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Properties

Label 4011.2.a.m
Level $4011$
Weight $2$
Character orbit 4011.a
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $29$
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: \(29\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 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 −2.76452 1.00000 5.64259 4.23744 −2.76452 −1.00000 −10.0700 1.00000 −11.7145
1.2 −2.55639 1.00000 4.53513 0.170446 −2.55639 −1.00000 −6.48077 1.00000 −0.435725
1.3 −2.32184 1.00000 3.39092 1.73819 −2.32184 −1.00000 −3.22949 1.00000 −4.03578
1.4 −2.24191 1.00000 3.02615 −1.20404 −2.24191 −1.00000 −2.30052 1.00000 2.69935
1.5 −2.08804 1.00000 2.35993 −2.57813 −2.08804 −1.00000 −0.751541 1.00000 5.38324
1.6 −2.00218 1.00000 2.00873 −0.971545 −2.00218 −1.00000 −0.0174879 1.00000 1.94521
1.7 −1.96996 1.00000 1.88076 4.31773 −1.96996 −1.00000 0.234907 1.00000 −8.50578
1.8 −1.47855 1.00000 0.186109 3.98947 −1.47855 −1.00000 2.68193 1.00000 −5.89863
1.9 −1.16967 1.00000 −0.631883 0.467682 −1.16967 −1.00000 3.07842 1.00000 −0.547032
1.10 −0.657179 1.00000 −1.56812 0.753891 −0.657179 −1.00000 2.34489 1.00000 −0.495441
1.11 −0.630217 1.00000 −1.60283 −2.79883 −0.630217 −1.00000 2.27056 1.00000 1.76387
1.12 −0.359948 1.00000 −1.87044 −1.76526 −0.359948 −1.00000 1.39316 1.00000 0.635404
1.13 −0.223362 1.00000 −1.95011 1.64565 −0.223362 −1.00000 0.882304 1.00000 −0.367576
1.14 −0.220924 1.00000 −1.95119 3.22358 −0.220924 −1.00000 0.872912 1.00000 −0.712166
1.15 0.336232 1.00000 −1.88695 4.17128 0.336232 −1.00000 −1.30692 1.00000 1.40252
1.16 0.797866 1.00000 −1.36341 0.229986 0.797866 −1.00000 −2.68355 1.00000 0.183498
1.17 0.830058 1.00000 −1.31100 −1.52882 0.830058 −1.00000 −2.74832 1.00000 −1.26901
1.18 1.15914 1.00000 −0.656403 −3.68396 1.15914 −1.00000 −3.07913 1.00000 −4.27022
1.19 1.18058 1.00000 −0.606227 0.961582 1.18058 −1.00000 −3.07686 1.00000 1.13523
1.20 1.22787 1.00000 −0.492335 2.78453 1.22787 −1.00000 −3.06026 1.00000 3.41904
See all 29 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.29
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.m ✓ 29
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4011.2.a.m ✓ 29 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{29} - 6 T_{2}^{28} - 31 T_{2}^{27} + 245 T_{2}^{26} + 318 T_{2}^{25} - 4363 T_{2}^{24} + \cdots - 2816 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\). Copy content Toggle raw display