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Properties

Label 14415.2.a.d
Level $14415$
Weight $2$
Character orbit 14415.a
Self dual yes
Analytic conductor $115.104$
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] = [14415,2,Mod(1,14415)] 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("14415.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14415, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 14415 = 3 \cdot 5 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 14415.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,-1,1,-1,0,3,1,-1,4,-1,2,0,1,-1,-2,-1,4,-1,0,-4,0,3,1, -2,1,0,2,-1,0,-5,4,2,0,-1,10,-4,2,3,10,0,-4,-4,1,0,8,-1,-7,-1,-2,-2,10, -1,4,0,4,-2,-4,-1,2,0,0,7,2,-4,12,2,0,0,-8,3,-10,-10,1,-4,0,-2,0,-1,1, -10,-12,0,-2,4,2,12,6,-1,0,0,0,-8,4,-5,2,7,4,-1] 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: \(115.104354514\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + 3 q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} + 2 q^{13} + q^{15} - q^{16} - 2 q^{17} - q^{18} + 4 q^{19} - q^{20} - 4 q^{22} + 3 q^{24} + q^{25}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(31\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.