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Properties

Label 6026.2.a.i
Level $6026$
Weight $2$
Character orbit 6026.a
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
Dimension $25$
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: \(1\)
Dimension: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 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 −2.98476 1.00000 1.57995 2.98476 2.90984 −1.00000 5.90879 −1.57995
1.2 −1.00000 −2.94469 1.00000 −3.10338 2.94469 2.18728 −1.00000 5.67118 3.10338
1.3 −1.00000 −2.94225 1.00000 2.28313 2.94225 −4.71427 −1.00000 5.65684 −2.28313
1.4 −1.00000 −2.39972 1.00000 1.46275 2.39972 0.813594 −1.00000 2.75865 −1.46275
1.5 −1.00000 −2.37203 1.00000 3.53118 2.37203 −2.86520 −1.00000 2.62654 −3.53118
1.6 −1.00000 −2.34651 1.00000 −0.801214 2.34651 2.16934 −1.00000 2.50610 0.801214
1.7 −1.00000 −1.97733 1.00000 −3.11644 1.97733 −3.94255 −1.00000 0.909824 3.11644
1.8 −1.00000 −1.70631 1.00000 −2.14849 1.70631 0.462300 −1.00000 −0.0885110 2.14849
1.9 −1.00000 −1.05724 1.00000 −2.13811 1.05724 3.42578 −1.00000 −1.88224 2.13811
1.10 −1.00000 −0.936776 1.00000 1.38125 0.936776 2.49293 −1.00000 −2.12245 −1.38125
1.11 −1.00000 −0.932148 1.00000 −0.513090 0.932148 0.0983188 −1.00000 −2.13110 0.513090
1.12 −1.00000 −0.665355 1.00000 0.670202 0.665355 −3.39786 −1.00000 −2.55730 −0.670202
1.13 −1.00000 −0.0412722 1.00000 −3.47552 0.0412722 −4.67489 −1.00000 −2.99830 3.47552
1.14 −1.00000 0.180068 1.00000 −3.11636 −0.180068 2.83625 −1.00000 −2.96758 3.11636
1.15 −1.00000 0.489389 1.00000 2.70694 −0.489389 1.75684 −1.00000 −2.76050 −2.70694
1.16 −1.00000 0.694821 1.00000 0.658132 −0.694821 −2.75018 −1.00000 −2.51722 −0.658132
1.17 −1.00000 0.888297 1.00000 2.86945 −0.888297 −2.14877 −1.00000 −2.21093 −2.86945
1.18 −1.00000 1.11977 1.00000 0.636447 −1.11977 1.86618 −1.00000 −1.74612 −0.636447
1.19 −1.00000 1.50502 1.00000 −2.72563 −1.50502 −2.36491 −1.00000 −0.734912 2.72563
1.20 −1.00000 1.76687 1.00000 −0.379310 −1.76687 −0.00141487 −1.00000 0.121841 0.379310
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
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.i ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6026.2.a.i ✓ 25 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\( T_{3}^{25} + 4 T_{3}^{24} - 39 T_{3}^{23} - 165 T_{3}^{22} + 640 T_{3}^{21} + 2914 T_{3}^{20} + \cdots + 480 \) Copy content Toggle raw display
\( T_{5}^{25} + 3 T_{5}^{24} - 60 T_{5}^{23} - 174 T_{5}^{22} + 1566 T_{5}^{21} + 4330 T_{5}^{20} + \cdots + 211472 \) Copy content Toggle raw display