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Properties

Label 10450.2.a.bf
Level $10450$
Weight $2$
Character orbit 10450.a
Self dual yes
Analytic conductor $83.444$
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] = [10450,2,Mod(1,10450)] 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("10450.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10450, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10450 = 2 \cdot 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10450.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,2,1,0,2,-2,1,1,0,-1,2,-2,-2,0,1,0,1,1,0,-4,-1,0,2,0,-2,-4, -2,-6,0,-4,1,-2,0,0,1,-8,1,-4,0,6,-4,-2,-1,0,0,12,2,-3,0,0,-2,12,-4,0, -2,2,-6,12,0,-10,-4,-2,1,0,-2,-14,0,0,0,0,1,-8,-8,0,1,2,-4,-16,0,-11,6, -6,-4,0,-2,-12,-1,6,0,4,0,-8,12,0,2,-8,-3,-1,0] 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: \(83.4436701122\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{14} + q^{16} + q^{18} + q^{19} - 4 q^{21} - q^{22} + 2 q^{24} - 2 q^{26} - 4 q^{27} - 2 q^{28}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(11\) \( +1 \)
\(19\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.