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Properties

Label 50101.2.a.b
Level $50101$
Weight $2$
Character orbit 50101.a
Self dual yes
Analytic conductor $400.058$
Dimension $2127$
CM no
Inner twists $1$

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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] = [50101,2,Mod(1,50101)] 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("50101.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50101, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 50101 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 50101.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2127] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(400.058499167\)
Dimension: \(2127\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 2127 q + 54 q^{2} + 162 q^{3} + 2202 q^{4} + 111 q^{5} + 96 q^{6} + 50 q^{7} + 159 q^{8} + 2281 q^{9} + 72 q^{10} + 290 q^{11} + 315 q^{12} + 72 q^{13} + 239 q^{14} + 158 q^{15} + 2344 q^{16} + 195 q^{17}+ \cdots + 805 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(50101\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 50101.2.a.b ✓ 2127
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
50101.2.a.b ✓ 2127 1.a even 1 1 trivial