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Properties

Label 45570.2.a.cr
Level $45570$
Weight $2$
Character orbit 45570.a
Self dual yes
Analytic conductor $363.878$
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] = [45570,2,Mod(1,45570)] 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("45570.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45570, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45570 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45570.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,-1,1,0,1,1,-1,-4,1,2,0,-1,1,6,1,-4,-1,0,-4,0,1,1,2,1, 0,6,-1,1,1,-4,6,0,1,-2,-4,2,-1,-10,0,-4,-4,-1,0,0,1,0,1,6,2,-2,1,4,0,-4, 6,-12,-1,-14,1,0,1,-2,-4,4,6,0,0,8,1,-2,-2,1,-4,0,2,8,-1,1,-10,-12,0,-6, -4,6,-4,-2,-1,0,0,1,0,4,1,14,0,-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: \(363.878282011\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} + 2 q^{13} - q^{15} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} - q^{20} - 4 q^{22} + q^{24} + q^{25} + 2 q^{26}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(31\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.