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Properties

Label 16245.2.a.b
Level $16245$
Weight $2$
Character orbit 16245.a
Self dual yes
Analytic conductor $129.717$
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] = [16245,2,Mod(1,16245)] 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("16245.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16245 = 3^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16245.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-2,0,2,1,0,-2,0,0,-2,3,0,6,4,0,-4,-6,0,0,2,0,-6,8,0,1,-12, 0,-4,-7,0,9,8,0,12,-2,0,-2,0,0,0,-6,0,10,6,0,-16,-4,0,-3,-2,0,12,-14,0, 3,0,0,14,-3,0,-7,-18,0,-8,6,0,4,-12,0,4,-7,0,2,4,0,0,-6,0,5,-4,0,12,6, 0,-6,-20,0,0,-3,0,-12,16,0,8,0,0,-12,6,0,2] 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: \(129.716978084\)
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)
 
\(f(q)\) \(=\) \( q - 2 q^{2} + 2 q^{4} + q^{5} - 2 q^{7} - 2 q^{10} + 3 q^{11} + 6 q^{13} + 4 q^{14} - 4 q^{16} - 6 q^{17} + 2 q^{20} - 6 q^{22} + 8 q^{23} + q^{25} - 12 q^{26} - 4 q^{28} - 7 q^{29} + 9 q^{31} + 8 q^{32}+ \cdots + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.