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Properties

Label 4011.2.a.j
Level $4011$
Weight $2$
Character orbit 4011.a
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $26$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 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 −2.79513 −1.00000 5.81272 0.438876 2.79513 −1.00000 −10.6570 1.00000 −1.22671
1.2 −2.64395 −1.00000 4.99049 −3.91233 2.64395 −1.00000 −7.90671 1.00000 10.3440
1.3 −2.56383 −1.00000 4.57324 −0.592667 2.56383 −1.00000 −6.59735 1.00000 1.51950
1.4 −2.43265 −1.00000 3.91781 2.62505 2.43265 −1.00000 −4.66537 1.00000 −6.38585
1.5 −1.95690 −1.00000 1.82947 −3.69601 1.95690 −1.00000 0.333702 1.00000 7.23273
1.6 −1.82745 −1.00000 1.33956 3.12821 1.82745 −1.00000 1.20691 1.00000 −5.71664
1.7 −1.71993 −1.00000 0.958143 2.53174 1.71993 −1.00000 1.79192 1.00000 −4.35441
1.8 −1.59694 −1.00000 0.550208 0.890069 1.59694 −1.00000 2.31523 1.00000 −1.42138
1.9 −1.07123 −1.00000 −0.852471 −1.60541 1.07123 −1.00000 3.05565 1.00000 1.71976
1.10 −1.03703 −1.00000 −0.924574 −1.10504 1.03703 −1.00000 3.03286 1.00000 1.14595
1.11 −0.713989 −1.00000 −1.49022 −2.22886 0.713989 −1.00000 2.49198 1.00000 1.59138
1.12 −0.596587 −1.00000 −1.64408 4.06129 0.596587 −1.00000 2.17401 1.00000 −2.42291
1.13 −0.163923 −1.00000 −1.97313 0.716872 0.163923 −1.00000 0.651287 1.00000 −0.117512
1.14 0.272327 −1.00000 −1.92584 −2.12381 −0.272327 −1.00000 −1.06911 1.00000 −0.578372
1.15 0.506999 −1.00000 −1.74295 3.81191 −0.506999 −1.00000 −1.89767 1.00000 1.93264
1.16 0.934309 −1.00000 −1.12707 0.782566 −0.934309 −1.00000 −2.92165 1.00000 0.731158
1.17 0.972990 −1.00000 −1.05329 4.14138 −0.972990 −1.00000 −2.97082 1.00000 4.02952
1.18 1.06777 −1.00000 −0.859868 0.128461 −1.06777 −1.00000 −3.05368 1.00000 0.137167
1.19 1.34762 −1.00000 −0.183926 −3.65993 −1.34762 −1.00000 −2.94310 1.00000 −4.93219
1.20 1.71722 −1.00000 0.948829 0.183092 −1.71722 −1.00000 −1.80509 1.00000 0.314408
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(7\) \(1\)
\(191\) \(-1\)

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 4011.2.a.j ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4011.2.a.j ✓ 26 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{26} - 43 T_{2}^{24} + 808 T_{2}^{22} - 2 T_{2}^{21} - 8731 T_{2}^{20} + 67 T_{2}^{19} + \cdots - 1856 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\). Copy content Toggle raw display