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Properties

Label 48050.2.a.k
Level $48050$
Weight $2$
Character orbit 48050.a
Self dual yes
Analytic conductor $383.681$
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] = [48050,2,Mod(1,48050)] 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("48050.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48050, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 48050 = 2 \cdot 5^{2} \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 48050.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,2,1,0,-2,-1,-1,1,0,-6,2,4,1,0,1,6,-1,2,0,-2,6,-3,-2,0,-4, -4,-1,6,0,0,-1,-12,-6,0,1,4,-2,8,0,6,2,4,-6,0,3,-9,2,-6,0,12,4,0,4,0,1, 4,-6,-12,0,10,0,-1,1,0,12,-10,6,-6,0,-3,-1,-11,-4,0,2,6,-8,1,0,-11,-6, 12,-2,0,-4,12,6,-6,0,-4,-3,0,9,0,-2,-7,6,-6,0] 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: \(383.681181712\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - q^{7} - q^{8} + q^{9} - 6 q^{11} + 2 q^{12} + 4 q^{13} + q^{14} + q^{16} + 6 q^{17} - q^{18} + 2 q^{19} - 2 q^{21} + 6 q^{22} - 3 q^{23} - 2 q^{24} - 4 q^{26}+ \cdots - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.