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Properties

Label 45486.2.a.gs
Level $45486$
Weight $2$
Character orbit 45486.a
Self dual yes
Analytic conductor $363.208$
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] = [45486,2,Mod(1,45486)] 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("45486.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45486, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45486 = 2 \cdot 3^{2} \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45486.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,12,0,12,0,0,-12,12,0,0,-4,0,-16,-12,0,12,-4,0,0,0,0,-4,-8, 0,36,-16,0,-12,-14,0,-16,12,0,-4,0,0,-4,0,0,0,-6,0,30,-4,0,-8,-20,0,12, 36,0,-16,14,0,-24,-12,0,-14,-18,0,-26,-16,0,12,0,0,8,-4,0,0,10,0,36,-4, 0,0,4,0,8,0,0,-6,-24,0,44,30,0,-4,18,0,16,-8,0,-20,0,0,-24,12,0,36] 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: \(363.207538634\)
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: \( x^{12} - 48 x^{10} - 8 x^{9} + 829 x^{8} + 248 x^{7} - 6078 x^{6} - 2056 x^{5} + 16945 x^{4} + \cdots - 304 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 12 q + 12 q^{2} + 12 q^{4} - 12 q^{7} + 12 q^{8} - 4 q^{11} - 16 q^{13} - 12 q^{14} + 12 q^{16} - 4 q^{17} - 4 q^{22} - 8 q^{23} + 36 q^{25} - 16 q^{26} - 12 q^{28} - 14 q^{29} - 16 q^{31} + 12 q^{32} - 4 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(7\) \( +1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.