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Properties

Label 19074.2.a.j
Level $19074$
Weight $2$
Character orbit 19074.a
Self dual yes
Analytic conductor $152.307$
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] = [19074,2,Mod(1,19074)] 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("19074.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19074, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 19074 = 2 \cdot 3 \cdot 11 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19074.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,-2,-1,4,-1,1,2,-1,1,0,-4,-2,1,0,-1,6,-2,4,1,0,-1,-1, 0,1,4,-6,2,-2,-1,-1,0,-8,1,-10,-6,0,2,-12,-4,2,-1,-2,0,8,1,9,1,0,0,-12, -1,2,-4,6,6,6,-2,-2,2,4,1,0,1,8,0,0,8,-8,-1,14,10,-1,6,-4,0,0,-2,1,12, -8,4,0,-2,-6,1,-2,2,0,0,-2,-8,-12,-1,12,-9,-1,-1] 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: \(152.306656815\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} + 2 q^{10} - q^{11} + q^{12} - 4 q^{14} - 2 q^{15} + q^{16} - q^{18} + 6 q^{19} - 2 q^{20} + 4 q^{21} + q^{22} - q^{24}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(11\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.