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Properties

Label 22491.2.a.d
Level $22491$
Weight $2$
Character orbit 22491.a
Self dual yes
Analytic conductor $179.592$
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] = [22491,2,Mod(1,22491)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22491, 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("22491.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 22491 = 3^{3} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22491.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-2,0,2,0,0,0,0,0,0,4,0,0,0,0,-4,1,0,6,0,0,-8,-7,0,-5,0,0,0, -1,0,-9,8,0,-2,0,0,6,-12,0,0,6,0,-9,8,0,14,-3,0,0,10,0,0,2,0,0,0,0,2,3, 0,-3,18,0,-8,0,0,13,2,0,0,-5,0,15,-12,0,12,0,0,8,0,0,-12,-12,0,0,18,0, 0,-15,0,0,-14,0,6,0,0,-3,0,0,-10] 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: \(179.591539186\)
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)
 
\(f(q)\) \(=\) \( q - 2 q^{2} + 2 q^{4} + 4 q^{11} - 4 q^{16} + q^{17} + 6 q^{19} - 8 q^{22} - 7 q^{23} - 5 q^{25} - q^{29} - 9 q^{31} + 8 q^{32} - 2 q^{34} + 6 q^{37} - 12 q^{38} + 6 q^{41} - 9 q^{43} + 8 q^{44} + 14 q^{46}+ \cdots - 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(7\) \( -1 \)
\(17\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.