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Properties

Label 6043.2.a.c
Level $6043$
Weight $2$
Character orbit 6043.a
Self dual yes
Analytic conductor $48.254$
Analytic rank $0$
Dimension $259$
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] = [6043,2,Mod(1,6043)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6043, 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("6043.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6043 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6043.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: \(48.2535979415\)
Analytic rank: \(0\)
Dimension: \(259\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 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 −2.74821 2.62862 5.55264 2.51369 −7.22400 −0.922798 −9.76337 3.90966 −6.90814
1.2 −2.71457 −1.54009 5.36892 −1.75287 4.18068 1.37518 −9.14518 −0.628138 4.75830
1.3 −2.69191 2.00966 5.24636 −1.44990 −5.40981 0.895791 −8.73889 1.03872 3.90300
1.4 −2.66716 0.658905 5.11375 −0.783297 −1.75741 −0.338104 −8.30489 −2.56584 2.08918
1.5 −2.66509 0.277531 5.10272 0.539093 −0.739647 3.78634 −8.26903 −2.92298 −1.43673
1.6 −2.66120 −0.520492 5.08201 3.83583 1.38513 −0.144514 −8.20186 −2.72909 −10.2079
1.7 −2.63895 −2.10254 4.96408 0.468058 5.54852 −0.663333 −7.82206 1.42069 −1.23518
1.8 −2.62452 −2.36333 4.88811 3.68491 6.20260 1.44250 −7.57990 2.58531 −9.67113
1.9 −2.58624 1.73815 4.68864 −2.85125 −4.49526 −1.90278 −6.95348 0.0211502 7.37403
1.10 −2.57414 1.55511 4.62619 −0.336132 −4.00307 −3.88876 −6.76018 −0.581626 0.865250
1.11 −2.53746 −1.57895 4.43871 2.23521 4.00652 −0.788927 −6.18813 −0.506916 −5.67175
1.12 −2.52420 −2.07136 4.37157 −1.62373 5.22852 0.688788 −5.98631 1.29054 4.09861
1.13 −2.51764 −0.610944 4.33849 0.176769 1.53813 −3.05611 −5.88747 −2.62675 −0.445041
1.14 −2.51568 2.81970 4.32863 2.54444 −7.09345 1.96405 −5.85808 4.95070 −6.40100
1.15 −2.51359 −1.58136 4.31814 −2.14765 3.97489 −4.03310 −5.82684 −0.499302 5.39832
1.16 −2.50362 3.44242 4.26813 0.601384 −8.61852 3.68483 −5.67855 8.85024 −1.50564
1.17 −2.45883 0.759848 4.04584 3.80282 −1.86834 2.58562 −5.03037 −2.42263 −9.35049
1.18 −2.44655 2.77282 3.98563 −0.534926 −6.78385 0.576903 −4.85795 4.68851 1.30873
1.19 −2.43851 1.58144 3.94631 0.896601 −3.85634 −4.81539 −4.74608 −0.499059 −2.18637
1.20 −2.43000 −2.97934 3.90490 2.39158 7.23980 −4.31478 −4.62892 5.87647 −5.81153
See next 80 embeddings (of 259 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.259
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(6043\) \(-1\)

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 6043.2.a.c ✓ 259
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6043.2.a.c ✓ 259 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{259} - 39 T_{2}^{258} + 366 T_{2}^{257} + 5410 T_{2}^{256} - 123334 T_{2}^{255} + \cdots - 32\!\cdots\!36 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6043))\). Copy content Toggle raw display