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Properties

Label 6026.2.a.m
Level $6026$
Weight $2$
Character orbit 6026.a
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $41$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(0\)
Dimension: \(41\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 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 1.00000 −3.33099 1.00000 −3.73356 −3.33099 2.28084 1.00000 8.09549 −3.73356
1.2 1.00000 −3.25480 1.00000 3.43025 −3.25480 2.34297 1.00000 7.59373 3.43025
1.3 1.00000 −3.22313 1.00000 −0.601968 −3.22313 −4.66050 1.00000 7.38856 −0.601968
1.4 1.00000 −3.13493 1.00000 2.02213 −3.13493 −2.34132 1.00000 6.82778 2.02213
1.5 1.00000 −2.99315 1.00000 −2.87948 −2.99315 −2.15668 1.00000 5.95893 −2.87948
1.6 1.00000 −2.68141 1.00000 3.69693 −2.68141 1.66171 1.00000 4.18994 3.69693
1.7 1.00000 −2.35219 1.00000 0.827343 −2.35219 0.166684 1.00000 2.53280 0.827343
1.8 1.00000 −2.27206 1.00000 0.0411842 −2.27206 3.26699 1.00000 2.16224 0.0411842
1.9 1.00000 −2.27011 1.00000 −1.81074 −2.27011 2.75406 1.00000 2.15338 −1.81074
1.10 1.00000 −2.01222 1.00000 −2.36434 −2.01222 3.66472 1.00000 1.04902 −2.36434
1.11 1.00000 −1.56181 1.00000 1.51273 −1.56181 2.72551 1.00000 −0.560757 1.51273
1.12 1.00000 −1.30065 1.00000 2.66833 −1.30065 −4.20545 1.00000 −1.30832 2.66833
1.13 1.00000 −1.27958 1.00000 2.95127 −1.27958 4.74723 1.00000 −1.36266 2.95127
1.14 1.00000 −1.08669 1.00000 −0.588357 −1.08669 −3.89024 1.00000 −1.81911 −0.588357
1.15 1.00000 −0.990574 1.00000 4.23904 −0.990574 −4.18696 1.00000 −2.01876 4.23904
1.16 1.00000 −0.830898 1.00000 −1.41489 −0.830898 −0.234026 1.00000 −2.30961 −1.41489
1.17 1.00000 −0.425330 1.00000 2.71720 −0.425330 −0.709481 1.00000 −2.81909 2.71720
1.18 1.00000 −0.356133 1.00000 3.98743 −0.356133 1.62862 1.00000 −2.87317 3.98743
1.19 1.00000 −0.352298 1.00000 −1.51534 −0.352298 −1.04103 1.00000 −2.87589 −1.51534
1.20 1.00000 −0.148340 1.00000 −1.78404 −0.148340 −0.469198 1.00000 −2.97800 −1.78404
See all 41 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.41
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(23\) \(-1\)
\(131\) \(-1\)

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 6026.2.a.m ✓ 41
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6026.2.a.m ✓ 41 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\( T_{3}^{41} - 4 T_{3}^{40} - 85 T_{3}^{39} + 351 T_{3}^{38} + 3269 T_{3}^{37} - 14026 T_{3}^{36} + \cdots + 13312 \) Copy content Toggle raw display
\( T_{5}^{41} - 9 T_{5}^{40} - 100 T_{5}^{39} + 1104 T_{5}^{38} + 3981 T_{5}^{37} - 61305 T_{5}^{36} + \cdots + 1803859328 \) Copy content Toggle raw display