Properties

Label 6026.2.a.g
Level $6026$
Weight $2$
Character orbit 6026.a
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
Dimension $21$
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: \(21\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −3.25554 1.00000 0.398003 −3.25554 0.686920 1.00000 7.59851 0.398003
1.2 1.00000 −2.96739 1.00000 −0.775054 −2.96739 0.413858 1.00000 5.80542 −0.775054
1.3 1.00000 −2.37676 1.00000 −2.07688 −2.37676 −0.108208 1.00000 2.64897 −2.07688
1.4 1.00000 −1.87480 1.00000 0.417125 −1.87480 −3.88487 1.00000 0.514862 0.417125
1.5 1.00000 −1.74967 1.00000 2.79997 −1.74967 0.229508 1.00000 0.0613311 2.79997
1.6 1.00000 −1.31043 1.00000 −3.45176 −1.31043 −4.90131 1.00000 −1.28277 −3.45176
1.7 1.00000 −1.30046 1.00000 −2.98653 −1.30046 2.26537 1.00000 −1.30880 −2.98653
1.8 1.00000 −1.08114 1.00000 0.379081 −1.08114 0.614832 1.00000 −1.83113 0.379081
1.9 1.00000 −0.293262 1.00000 2.91518 −0.293262 −1.20061 1.00000 −2.91400 2.91518
1.10 1.00000 −0.104929 1.00000 −0.922657 −0.104929 4.49446 1.00000 −2.98899 −0.922657
1.11 1.00000 0.104111 1.00000 1.37645 0.104111 −2.65513 1.00000 −2.98916 1.37645
1.12 1.00000 0.775060 1.00000 0.913280 0.775060 −1.54834 1.00000 −2.39928 0.913280
1.13 1.00000 0.780842 1.00000 −0.582778 0.780842 2.23605 1.00000 −2.39029 −0.582778
1.14 1.00000 0.825726 1.00000 −2.91252 0.825726 −1.72528 1.00000 −2.31818 −2.91252
1.15 1.00000 0.938474 1.00000 0.929839 0.938474 −1.00873 1.00000 −2.11927 0.929839
1.16 1.00000 1.13204 1.00000 −3.67213 1.13204 −0.943976 1.00000 −1.71848 −3.67213
1.17 1.00000 1.44805 1.00000 3.26245 1.44805 −3.72778 1.00000 −0.903151 3.26245
1.18 1.00000 1.90172 1.00000 −3.81206 1.90172 1.69979 1.00000 0.616557 −3.81206
1.19 1.00000 2.43324 1.00000 −0.544807 2.43324 −1.90449 1.00000 2.92064 −0.544807
1.20 1.00000 2.71715 1.00000 −1.49550 2.71715 −4.64653 1.00000 4.38289 −1.49550
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
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.g 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6026.2.a.g 21 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\( T_{3}^{21} - 35 T_{3}^{19} + 3 T_{3}^{18} + 494 T_{3}^{17} - 88 T_{3}^{16} - 3661 T_{3}^{15} + 1012 T_{3}^{14} + 15586 T_{3}^{13} - 5966 T_{3}^{12} - 39200 T_{3}^{11} + 19523 T_{3}^{10} + 57285 T_{3}^{9} - 35664 T_{3}^{8} + \cdots - 14 \) Copy content Toggle raw display
\( T_{5}^{21} + 13 T_{5}^{20} + 31 T_{5}^{19} - 277 T_{5}^{18} - 1485 T_{5}^{17} + 679 T_{5}^{16} + 17587 T_{5}^{15} + 21616 T_{5}^{14} - 79704 T_{5}^{13} - 183069 T_{5}^{12} + 107778 T_{5}^{11} + 518881 T_{5}^{10} + \cdots - 1834 \) Copy content Toggle raw display