↑

Properties

Label 6029.2.a.b
Level $6029$
Weight $2$
Character orbit 6029.a
Self dual yes
Analytic conductor $48.142$
Analytic rank $0$
Dimension $268$
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] = [6029,2,Mod(1,6029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6029 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6029.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: \(48.1418073786\)
Analytic rank: \(0\)
Dimension: \(268\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 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 −2.82279 1.45736 5.96816 −4.32160 −4.11382 −2.12666 −11.2013 −0.876107 12.1990
1.2 −2.79474 −0.330575 5.81059 −0.623259 0.923873 −2.39329 −10.6496 −2.89072 1.74185
1.3 −2.76630 −1.88876 5.65241 −2.53163 5.22487 3.60505 −10.1037 0.567402 7.00325
1.4 −2.76187 −2.45998 5.62792 2.94480 6.79415 1.83308 −10.0198 3.05151 −8.13315
1.5 −2.74676 2.86871 5.54471 2.35059 −7.87968 4.12455 −9.73648 5.22952 −6.45653
1.6 −2.73508 2.32253 5.48068 −2.83868 −6.35232 −0.0775144 −9.51993 2.39417 7.76402
1.7 −2.71891 −2.75648 5.39247 −2.65361 7.49462 −3.09784 −9.22383 4.59818 7.21494
1.8 −2.69661 0.0652072 5.27173 −0.769773 −0.175839 2.92622 −8.82260 −2.99575 2.07578
1.9 −2.67015 2.28839 5.12969 1.33703 −6.11033 −2.43023 −8.35672 2.23672 −3.57008
1.10 −2.66582 −1.97296 5.10658 1.39801 5.25954 −2.57413 −8.28157 0.892553 −3.72685
1.11 −2.66314 1.33494 5.09234 −1.13177 −3.55514 4.13938 −8.23535 −1.21793 3.01407
1.12 −2.66122 1.83704 5.08208 −0.683386 −4.88877 2.95312 −8.20207 0.374729 1.81864
1.13 −2.65863 −3.04392 5.06833 −3.14510 8.09266 2.18672 −8.15755 6.26543 8.36165
1.14 −2.64287 3.18125 4.98477 0.556594 −8.40764 −4.05191 −7.88836 7.12036 −1.47101
1.15 −2.64062 −0.800557 4.97285 2.95022 2.11396 2.31379 −7.85015 −2.35911 −7.79040
1.16 −2.62126 −0.553016 4.87101 −3.94850 1.44960 2.94765 −7.52568 −2.69417 10.3501
1.17 −2.54540 −3.20721 4.47904 0.372386 8.16363 −2.83053 −6.31014 7.28621 −0.947871
1.18 −2.51173 −2.30209 4.30878 −2.37349 5.78222 −4.88111 −5.79902 2.29960 5.96156
1.19 −2.51050 0.264508 4.30262 3.31299 −0.664049 1.39465 −5.78073 −2.93004 −8.31726
1.20 −2.50934 −1.29295 4.29679 −2.86314 3.24445 3.23051 −5.76344 −1.32829 7.18460
See next 80 embeddings (of 268 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.268
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(6029\) \(-1\)

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 6029.2.a.b ✓ 268
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6029.2.a.b ✓ 268 1.a even 1 1 trivial