [799,6,Mod(1,799)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(799, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("799.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 799.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: \(128.146672031\)
Analytic rank: \(0\)
Dimension: \(82\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 82 q + 21 q^{2} + 27 q^{3} + 1435 q^{4} + 359 q^{5} + 311 q^{6} + 89 q^{7} + 903 q^{8} + 8181 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 82 q + 21 q^{2} + 27 q^{3} + 1435 q^{4} + 359 q^{5} + 311 q^{6} + 89 q^{7} + 903 q^{8} + 8181 q^{9} + 248 q^{10} + 666 q^{11} + 1152 q^{12} + 601 q^{13} + 2205 q^{14} + 1853 q^{15} + 23755 q^{16} - 23698 q^{17} + 3186 q^{18} + 4207 q^{19} + 9519 q^{20} + 17598 q^{21} - 1925 q^{22} + 8122 q^{23} + 7458 q^{24} + 65025 q^{25} + 42335 q^{26} + 13962 q^{27} + 16977 q^{28} + 10274 q^{29} + 48573 q^{30} + 8038 q^{31} + 31967 q^{32} + 30849 q^{33} - 6069 q^{34} + 5693 q^{35} + 235552 q^{36} - 2636 q^{37} + 64917 q^{38} + 41567 q^{39} + 78133 q^{40} + 80755 q^{41} + 4737 q^{42} + 28101 q^{43} + 51004 q^{44} + 69573 q^{45} + 3222 q^{46} + 181138 q^{47} + 71960 q^{48} + 245289 q^{49} + 133123 q^{50} - 7803 q^{51} + 71076 q^{52} + 50559 q^{53} - 85357 q^{54} + 50261 q^{55} + 258178 q^{56} - 53626 q^{57} - 87493 q^{58} + 85927 q^{59} + 326995 q^{60} + 9069 q^{61} + 92163 q^{62} + 54307 q^{63} + 488401 q^{64} + 29792 q^{65} + 131386 q^{66} - 32606 q^{67} - 414715 q^{68} + 191415 q^{69} + 273557 q^{70} + 204435 q^{71} + 385804 q^{72} - 40350 q^{73} + 251603 q^{74} + 221234 q^{75} + 120893 q^{76} + 292038 q^{77} - 900 q^{78} + 167514 q^{79} + 437722 q^{80} + 1106314 q^{81} - 70789 q^{82} + 184803 q^{83} + 651276 q^{84} - 103751 q^{85} + 302038 q^{86} + 434679 q^{87} - 131993 q^{88} + 742685 q^{89} + 430858 q^{90} + 288535 q^{91} + 217338 q^{92} + 454287 q^{93} + 46389 q^{94} + 550108 q^{95} + 730442 q^{96} + 34757 q^{97} + 291456 q^{98} + 207115 q^{99}+O(q^{100}) \) 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 −11.1709 −25.5854 92.7881 −20.9540 285.811 −199.375 −679.055 411.615 234.074
1.2 −11.0626 13.0302 90.3805 −32.0535 −144.148 −16.3722 −645.839 −73.2135 354.595
1.3 −10.5393 26.9102 79.0776 100.760 −283.616 69.2138 −496.166 481.159 −1061.94
1.4 −10.4826 7.18846 77.8843 45.9808 −75.3535 −90.4675 −480.985 −191.326 −481.997
1.5 −10.3857 −2.89393 75.8622 51.1048 30.0554 −208.537 −455.538 −234.625 −530.758
1.6 −9.85819 −25.1474 65.1839 −34.2467 247.908 190.971 −327.133 389.391 337.611
1.7 −9.55610 −5.20173 59.3191 −5.79356 49.7082 193.560 −261.065 −215.942 55.3639
1.8 −9.52602 25.3330 58.7451 −83.3874 −241.323 120.419 −254.775 398.762 794.350
1.9 −9.47550 −15.1614 57.7852 −73.6850 143.662 −47.0408 −244.328 −13.1318 698.203
1.10 −9.31724 −23.7219 54.8110 49.2016 221.023 82.9759 −212.536 319.728 −458.423
1.11 −8.87280 8.35209 46.7266 10.4494 −74.1064 −115.244 −130.666 −173.243 −92.7154
1.12 −8.30932 −0.803001 37.0448 −101.175 6.67239 72.5998 −41.9189 −242.355 840.695
1.13 −8.12374 19.8099 33.9952 −74.5709 −160.930 −56.6142 −16.2087 149.430 605.795
1.14 −7.75151 31.1211 28.0859 −51.1517 −241.235 176.159 30.3404 725.520 396.503
1.15 −7.58025 30.3826 25.4603 25.1819 −230.308 −177.097 49.5729 680.105 −190.885
1.16 −7.54794 −14.9492 24.9715 95.0157 112.836 215.858 53.0509 −19.5220 −717.174
1.17 −7.39566 16.6855 22.6958 71.8668 −123.401 165.402 68.8105 35.4074 −531.503
1.18 −7.36374 −22.1045 22.2247 55.5955 162.772 1.21355 71.9828 245.610 −409.391
1.19 −7.29820 −6.13653 21.2637 79.7564 44.7856 −173.642 78.3556 −205.343 −582.078
1.20 −7.09919 −19.9872 18.3985 −22.0690 141.893 13.2026 96.5596 156.487 156.672
See all 82 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.82
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(17\) \(1\)
\(47\) \(-1\)

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 799.6.a.d ✓ 82
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
799.6.a.d ✓ 82 1.a even 1 1 trivial