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Properties

Label 35574.2.a.bj
Level $35574$
Weight $2$
Character orbit 35574.a
Self dual yes
Analytic conductor $284.060$
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] = [35574,2,Mod(1,35574)] 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("35574.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35574, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 35574 = 2 \cdot 3 \cdot 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35574.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,2,-1,0,-1,1,-2,0,1,6,0,2,1,2,-1,-4,2,0,0,8,-1,-1,-6, 1,0,2,-2,0,-1,0,-2,0,1,-10,4,6,-2,-6,0,4,0,2,-8,0,1,0,1,2,6,6,-1,0,0,-4, -2,-4,2,6,0,0,1,12,0,4,2,8,0,8,-1,10,10,-1,-4,0,-6,0,2,1,6,-4,0,4,-4,2, 0,6,-2,0,8,0,0,-8,-1,14,0,0,-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: \(284.059820151\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} - q^{8} + q^{9} - 2 q^{10} + q^{12} + 6 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + 2 q^{20} + 8 q^{23} - q^{24} - q^{25} - 6 q^{26}+ \cdots + 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.