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Properties

Label 5077.2.a.c
Level $5077$
Weight $2$
Character orbit 5077.a
Self dual yes
Analytic conductor $40.540$
Analytic rank $0$
Dimension $216$
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] = [5077,2,Mod(1,5077)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5077, 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("5077.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5077 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5077.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: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 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 −2.74765 1.79689 5.54960 −1.53731 −4.93723 −2.66154 −9.75307 0.228810 4.22399
1.2 −2.71481 1.77107 5.37017 1.86347 −4.80810 4.83883 −9.14936 0.136673 −5.05896
1.3 −2.71273 −1.56061 5.35892 1.41855 4.23352 −1.24026 −9.11187 −0.564498 −3.84815
1.4 −2.68288 3.14006 5.19783 4.08506 −8.42439 −2.34598 −8.57939 6.85996 −10.9597
1.5 −2.66174 −1.61696 5.08487 2.63611 4.30394 0.680658 −8.21113 −0.385425 −7.01664
1.6 −2.65978 0.381674 5.07442 4.30968 −1.01517 0.973203 −8.17726 −2.85433 −11.4628
1.7 −2.65348 −0.258723 5.04097 −1.45018 0.686516 −0.380682 −8.06916 −2.93306 3.84804
1.8 −2.60586 −2.49081 4.79053 −1.82309 6.49071 1.00898 −7.27175 3.20413 4.75073
1.9 −2.60140 3.18807 4.76730 −0.824320 −8.29345 −1.42597 −7.19885 7.16377 2.14439
1.10 −2.52071 −0.980647 4.35400 −1.18681 2.47193 −1.94632 −5.93376 −2.03833 2.99161
1.11 −2.50572 0.313570 4.27863 0.450260 −0.785719 −2.26718 −5.70960 −2.90167 −1.12823
1.12 −2.49199 1.36067 4.21003 −1.81458 −3.39077 0.512290 −5.50738 −1.14858 4.52191
1.13 −2.48492 −1.01672 4.17484 0.988176 2.52648 3.63719 −5.40431 −1.96628 −2.45554
1.14 −2.46114 2.54758 4.05723 0.498025 −6.26997 −4.84312 −5.06313 3.49018 −1.22571
1.15 −2.46105 −2.68177 4.05676 2.96431 6.59997 0.509421 −5.06178 4.19189 −7.29531
1.16 −2.45990 1.58815 4.05112 −3.55113 −3.90668 −1.72696 −5.04554 −0.477790 8.73542
1.17 −2.43559 3.36410 3.93211 0.698081 −8.19357 2.30447 −4.70583 8.31717 −1.70024
1.18 −2.43502 2.39261 3.92934 2.97521 −5.82606 3.62580 −4.69798 2.72458 −7.24469
1.19 −2.42574 −1.56213 3.88424 2.05918 3.78933 −2.28895 −4.57068 −0.559747 −4.99504
1.20 −2.38830 −1.75089 3.70399 −3.96718 4.18166 −4.47052 −4.06966 0.0656264 9.47483
See next 80 embeddings (of 216 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.216
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5077\) \(-1\)

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 5077.2.a.c ✓ 216
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5077.2.a.c ✓ 216 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{216} - 25 T_{2}^{215} - 15 T_{2}^{214} + 5525 T_{2}^{213} - 31805 T_{2}^{212} + \cdots - 491029512192 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5077))\). Copy content Toggle raw display