Properties

Label 11.33.b.a
Level 1111
Weight 3333
Character orbit 11.b
Self dual yes
Analytic conductor 71.35371.353
Analytic rank 00
Dimension 11
CM discriminant -11
Inner twists 22

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [11,33,Mod(10,11)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 33, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("11.10"); S:= CuspForms(chi, 33); N := Newforms(S);
 
Level: N N == 11 11
Weight: k k == 33 33
Character orbit: [χ][\chi] == 11.b (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 71.353320656571.3533206565
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: U(1)[D2]\mathrm{U}(1)[D_{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) == q85968833q3+4294967296q49728091649q5+55 ⁣ ⁣48q9+45 ⁣ ⁣61q1136 ⁣ ⁣68q12+83 ⁣ ⁣17q15+18 ⁣ ⁣16q1641 ⁣ ⁣04q20+36 ⁣ ⁣47q23++25 ⁣ ⁣28q99+O(q100) q - 85968833 q^{3} + 4294967296 q^{4} - 9728091649 q^{5} + 55\!\cdots\!48 q^{9} + 45\!\cdots\!61 q^{11} - 36\!\cdots\!68 q^{12} + 83\!\cdots\!17 q^{15} + 18\!\cdots\!16 q^{16} - 41\!\cdots\!04 q^{20} + 36\!\cdots\!47 q^{23}+ \cdots + 25\!\cdots\!28 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/11Z)×\left(\mathbb{Z}/11\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) 1-1

Embeddings

For each embedding ιm\iota_m of the coefficient field, the values ιm(an)\iota_m(a_n) are shown below.

For more information on an embedded modular form you can click on its label.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   ιm(ν)\iota_m(\nu) a2 a_{2} a3 a_{3} a4 a_{4} a5 a_{5} a6 a_{6} a7 a_{7} a8 a_{8} a9 a_{9} a10 a_{10}
10.1
0
0 −8.59688e7 4.29497e9 −9.72809e9 0 0 0 5.53762e15 0
nn: e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.b odd 2 1 CM by Q(11)\Q(\sqrt{-11})

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 11.33.b.a 1
11.b odd 2 1 CM 11.33.b.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
11.33.b.a 1 1.a even 1 1 trivial
11.33.b.a 1 11.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2 T_{2} acting on S33new(11,[χ])S_{33}^{\mathrm{new}}(11, [\chi]). Copy content Toggle raw display

Hecke characteristic polynomials

pp Fp(T)F_p(T)
22 T T Copy content Toggle raw display
33 T+85968833 T + 85968833 Copy content Toggle raw display
55 T+9728091649 T + 9728091649 Copy content Toggle raw display
77 T T Copy content Toggle raw display
1111 T45 ⁣ ⁣61 T - 45\!\cdots\!61 Copy content Toggle raw display
1313 T T Copy content Toggle raw display
1717 T T Copy content Toggle raw display
1919 T T Copy content Toggle raw display
2323 T36 ⁣ ⁣47 T - 36\!\cdots\!47 Copy content Toggle raw display
2929 T T Copy content Toggle raw display
3131 T+10 ⁣ ⁣13 T + 10\!\cdots\!13 Copy content Toggle raw display
3737 T17 ⁣ ⁣07 T - 17\!\cdots\!07 Copy content Toggle raw display
4141 T T Copy content Toggle raw display
4343 T T Copy content Toggle raw display
4747 T+10 ⁣ ⁣58 T + 10\!\cdots\!58 Copy content Toggle raw display
5353 T40 ⁣ ⁣42 T - 40\!\cdots\!42 Copy content Toggle raw display
5959 T33 ⁣ ⁣07 T - 33\!\cdots\!07 Copy content Toggle raw display
6161 T T Copy content Toggle raw display
6767 T+15 ⁣ ⁣13 T + 15\!\cdots\!13 Copy content Toggle raw display
7171 T70 ⁣ ⁣67 T - 70\!\cdots\!67 Copy content Toggle raw display
7373 T T Copy content Toggle raw display
7979 T T Copy content Toggle raw display
8383 T T Copy content Toggle raw display
8989 T+30 ⁣ ⁣53 T + 30\!\cdots\!53 Copy content Toggle raw display
9797 T+40 ⁣ ⁣33 T + 40\!\cdots\!33 Copy content Toggle raw display
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