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Properties

Label 49818.2.a.o
Level $49818$
Weight $2$
Character orbit 49818.a
Self dual yes
Analytic conductor $397.799$
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] = [49818,2,Mod(1,49818)] 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("49818.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49818, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 49818 = 2 \cdot 3 \cdot 19^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 49818.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,1,-1,4,-1,1,-1,-3,1,6,-4,1,1,4,-1,0,1,4,3,-1,-1,-4, -6,1,4,-2,-1,-3,-1,-3,-4,4,1,-7,0,6,-1,5,-4,4,-3,1,1,3,1,9,4,4,6,1,-1, -3,-4,0,2,8,1,10,3,4,1,6,3,12,4,-1,-4,5,-1,-14,7,-4,0,-12,-6,14,1,1,-5, -3,4,4,-4,-2,3,0,-1,24,-1,-3,-3,0,-1,10,-9,-3,-4] 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: \(397.798732790\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} - q^{10} - 3 q^{11} + q^{12} + 6 q^{13} - 4 q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} + q^{20} + 4 q^{21} + 3 q^{22}+ \cdots - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(19\) \( +1 \)
\(23\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.