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Properties

Label 37440.2.a.i
Level $37440$
Weight $2$
Character orbit 37440.a
Self dual yes
Analytic conductor $298.960$
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] = [37440,2,Mod(1,37440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(37440, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("37440.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 37440 = 2^{6} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 37440.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,-1,0,-4,0,0,0,4,0,-1,0,0,0,6,0,0,0,0,0,8,0,1,0,0,0,6, 0,-4,0,0,0,4,0,2,0,0,0,10,0,4,0,0,0,8,0,9,0,0,0,-2,0,-4,0,0,0,12,0,2,0, 0,0,1,0,16,0,0,0,8,0,-6,0,0,0,-16,0,-16,0,0,0,4,0,-6,0,0,0,2,0,4,0,0,0, 0,0,2,0,0,0] 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: \(298.959905168\)
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)
 
\(f(q)\) \(=\) \( q - q^{5} - 4 q^{7} + 4 q^{11} - q^{13} + 6 q^{17} + 8 q^{23} + q^{25} + 6 q^{29} - 4 q^{31} + 4 q^{35} + 2 q^{37} + 10 q^{41} + 4 q^{43} + 8 q^{47} + 9 q^{49} - 2 q^{53} - 4 q^{55} + 12 q^{59} + 2 q^{61}+ \cdots + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.