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Properties

Label 45570.2.a.hx
Level $45570$
Weight $2$
Character orbit 45570.a
Self dual yes
Analytic conductor $363.878$
Dimension $18$

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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] = [45570,2,Mod(1,45570)] 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("45570.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45570, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45570 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45570.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [18,-18,-18,18,18,18,0,-18,18,-18,-4,-18,-6,0,-18,18,-6,-18,-6, 18,0,4,-20,18,18,6,-18,0,0,18,18,-18,4,6,0,18,0,6,6,-18,6,0,-4,-4,18,20, -28,-18,0,-18,6,-6,-34,18,-4,0,6,0,16,-18,4,-18,0,18,-6,-4,6,-6,20,0,0, -18,0,0,-18,-6,0,-6,16,18,18,-6,-4,0,-6,4,0,4,8,-18,0,-20,-18,28,-6,18, -10,0,-4,18] 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: \(363.878282011\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 4 x^{17} - 134 x^{16} + 516 x^{15} + 7372 x^{14} - 27016 x^{13} - 216326 x^{12} + \cdots + 168254464 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 18 q - 18 q^{2} - 18 q^{3} + 18 q^{4} + 18 q^{5} + 18 q^{6} - 18 q^{8} + 18 q^{9} - 18 q^{10} - 4 q^{11} - 18 q^{12} - 6 q^{13} - 18 q^{15} + 18 q^{16} - 6 q^{17} - 18 q^{18} - 6 q^{19} + 18 q^{20} + 4 q^{22}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(7\) \( +1 \)
\(31\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.