Properties

Label 28665.2.a.ec
Level $28665$
Weight $2$
Character orbit 28665.a
Self dual yes
Analytic conductor $228.891$
Dimension $7$

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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] = [28665,2,Mod(1,28665)] 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("28665.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28665, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 28665 = 3^{2} \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28665.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [7,1,0,7,7,0,0,0,0,1,0,0,7,0,0,-5,5,0,0,7,0,-9,14,0,7,1,0,0,20, 0,2,1,0,-16,0,0,-14,8,0,0,5,0,3,-5,0,-23,15,0,0,1,0,7,35,0,0,0,0,2,15, 0,-22,-3,0,4,7,0,-11,-9,0,0,3,0,27,38,0,5,0,0,10,-5,0,-12,1,0,5,14,0,-78, 11,0,0,26,0,37,0,0,47,0,0,7] 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: \(228.891177394\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 10x^{5} + 9x^{4} + 28x^{3} - 21x^{2} - 23x + 15 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 7 q + q^{2} + 7 q^{4} + 7 q^{5} + q^{10} + 7 q^{13} - 5 q^{16} + 5 q^{17} + 7 q^{20} - 9 q^{22} + 14 q^{23} + 7 q^{25} + q^{26} + 20 q^{29} + 2 q^{31} + q^{32} - 16 q^{34} - 14 q^{37} + 8 q^{38} + 5 q^{41}+ \cdots + 47 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(5\) \( -1 \)
\(7\) \( +1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.