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Properties

Label 38025.2.a.bi
Level $38025$
Weight $2$
Character orbit 38025.a
Self dual yes
Analytic conductor $303.631$
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] = [38025,2,Mod(1,38025)] 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("38025.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 38025 = 3^{2} \cdot 5^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38025.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,-2,0,0,-4,0,0,0,0,0,0,0,0,4,0,0,-7,0,0,0,0,0,0,0,0,8,0, 0,-7,0,0,0,0,0,-10,0,0,0,0,0,8,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,0,-13,0, 0,-8,0,0,-16,0,0,0,0,0,-7,0,0,14,0,0,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,5,0,0,0] 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: \(303.631153686\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: not computed

$q$-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)
 
\(f(q)\) \(=\) \( q - 2 q^{4} - 4 q^{7} + 4 q^{16} - 7 q^{19} + 8 q^{28} - 7 q^{31} - 10 q^{37} + 8 q^{43} + 9 q^{49} - 13 q^{61} - 8 q^{64} - 16 q^{67} - 7 q^{73} + 14 q^{76} + 17 q^{79} + 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.