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Properties

Label 30345.2.a.t
Level $30345$
Weight $2$
Character orbit 30345.a
Self dual yes
Analytic conductor $242.306$
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] = [30345,2,Mod(1,30345)] 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("30345.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30345, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 30345.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,-1,-1,-1,-1,-3,1,-1,0,1,-6,-1,1,-1,0,1,-8,1,1,0,-8,3, 1,-6,-1,1,2,1,-4,5,0,0,1,-1,2,-8,6,3,6,1,4,0,-1,-8,8,1,1,1,0,6,10,-1,0, 3,8,2,4,-1,2,-4,-1,7,6,0,4,0,8,1,12,-3,2,2,-1,8,0,6,-8,1,1,6,-4,-1,0,4, -2,0,-6,-1,6,8,4,8,8,-5,18,1,0,-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: \(242.306044934\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - q^{7} - 3 q^{8} + q^{9} - q^{10} + q^{12} - 6 q^{13} - q^{14} + q^{15} - q^{16} + q^{18} - 8 q^{19} + q^{20} + q^{21} - 8 q^{23} + 3 q^{24} + q^{25}+ \cdots + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.