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Properties

Label 27300.2.a.w
Level $27300$
Weight $2$
Character orbit 27300.a
Self dual yes
Analytic conductor $217.992$
Dimension $1$

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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 = [1,0,1,0,0,0,1,0,1,0,2,0,-1,0,0,0,4,0,1,0,1,0,3,0,0,0,1,0,3,0, 5,0,2,0,0,0,8,0,-1,0,-10,0,-1,0,0,0,13,0,1,0,4,0,1,0,0,0,1,0,-8,0,-14, 0,1,0,0,0,-2,0,3,0,4,0,7,0,0,0,2,0,17,0,1,0,9,0,0,0,3,0,5,0,-1,0,5,0,0, 0,-13,0,2,0] 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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q + q^{3} + q^{7} + q^{9} + 2 q^{11} - q^{13} + 4 q^{17} + q^{19} + q^{21} + 3 q^{23} + q^{27} + 3 q^{29} + 5 q^{31} + 2 q^{33} + 8 q^{37} - q^{39} - 10 q^{41} - q^{43} + 13 q^{47} + q^{49} + 4 q^{51}+ \cdots + 2 q^{99}+O(q^{100}) \) 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.