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Properties

Label 4334.2.a.f
Level $4334$
Weight $2$
Character orbit 4334.a
Self dual yes
Analytic conductor $34.607$
Analytic rank $0$
Dimension $24$
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: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 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 −3.03203 1.00000 0.166109 −3.03203 −3.81414 1.00000 6.19318 0.166109
1.2 1.00000 −2.68443 1.00000 2.21213 −2.68443 4.45954 1.00000 4.20617 2.21213
1.3 1.00000 −2.41920 1.00000 1.09702 −2.41920 −0.318081 1.00000 2.85254 1.09702
1.4 1.00000 −2.38598 1.00000 −3.46177 −2.38598 0.0815889 1.00000 2.69289 −3.46177
1.5 1.00000 −2.11945 1.00000 2.85950 −2.11945 0.696891 1.00000 1.49205 2.85950
1.6 1.00000 −1.69982 1.00000 −2.89069 −1.69982 4.96470 1.00000 −0.110611 −2.89069
1.7 1.00000 −1.57237 1.00000 −0.555853 −1.57237 −2.43578 1.00000 −0.527653 −0.555853
1.8 1.00000 −0.533021 1.00000 −1.76896 −0.533021 −1.67093 1.00000 −2.71589 −1.76896
1.9 1.00000 −0.469459 1.00000 1.92533 −0.469459 −0.231234 1.00000 −2.77961 1.92533
1.10 1.00000 −0.352502 1.00000 −2.30147 −0.352502 2.78311 1.00000 −2.87574 −2.30147
1.11 1.00000 −0.0840258 1.00000 −4.26587 −0.0840258 −4.02549 1.00000 −2.99294 −4.26587
1.12 1.00000 0.272392 1.00000 2.45255 0.272392 2.51117 1.00000 −2.92580 2.45255
1.13 1.00000 0.709515 1.00000 1.53976 0.709515 3.26507 1.00000 −2.49659 1.53976
1.14 1.00000 0.844390 1.00000 4.22697 0.844390 −3.69998 1.00000 −2.28700 4.22697
1.15 1.00000 1.07362 1.00000 −2.05678 1.07362 −3.40944 1.00000 −1.84733 −2.05678
1.16 1.00000 1.56353 1.00000 −2.07613 1.56353 4.64853 1.00000 −0.555380 −2.07613
1.17 1.00000 1.76169 1.00000 −3.63225 1.76169 −3.98143 1.00000 0.103544 −3.63225
1.18 1.00000 1.85453 1.00000 3.38544 1.85453 1.90407 1.00000 0.439283 3.38544
1.19 1.00000 2.48464 1.00000 3.25684 2.48464 4.41893 1.00000 3.17343 3.25684
1.20 1.00000 2.64860 1.00000 0.167624 2.64860 −0.427188 1.00000 4.01506 0.167624
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
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.f ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4334.2.a.f ✓ 24 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} - 8 T_{3}^{23} - 18 T_{3}^{22} + 291 T_{3}^{21} - 165 T_{3}^{20} - 4323 T_{3}^{19} + 7188 T_{3}^{18} + 33320 T_{3}^{17} - 82504 T_{3}^{16} - 136319 T_{3}^{15} + 486835 T_{3}^{14} + 235205 T_{3}^{13} - 1631078 T_{3}^{12} + \cdots - 980 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4334))\). Copy content Toggle raw display