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Properties

Label 6029.2.a.a
Level $6029$
Weight $2$
Character orbit 6029.a
Self dual yes
Analytic conductor $48.142$
Analytic rank $1$
Dimension $234$
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] = [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: \(1\)
Dimension: \(234\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 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 −2.80022 1.58457 5.84121 4.15609 −4.43714 −3.16901 −10.7562 −0.489138 −11.6379
1.2 −2.76066 −0.121634 5.62124 3.66459 0.335789 3.49852 −9.99702 −2.98521 −10.1167
1.3 −2.74392 −0.541748 5.52907 0.314458 1.48651 −1.33061 −9.68348 −2.70651 −0.862845
1.4 −2.69522 −2.18729 5.26421 −2.45102 5.89522 −1.76465 −8.79776 1.78423 6.60605
1.5 −2.69066 −3.28902 5.23964 1.48988 8.84962 3.81047 −8.71676 7.81762 −4.00877
1.6 −2.66544 −2.15906 5.10457 0.849689 5.75486 1.23234 −8.27506 1.66156 −2.26480
1.7 −2.65389 2.88360 5.04315 −1.32989 −7.65277 −0.791725 −8.07619 5.31516 3.52939
1.8 −2.64551 −0.0881828 4.99870 −0.825561 0.233288 −0.584332 −7.93309 −2.99222 2.18403
1.9 −2.64305 3.09579 4.98571 −1.08129 −8.18234 −0.0368624 −7.89138 6.58394 2.85790
1.10 −2.59814 1.65321 4.75033 2.01329 −4.29528 1.44236 −7.14575 −0.266887 −5.23080
1.11 −2.58537 1.21501 4.68413 −1.54408 −3.14124 −3.29615 −6.93947 −1.52375 3.99201
1.12 −2.57920 −2.40579 4.65225 2.56752 6.20501 −4.72770 −6.84068 2.78784 −6.62214
1.13 −2.56265 1.36912 4.56717 2.03853 −3.50857 −0.777924 −6.57875 −1.12552 −5.22404
1.14 −2.53440 2.84813 4.42317 1.96183 −7.21830 −0.128324 −6.14128 5.11186 −4.97206
1.15 −2.51561 0.109654 4.32830 −3.06491 −0.275847 2.34212 −5.85711 −2.98798 7.71012
1.16 −2.49760 −0.682777 4.23800 −3.80739 1.70530 −3.54561 −5.58962 −2.53382 9.50934
1.17 −2.46346 −0.561509 4.06866 1.69947 1.38326 −4.80905 −5.09606 −2.68471 −4.18658
1.18 −2.45423 2.05779 4.02326 −1.79809 −5.05030 3.33599 −4.96555 1.23450 4.41293
1.19 −2.40890 −0.528400 3.80280 3.29514 1.27286 −3.46004 −4.34278 −2.72079 −7.93767
1.20 −2.38600 0.681249 3.69302 0.452211 −1.62546 3.54719 −4.03955 −2.53590 −1.07898
See next 80 embeddings (of 234 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.234
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.a ✓ 234
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6029.2.a.a ✓ 234 1.a even 1 1 trivial