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Properties

Label 34398.2.a.c
Level $34398$
Weight $2$
Character orbit 34398.a
Self dual yes
Analytic conductor $274.669$
Dimension $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [34398,2,Mod(1,34398)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("34398.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(34398, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 34398 = 2 \cdot 3^{3} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 34398.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,-3,0,0,-1,0,3,-6,0,-1,0,0,1,-3,0,4,-3,0,6,-6,0,4,1, 0,0,-3,0,1,-1,0,3,0,0,2,-4,0,3,-6,0,-4,-6,0,6,12,0,0,-4,0,-1,6,0,18,0, 0,3,-3,0,-2,-1,0,1,3,0,5,-3,0,0,-15,0,1,-2,0,4,0,0,-1,-3,0,6,15,0,9,4, 0,6,-6,0,0,-6,0,-12,-12,0,7,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(274.669412873\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} - 6 q^{11} - q^{13} + q^{16} - 3 q^{17} + 4 q^{19} - 3 q^{20} + 6 q^{22} - 6 q^{23} + 4 q^{25} + q^{26} - 3 q^{29} + q^{31} - q^{32} + 3 q^{34} + 2 q^{37}+ \cdots + 7 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.