Properties

Label 6026.2.a.k
Level $6026$
Weight $2$
Character orbit 6026.a
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $35$
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: \(35\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 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 −3.43871 1.00000 −4.28403 −3.43871 1.96690 1.00000 8.82470 −4.28403
1.2 1.00000 −3.36223 1.00000 2.69270 −3.36223 −4.35375 1.00000 8.30456 2.69270
1.3 1.00000 −3.00053 1.00000 0.314170 −3.00053 4.93238 1.00000 6.00320 0.314170
1.4 1.00000 −2.88440 1.00000 3.48712 −2.88440 4.69814 1.00000 5.31979 3.48712
1.5 1.00000 −2.84834 1.00000 3.81635 −2.84834 −2.03504 1.00000 5.11302 3.81635
1.6 1.00000 −2.77524 1.00000 −2.60760 −2.77524 −2.68280 1.00000 4.70196 −2.60760
1.7 1.00000 −2.41881 1.00000 −3.09594 −2.41881 0.393889 1.00000 2.85065 −3.09594
1.8 1.00000 −2.41686 1.00000 −1.19985 −2.41686 −1.78090 1.00000 2.84122 −1.19985
1.9 1.00000 −2.05490 1.00000 0.786161 −2.05490 −2.31145 1.00000 1.22260 0.786161
1.10 1.00000 −1.74363 1.00000 1.36417 −1.74363 0.246249 1.00000 0.0402388 1.36417
1.11 1.00000 −1.69112 1.00000 −3.34531 −1.69112 0.398747 1.00000 −0.140113 −3.34531
1.12 1.00000 −1.65659 1.00000 −0.00351955 −1.65659 −4.74512 1.00000 −0.255700 −0.00351955
1.13 1.00000 −1.52794 1.00000 1.80988 −1.52794 2.28195 1.00000 −0.665396 1.80988
1.14 1.00000 −0.824185 1.00000 2.25531 −0.824185 4.15544 1.00000 −2.32072 2.25531
1.15 1.00000 −0.783973 1.00000 4.00344 −0.783973 0.255131 1.00000 −2.38539 4.00344
1.16 1.00000 −0.711607 1.00000 −3.74432 −0.711607 2.05633 1.00000 −2.49362 −3.74432
1.17 1.00000 −0.339838 1.00000 −2.83329 −0.339838 −3.26036 1.00000 −2.88451 −2.83329
1.18 1.00000 0.0639197 1.00000 0.144901 0.0639197 −1.36969 1.00000 −2.99591 0.144901
1.19 1.00000 0.0851442 1.00000 −0.378458 0.0851442 4.38766 1.00000 −2.99275 −0.378458
1.20 1.00000 0.671472 1.00000 3.81346 0.671472 3.17342 1.00000 −2.54913 3.81346
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
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.k 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6026.2.a.k 35 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

\( T_{3}^{35} + 3 T_{3}^{34} - 75 T_{3}^{33} - 221 T_{3}^{32} + 2549 T_{3}^{31} + 7362 T_{3}^{30} - 51953 T_{3}^{29} - 146684 T_{3}^{28} + 708385 T_{3}^{27} + 1948411 T_{3}^{26} - 6827279 T_{3}^{25} - 18207157 T_{3}^{24} + \cdots + 336640 \) Copy content Toggle raw display
\( T_{5}^{35} - 10 T_{5}^{34} - 78 T_{5}^{33} + 1077 T_{5}^{32} + 1791 T_{5}^{31} - 50978 T_{5}^{30} + 24035 T_{5}^{29} + 1394260 T_{5}^{28} - 2305664 T_{5}^{27} - 24321424 T_{5}^{26} + 61493531 T_{5}^{25} + \cdots - 4543552 \) Copy content Toggle raw display