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Properties

Label 6026.2.a.l
Level $6026$
Weight $2$
Character orbit 6026.a
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $36$
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: \(36\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 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 −3.41962 1.00000 −1.05998 3.41962 −0.874431 −1.00000 8.69383 1.05998
1.2 −1.00000 −3.00646 1.00000 2.50601 3.00646 −2.50762 −1.00000 6.03882 −2.50601
1.3 −1.00000 −2.95632 1.00000 1.44309 2.95632 4.32514 −1.00000 5.73985 −1.44309
1.4 −1.00000 −2.75069 1.00000 −4.14565 2.75069 −3.93457 −1.00000 4.56631 4.14565
1.5 −1.00000 −2.51058 1.00000 −0.511257 2.51058 2.88576 −1.00000 3.30300 0.511257
1.6 −1.00000 −2.27426 1.00000 0.325199 2.27426 −2.71769 −1.00000 2.17227 −0.325199
1.7 −1.00000 −2.19697 1.00000 0.174713 2.19697 3.49233 −1.00000 1.82670 −0.174713
1.8 −1.00000 −2.09135 1.00000 2.51915 2.09135 −0.00923183 −1.00000 1.37373 −2.51915
1.9 −1.00000 −2.07888 1.00000 2.71554 2.07888 −2.97474 −1.00000 1.32176 −2.71554
1.10 −1.00000 −1.66763 1.00000 1.81504 1.66763 3.25466 −1.00000 −0.218995 −1.81504
1.11 −1.00000 −1.53572 1.00000 −3.94419 1.53572 4.26764 −1.00000 −0.641564 3.94419
1.12 −1.00000 −1.53570 1.00000 −3.27140 1.53570 1.87914 −1.00000 −0.641618 3.27140
1.13 −1.00000 −0.919839 1.00000 −1.90352 0.919839 0.476690 −1.00000 −2.15390 1.90352
1.14 −1.00000 −0.633980 1.00000 3.82144 0.633980 0.499597 −1.00000 −2.59807 −3.82144
1.15 −1.00000 −0.478528 1.00000 −0.306849 0.478528 −3.45315 −1.00000 −2.77101 0.306849
1.16 −1.00000 −0.303391 1.00000 0.0493123 0.303391 −2.29306 −1.00000 −2.90795 −0.0493123
1.17 −1.00000 −0.179106 1.00000 0.789963 0.179106 −0.160696 −1.00000 −2.96792 −0.789963
1.18 −1.00000 0.325322 1.00000 −2.89999 −0.325322 0.0543655 −1.00000 −2.89417 2.89999
1.19 −1.00000 0.372945 1.00000 −2.66658 −0.372945 3.34934 −1.00000 −2.86091 2.66658
1.20 −1.00000 0.455108 1.00000 −2.88071 −0.455108 −3.99338 −1.00000 −2.79288 2.88071
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.36
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.l ✓ 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6026.2.a.l ✓ 36 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\( T_{3}^{36} - 4 T_{3}^{35} - 69 T_{3}^{34} + 283 T_{3}^{33} + 2127 T_{3}^{32} - 9012 T_{3}^{31} + \cdots - 364600 \) Copy content Toggle raw display
\( T_{5}^{36} - T_{5}^{35} - 114 T_{5}^{34} + 104 T_{5}^{33} + 5859 T_{5}^{32} - 4863 T_{5}^{31} + \cdots - 67756950 \) Copy content Toggle raw display