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Properties

Label 45570.2.a.hi
Level $45570$
Weight $2$
Character orbit 45570.a
Self dual yes
Analytic conductor $363.878$
Dimension $10$

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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 = [10,10,10,10,10,10,0,10,10,10,-8,10,-14,0,10,10,-6,10,-14,10, 0,-8,-12,10,10,-14,10,0,-8,10,10,10,-8,-6,0,10,-20,-14,-14,10,-10,0,-28, -8,10,-12,-16,10,0,10,-6,-14,-10,10,-8,0,-14,-8,-16,10,-8,10,0,10,-14, -8,-22,-6,-12,0,-40,10,-52,-20,10,-14,0,-14,-4,10,10,-10,-20,0,-6,-28, -8,-8,-60,10,0,-12,10,-16,-14,10,-34,0,-8,10] 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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 19x^{8} + 16x^{7} + 120x^{6} + 16x^{5} - 188x^{4} - 48x^{3} + 87x^{2} + 18x - 9 \) 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.

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