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Properties

Label 27300.2.a.bl
Level $27300$
Weight $2$
Character orbit 27300.a
Self dual yes
Analytic conductor $217.992$
Dimension $3$

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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] = [27300,2,Mod(1,27300)] 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("27300.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27300, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 27300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27300.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,-3,0,0,0,3,0,3,0,2,0,-3,0,0,0,2,0,-3,0,-3,0,-3,0,0,0,-3, 0,-3,0,-2,0,-2,0,0,0,-12,0,3,0,10,0,13,0,0,0,-12,0,3,0,-2,0,-10,0,0,0, 3,0,1,0,12,0,3,0,0,0,-8,0,3,0,25,0,0,0,0,0,2,0,3,0,3,0,-9,0,0,0,3,0,7, 0,-3,0,2,0,0,0,-11,0,2,0] 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: \(217.991597518\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 4x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{3} + 3 q^{7} + 3 q^{9} + 2 q^{11} - 3 q^{13} + 2 q^{17} - 3 q^{19} - 3 q^{21} - 3 q^{23} - 3 q^{27} - 3 q^{29} - 2 q^{31} - 2 q^{33} - 12 q^{37} + 3 q^{39} + 10 q^{41} + 13 q^{43} - 12 q^{47}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.