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Properties

Label 28900.2.a.cg
Level $28900$
Weight $2$
Character orbit 28900.a
Self dual yes
Analytic conductor $230.768$
Dimension $15$

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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] = [28900,2,Mod(1,28900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28900, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("28900.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 28900 = 2^{2} \cdot 5^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28900.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [15,0,3,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,-6,0,-18,0,0,0,0,0,12, 0,6,0,0,0,12,0,0,0,12,0,9,0,6,0,3,0,0,0,3,0,15,0,0,0,24,0,0,0,9,0,6,0, 21,0,0,0,0,0,-6,0,-18,0,-6,0,9,0,0,0,6,0,3,0,-21,0,9,0,0,0,27,0,24,0,15, 0,-78,0,0,0,24,0,-18,0] 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: \(230.767661842\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{15} - 3 x^{14} - 24 x^{13} + 71 x^{12} + 222 x^{11} - 636 x^{10} - 1019 x^{9} + 2739 x^{8} + \cdots + 81 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 15 q + 3 q^{3} + 12 q^{9} - 6 q^{19} - 18 q^{21} + 12 q^{27} + 6 q^{29} + 12 q^{33} + 12 q^{37} + 9 q^{39} + 6 q^{41} + 3 q^{43} + 3 q^{47} + 15 q^{49} + 24 q^{53} + 9 q^{57} + 6 q^{59} + 21 q^{61} - 6 q^{67}+ \cdots - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.