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Properties

Label 17298.2.a.ch
Level $17298$
Weight $2$
Character orbit 17298.a
Self dual yes
Analytic conductor $138.125$
Dimension $4$

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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] = [17298,2,Mod(1,17298)] 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("17298.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17298, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 17298 = 2 \cdot 3^{2} \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17298.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-4,0,4,2,0,-4,-4,0,-2,-9,0,7,4,0,4,-4,0,-7,2,0,9,11,0,0,-7, 0,-4,-4,0,0,-4,0,4,9,0,26,7,0,-2,-2,0,4,-9,0,-11,10,0,30,0,0,7,-6,0,9, 4,0,4,-1,0,2,0,0,4,-10,0,-13,-4,0,-9,0,0,13,-26,0,-7,-7,0,-21,2,0,2,-14, 0,-10,-4,0,9,-38,0,9,11,0,-10,-9,0,-30,-30,0,0] 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: \(138.125225416\)
Dimension: \(4\)
Coefficient field: 4.4.4525.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 7x^{2} + 3x + 9 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} - 2 q^{10} - 9 q^{11} + 7 q^{13} + 4 q^{14} + 4 q^{16} - 4 q^{17} - 7 q^{19} + 2 q^{20} + 9 q^{22} + 11 q^{23} - 7 q^{26} - 4 q^{28} - 4 q^{29} - 4 q^{32}+ \cdots - 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.