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Properties

Label 13754.2.a.d
Level 1375413754
Weight 22
Character orbit 13754.a
Self dual yes
Analytic conductor 109.826109.826
Dimension 11

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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] = [13754,2,Mod(1,13754)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13754, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("13754.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 13754=2⋅13⋅232 13754 = 2 \cdot 13 \cdot 23^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 13754.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,2,0,4,-1,-3,-2,-5,0,-1,-4,0,1,-7,3,-7,2,0,5,0,0,-1, 1,0,4,5,0,9,-1,0,7,8,-3,4,7,0,-2,12,0,2,-5,-6,0,-9,0,9,1,0,-1,-11,0,-10, -4,0,-5,3,0,14,-9,-12,1,-2,0,1,-7,0,-8,0,3,-6,-4,0,-7,-20,0,6,2,9,-12, 4,0,-14,-2,0,5,6,6,-4,0,0,9,-14,0,12,-9,15,-1] 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: 109.826242940109.826242940
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: not computed
Fricke sign: −1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

qq-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)f(q) == q−q2+q4+2q5+4q7−q8−3q9−2q10−5q11−q13−4q14+q16−7q17+3q18−7q19+2q20+5q22−q25+q26+4q28+5q29+⋯+15q99+O(q100) q - q^{2} + q^{4} + 2 q^{5} + 4 q^{7} - q^{8} - 3 q^{9} - 2 q^{10} - 5 q^{11} - q^{13} - 4 q^{14} + q^{16} - 7 q^{17} + 3 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{22} - q^{25} + q^{26} + 4 q^{28} + 5 q^{29}+ \cdots + 15 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 +1 +1
1313 +1 +1
2323 −1 -1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.