Properties

Label 6026.2.a.j
Level $6026$
Weight $2$
Character orbit 6026.a
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $33$
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: \(33\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 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 −3.30495 1.00000 3.30220 3.30495 3.90022 −1.00000 7.92270 −3.30220
1.2 −1.00000 −2.92506 1.00000 0.618794 2.92506 −2.50272 −1.00000 5.55600 −0.618794
1.3 −1.00000 −2.90304 1.00000 −1.99628 2.90304 −0.299170 −1.00000 5.42764 1.99628
1.4 −1.00000 −2.82338 1.00000 −3.52183 2.82338 3.82891 −1.00000 4.97150 3.52183
1.5 −1.00000 −2.71066 1.00000 −2.38566 2.71066 −4.13924 −1.00000 4.34767 2.38566
1.6 −1.00000 −2.31184 1.00000 −1.83764 2.31184 0.291912 −1.00000 2.34459 1.83764
1.7 −1.00000 −1.90551 1.00000 3.90912 1.90551 1.35086 −1.00000 0.630974 −3.90912
1.8 −1.00000 −1.82570 1.00000 −3.75704 1.82570 0.299528 −1.00000 0.333191 3.75704
1.9 −1.00000 −1.80561 1.00000 −1.32735 1.80561 −4.32567 −1.00000 0.260232 1.32735
1.10 −1.00000 −1.47729 1.00000 2.55278 1.47729 −3.54262 −1.00000 −0.817604 −2.55278
1.11 −1.00000 −1.46112 1.00000 2.24970 1.46112 −0.440676 −1.00000 −0.865116 −2.24970
1.12 −1.00000 −0.987482 1.00000 −4.26130 0.987482 0.584751 −1.00000 −2.02488 4.26130
1.13 −1.00000 −0.968563 1.00000 −0.0731928 0.968563 −0.501115 −1.00000 −2.06189 0.0731928
1.14 −1.00000 −0.909549 1.00000 0.734986 0.909549 5.27401 −1.00000 −2.17272 −0.734986
1.15 −1.00000 −0.471999 1.00000 1.82038 0.471999 −1.64482 −1.00000 −2.77722 −1.82038
1.16 −1.00000 −0.0820624 1.00000 −3.26458 0.0820624 −0.430136 −1.00000 −2.99327 3.26458
1.17 −1.00000 0.189963 1.00000 2.89176 −0.189963 3.54124 −1.00000 −2.96391 −2.89176
1.18 −1.00000 0.214096 1.00000 2.53148 −0.214096 4.82861 −1.00000 −2.95416 −2.53148
1.19 −1.00000 0.539204 1.00000 −2.22740 −0.539204 4.94386 −1.00000 −2.70926 2.22740
1.20 −1.00000 0.581698 1.00000 −2.21086 −0.581698 1.23881 −1.00000 −2.66163 2.21086
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
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.j 33
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6026.2.a.j 33 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\( T_{3}^{33} - 3 T_{3}^{32} - 67 T_{3}^{31} + 199 T_{3}^{30} + 2019 T_{3}^{29} - 5910 T_{3}^{28} - 36253 T_{3}^{27} + 103878 T_{3}^{26} + 433361 T_{3}^{25} - 1203529 T_{3}^{24} - 3650865 T_{3}^{23} + 9688729 T_{3}^{22} + \cdots - 92016 \) Copy content Toggle raw display
\( T_{5}^{33} + 4 T_{5}^{32} - 99 T_{5}^{31} - 389 T_{5}^{30} + 4393 T_{5}^{29} + 16959 T_{5}^{28} - 115344 T_{5}^{27} - 438324 T_{5}^{26} + 1991845 T_{5}^{25} + 7484524 T_{5}^{24} - 23774155 T_{5}^{23} + \cdots + 5425110 \) Copy content Toggle raw display