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Properties

Label 38025.2.a.bz
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 = [1,1,0,-1,0,0,-5,-3,0,0,3,0,0,-5,0,-1,5,0,4,0,0,3,4,0,0,0,0,5, 1,0,-1,5,0,5,0,0,4,4,0,0,-8,0,4,-3,0,4,7,0,18,0,0,0,3,0,0,15,0,1,-3,0, 1,-1,0,7,0,0,-3,-5,0,0,8,0,4,4,0,-4,-15,0,10,0,0,-8,-9,0,0,4,0,-9,-18, 0,0,-4,0,7,0,0,14,18,0,0] 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: $\mathrm{SU}(2)$

$q$-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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{4} - 5 q^{7} - 3 q^{8} + 3 q^{11} - 5 q^{14} - q^{16} + 5 q^{17} + 4 q^{19} + 3 q^{22} + 4 q^{23} + 5 q^{28} + q^{29} - q^{31} + 5 q^{32} + 5 q^{34} + 4 q^{37} + 4 q^{38} - 8 q^{41}+ \cdots + 18 q^{98}+O(q^{100}) \) 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.