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Properties

Label 4334.2.a.h
Level $4334$
Weight $2$
Character orbit 4334.a
Self dual yes
Analytic conductor $34.607$
Analytic rank $0$
Dimension $27$
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: \(27\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) \) 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 −3.32608 1.00000 3.07836 3.32608 −4.99294 −1.00000 8.06282 −3.07836
1.2 −1.00000 −3.27909 1.00000 −0.172349 3.27909 4.49591 −1.00000 7.75244 0.172349
1.3 −1.00000 −3.12559 1.00000 4.00012 3.12559 −0.0131838 −1.00000 6.76933 −4.00012
1.4 −1.00000 −2.76463 1.00000 −0.249776 2.76463 −2.52527 −1.00000 4.64317 0.249776
1.5 −1.00000 −2.46207 1.00000 −2.57755 2.46207 −3.72083 −1.00000 3.06177 2.57755
1.6 −1.00000 −2.45740 1.00000 −4.36120 2.45740 2.66113 −1.00000 3.03881 4.36120
1.7 −1.00000 −2.09175 1.00000 −0.380034 2.09175 −1.49841 −1.00000 1.37543 0.380034
1.8 −1.00000 −1.37214 1.00000 0.332573 1.37214 4.01205 −1.00000 −1.11723 −0.332573
1.9 −1.00000 −1.36128 1.00000 1.41439 1.36128 1.06104 −1.00000 −1.14691 −1.41439
1.10 −1.00000 −1.15238 1.00000 −0.0196651 1.15238 3.79263 −1.00000 −1.67203 0.0196651
1.11 −1.00000 −0.982227 1.00000 −0.607693 0.982227 −0.935926 −1.00000 −2.03523 0.607693
1.12 −1.00000 −0.593027 1.00000 0.744487 0.593027 −4.68885 −1.00000 −2.64832 −0.744487
1.13 −1.00000 −0.127044 1.00000 −4.01526 0.127044 0.758073 −1.00000 −2.98386 4.01526
1.14 −1.00000 −0.0408121 1.00000 3.97341 0.0408121 4.79303 −1.00000 −2.99833 −3.97341
1.15 −1.00000 0.181771 1.00000 4.29102 −0.181771 −3.68727 −1.00000 −2.96696 −4.29102
1.16 −1.00000 0.309146 1.00000 2.79911 −0.309146 0.293952 −1.00000 −2.90443 −2.79911
1.17 −1.00000 1.05524 1.00000 −3.32834 −1.05524 −3.79792 −1.00000 −1.88648 3.32834
1.18 −1.00000 1.14059 1.00000 −0.375030 −1.14059 0.176944 −1.00000 −1.69906 0.375030
1.19 −1.00000 1.56203 1.00000 −0.643018 −1.56203 3.99306 −1.00000 −0.560072 0.643018
1.20 −1.00000 1.80604 1.00000 −3.59945 −1.80604 3.05375 −1.00000 0.261765 3.59945
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
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.h ✓ 27
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4334.2.a.h ✓ 27 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{27} - 62 T_{3}^{25} + T_{3}^{24} + 1679 T_{3}^{23} - 49 T_{3}^{22} - 26122 T_{3}^{21} + 988 T_{3}^{20} + 258456 T_{3}^{19} - 10441 T_{3}^{18} - 1701115 T_{3}^{17} + 59569 T_{3}^{16} + 7573932 T_{3}^{15} - 150131 T_{3}^{14} + \cdots - 1472 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4334))\). Copy content Toggle raw display