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Properties

Label 799.4.a.b
Level $799$
Weight $4$
Character orbit 799.a
Self dual yes
Analytic conductor $47.143$
Analytic rank $1$
Dimension $43$
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] = [799,4,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, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("799.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(47.1425260946\)
Analytic rank: \(1\)
Dimension: \(43\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 43 q - 5 q^{2} - 12 q^{3} + 159 q^{4} - 92 q^{5} - 103 q^{6} - 32 q^{7} - 81 q^{8} + 261 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 43 q - 5 q^{2} - 12 q^{3} + 159 q^{4} - 92 q^{5} - 103 q^{6} - 32 q^{7} - 81 q^{8} + 261 q^{9} - 112 q^{10} - 188 q^{11} - 168 q^{12} - 56 q^{13} - 231 q^{14} - 112 q^{15} + 747 q^{16} + 731 q^{17} - 12 q^{18} - 264 q^{19} - 775 q^{20} - 348 q^{21} - 175 q^{22} - 442 q^{23} - 720 q^{24} + 685 q^{25} - 261 q^{26} - 312 q^{27} - 151 q^{28} - 1218 q^{29} + 549 q^{30} - 1022 q^{31} - 653 q^{32} - 1254 q^{33} - 85 q^{34} - 768 q^{35} + 1012 q^{36} - 988 q^{37} - 563 q^{38} - 1132 q^{39} - 1241 q^{40} - 2930 q^{41} - 471 q^{42} - 456 q^{43} - 2000 q^{44} - 3228 q^{45} - 1174 q^{46} - 2021 q^{47} - 1378 q^{48} + 263 q^{49} - 951 q^{50} - 204 q^{51} - 1312 q^{52} - 1320 q^{53} - 1651 q^{54} + 230 q^{55} - 3408 q^{56} - 1546 q^{57} - 2319 q^{58} - 1604 q^{59} - 3005 q^{60} - 1514 q^{61} - 3421 q^{62} - 1832 q^{63} + 1201 q^{64} - 2140 q^{65} - 1226 q^{66} + 458 q^{67} + 2703 q^{68} + 474 q^{69} - 1067 q^{70} - 1634 q^{71} - 2156 q^{72} - 5020 q^{73} - 3741 q^{74} + 1592 q^{75} - 2707 q^{76} - 3324 q^{77} - 3864 q^{78} - 438 q^{79} - 6242 q^{80} + 151 q^{81} - 5019 q^{82} - 644 q^{83} - 60 q^{84} - 1564 q^{85} - 4662 q^{86} + 1812 q^{87} - 1565 q^{88} - 9818 q^{89} - 3434 q^{90} - 2276 q^{91} - 7034 q^{92} - 2130 q^{93} + 235 q^{94} - 1474 q^{95} - 13798 q^{96} - 5616 q^{97} - 4690 q^{98} - 2678 q^{99}+O(q^{100}) \) 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 −5.55266 3.67955 22.8321 10.8067 −20.4313 8.45729 −82.3576 −13.4609 −60.0060
1.2 −5.28339 8.52364 19.9142 −21.4982 −45.0337 18.4391 −62.9474 45.6524 113.583
1.3 −5.24379 −2.32253 19.4974 7.34716 12.1788 −24.8611 −60.2899 −21.6059 −38.5270
1.4 −5.20461 −8.19269 19.0880 −10.8485 42.6398 17.0848 −57.7086 40.1202 56.4622
1.5 −4.82454 1.69717 15.2762 −12.6998 −8.18808 0.577283 −35.1042 −24.1196 61.2708
1.6 −4.33832 3.14615 10.8210 14.2550 −13.6490 −10.2941 −12.2386 −17.1017 −61.8427
1.7 −4.22638 −9.53221 9.86228 10.4988 40.2867 4.49390 −7.87068 63.8630 −44.3718
1.8 −3.80993 9.03338 6.51557 −5.73089 −34.4166 −26.0219 5.65558 54.6020 21.8343
1.9 −3.71037 −1.90084 5.76687 −14.8808 7.05281 −21.0393 8.28575 −23.3868 55.2132
1.10 −3.50465 −1.91251 4.28256 2.39813 6.70269 36.4351 13.0283 −23.3423 −8.40459
1.11 −3.50444 4.91524 4.28113 −5.36516 −17.2252 28.3736 13.0326 −2.84039 18.8019
1.12 −3.50263 −5.45068 4.26843 7.97776 19.0917 4.46967 13.0703 2.70990 −27.9432
1.13 −3.21084 6.06541 2.30948 9.32148 −19.4751 2.33951 18.2713 9.78924 −29.9298
1.14 −2.83690 −3.98648 0.0479935 −14.7793 11.3092 −28.7476 22.5590 −11.1080 41.9274
1.15 −1.77752 −5.77447 −4.84040 −1.07005 10.2643 25.2727 22.8241 6.34454 1.90203
1.16 −1.37070 4.02641 −6.12117 −11.9023 −5.51901 −0.790565 19.3559 −10.7880 16.3145
1.17 −1.23521 5.76867 −6.47427 −8.64730 −7.12550 −0.180238 17.8787 6.27759 10.6812
1.18 −1.15964 −0.857137 −6.65524 15.8123 0.993970 −16.9275 16.9948 −26.2653 −18.3366
1.19 −0.930007 −1.34781 −7.13509 6.07285 1.25347 −16.2870 14.0757 −25.1834 −5.64779
1.20 −0.468990 9.30914 −7.78005 12.7254 −4.36589 −27.5399 7.40068 59.6600 −5.96807
See all 43 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.43
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 799.4.a.b ✓ 43
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
799.4.a.b ✓ 43 1.a even 1 1 trivial