↑

Properties

Label 37845.2.a.d
Level 3784537845
Weight 22
Character orbit 37845.a
Self dual yes
Analytic conductor 302.194302.194
Dimension 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [37845,2,Mod(1,37845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(37845, 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("37845.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 37845=32⋅5⋅292 37845 = 3^{2} \cdot 5 \cdot 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 37845.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,-1,-1,0,0,3,0,1,-4,0,-2,0,0,-1,2,0,-4,1,0,4,0,0,1,2,0, 0,0,0,0,-5,0,-2,0,0,10,4,0,-3,10,0,-4,4,0,0,8,0,-7,-1,0,2,10,0,4,0,0,0, 4,0,2,0,0,7,2,0,12,-2,0,0,8,0,-10,-10,0,4,0,0,0,1,0,-10,-12,0,-2,4,0,-12, -6,0,0,0,0,-8,4,0,-2,7,0,-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: 302.193846450302.193846450
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−q5+3q8+q10−4q11−2q13−q16+2q17−4q19+q20+4q22+q25+2q26−5q32−2q34+10q37+4q38−3q40+⋯+7q98+O(q100) q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} - 4 q^{11} - 2 q^{13} - q^{16} + 2 q^{17} - 4 q^{19} + q^{20} + 4 q^{22} + q^{25} + 2 q^{26} - 5 q^{32} - 2 q^{34} + 10 q^{37} + 4 q^{38} - 3 q^{40}+ \cdots + 7 q^{98}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
33 −1 -1
55 +1 +1
2929 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.