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Properties

Label 4334.2.a.g
Level $4334$
Weight $2$
Character orbit 4334.a
Self dual yes
Analytic conductor $34.607$
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] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, 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("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 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 −3.24183 1.00000 −2.34759 −3.24183 0.935308 1.00000 7.50947 −2.34759
1.2 1.00000 −2.89563 1.00000 −0.0366624 −2.89563 −1.61517 1.00000 5.38466 −0.0366624
1.3 1.00000 −2.44791 1.00000 3.56167 −2.44791 3.03410 1.00000 2.99228 3.56167
1.4 1.00000 −2.11321 1.00000 4.02507 −2.11321 1.12513 1.00000 1.46567 4.02507
1.5 1.00000 −1.88207 1.00000 −1.63726 −1.88207 4.48475 1.00000 0.542179 −1.63726
1.6 1.00000 −1.47859 1.00000 −2.50873 −1.47859 −2.19131 1.00000 −0.813757 −2.50873
1.7 1.00000 −1.44389 1.00000 −0.880270 −1.44389 −5.04870 1.00000 −0.915168 −0.880270
1.8 1.00000 −1.17873 1.00000 1.80794 −1.17873 −0.890925 1.00000 −1.61059 1.80794
1.9 1.00000 −0.943634 1.00000 2.82946 −0.943634 5.06500 1.00000 −2.10955 2.82946
1.10 1.00000 −0.614404 1.00000 2.62767 −0.614404 −2.77855 1.00000 −2.62251 2.62767
1.11 1.00000 0.193084 1.00000 −2.38572 0.193084 0.690799 1.00000 −2.96272 −2.38572
1.12 1.00000 0.279564 1.00000 1.09296 0.279564 1.36005 1.00000 −2.92184 1.09296
1.13 1.00000 0.378852 1.00000 −3.54688 0.378852 2.78687 1.00000 −2.85647 −3.54688
1.14 1.00000 0.558474 1.00000 −0.515160 0.558474 −5.08632 1.00000 −2.68811 −0.515160
1.15 1.00000 0.683877 1.00000 2.76760 0.683877 4.51462 1.00000 −2.53231 2.76760
1.16 1.00000 1.67736 1.00000 2.35708 1.67736 2.46776 1.00000 −0.186467 2.35708
1.17 1.00000 2.04930 1.00000 3.63723 2.04930 −0.447524 1.00000 1.19962 3.63723
1.18 1.00000 2.16110 1.00000 3.79456 2.16110 0.294155 1.00000 1.67035 3.79456
1.19 1.00000 2.18604 1.00000 0.389300 2.18604 4.93283 1.00000 1.77878 0.389300
1.20 1.00000 2.26689 1.00000 −4.31390 2.26689 1.45520 1.00000 2.13877 −4.31390
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
\(2\) \(-1\)
\(11\) \(-1\)
\(197\) \(-1\)

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 4334.2.a.g ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4334.2.a.g ✓ 26 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{26} - 12 T_{3}^{25} + 14 T_{3}^{24} + 371 T_{3}^{23} - 1401 T_{3}^{22} - 3699 T_{3}^{21} + 26442 T_{3}^{20} + 1884 T_{3}^{19} - 238998 T_{3}^{18} + 241769 T_{3}^{17} + 1196551 T_{3}^{16} - 2124861 T_{3}^{15} + \cdots + 25136 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4334))\). Copy content Toggle raw display