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Properties

Label 45570.2.a.hn
Level $45570$
Weight $2$
Character orbit 45570.a
Self dual yes
Analytic conductor $363.878$
Dimension $12$

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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 = [12,-12,-12,12,12,12,0,-12,12,-12,4,-12,2,0,-12,12,-2,-12,14, 12,0,-4,8,12,12,-2,-12,0,-12,12,-12,-12,-4,2,0,12,-8,-14,-2,-12,-22,0, 0,4,12,-8,20,-12,0,-12,2,2,10,12,4,0,-14,12,4,-12,8,12,0,12,2,4,-6,-2, -8,0,0,-12,4,8,-12,14,0,2,-48,12,12,22,20,0,-2,0,12,-4,8,-12,0,8,12,-20, 14,12,18,0,4,12] 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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} - 41 x^{10} + 44 x^{9} + 627 x^{8} - 130 x^{7} - 4015 x^{6} - 1600 x^{5} + 8422 x^{4} + \cdots + 2056 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} + 12 q^{5} + 12 q^{6} - 12 q^{8} + 12 q^{9} - 12 q^{10} + 4 q^{11} - 12 q^{12} + 2 q^{13} - 12 q^{15} + 12 q^{16} - 2 q^{17} - 12 q^{18} + 14 q^{19} + 12 q^{20} - 4 q^{22}+ \cdots + 4 q^{99}+O(q^{100}) \) 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.