↑

Properties

Label 1166.2.c.b
Level $1166$
Weight $2$
Character orbit 1166.c
Analytic conductor $9.311$
Analytic rank $0$
Dimension $22$
Inner twists $2$

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] = [1166,2,Mod(529,1166)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1166, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) 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("1166.529"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1166 = 2 \cdot 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1166.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [22,0,0,-22,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.31055687568\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 22 q^{4} - 6 q^{6} - 24 q^{9} + 4 q^{10} - 22 q^{11} + 6 q^{13} + 30 q^{15} + 22 q^{16} + 18 q^{17} + 6 q^{24} - 30 q^{25} + 28 q^{29} + 24 q^{36} - 34 q^{37} - 18 q^{38} - 4 q^{40} + 4 q^{42} - 34 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
529.1 − 1.00000i − 3.30239i −1.00000 − 1.72694i −3.30239 −0.983038 1.00000i −7.90579 −1.72694
529.2 − 1.00000i − 2.64745i −1.00000 4.24100i −2.64745 −3.05926 1.00000i −4.00901 4.24100
529.3 − 1.00000i − 2.17721i −1.00000 1.32192i −2.17721 −1.38716 1.00000i −1.74022 1.32192
529.4 − 1.00000i − 1.70350i −1.00000 1.22065i −1.70350 3.68277 1.00000i 0.0980910 1.22065
529.5 − 1.00000i − 1.17320i −1.00000 − 0.758553i −1.17320 −0.338318 1.00000i 1.62361 −0.758553
529.6 − 1.00000i − 0.119759i −1.00000 0.799223i −0.119759 2.42938 1.00000i 2.98566 0.799223
529.7 − 1.00000i 0.486719i −1.00000 2.55211i 0.486719 −2.87431 1.00000i 2.76310 2.55211
529.8 − 1.00000i 0.796611i −1.00000 − 3.27208i 0.796611 4.51075 1.00000i 2.36541 −3.27208
529.9 − 1.00000i 1.49995i −1.00000 − 4.12793i 1.49995 −0.327299 1.00000i 0.750159 −4.12793
529.10 − 1.00000i 2.09046i −1.00000 2.97150i 2.09046 2.18061 1.00000i −1.37003 2.97150
529.11 − 1.00000i 3.24977i −1.00000 − 1.22090i 3.24977 −3.83413 1.00000i −7.56098 −1.22090
529.12 1.00000i − 3.24977i −1.00000 1.22090i 3.24977 −3.83413 − 1.00000i −7.56098 −1.22090
529.13 1.00000i − 2.09046i −1.00000 − 2.97150i 2.09046 2.18061 − 1.00000i −1.37003 2.97150
529.14 1.00000i − 1.49995i −1.00000 4.12793i 1.49995 −0.327299 − 1.00000i 0.750159 −4.12793
529.15 1.00000i − 0.796611i −1.00000 3.27208i 0.796611 4.51075 − 1.00000i 2.36541 −3.27208
529.16 1.00000i − 0.486719i −1.00000 − 2.55211i 0.486719 −2.87431 − 1.00000i 2.76310 2.55211
529.17 1.00000i 0.119759i −1.00000 − 0.799223i −0.119759 2.42938 − 1.00000i 2.98566 0.799223
529.18 1.00000i 1.17320i −1.00000 0.758553i −1.17320 −0.338318 − 1.00000i 1.62361 −0.758553
529.19 1.00000i 1.70350i −1.00000 − 1.22065i −1.70350 3.68277 − 1.00000i 0.0980910 1.22065
529.20 1.00000i 2.17721i −1.00000 − 1.32192i −2.17721 −1.38716 − 1.00000i −1.74022 1.32192
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 529.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
53.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1166.2.c.b ✓ 22
53.b even 2 1 inner 1166.2.c.b ✓ 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1166.2.c.b ✓ 22 1.a even 1 1 trivial
1166.2.c.b ✓ 22 53.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{22} + 45 T_{3}^{20} + 844 T_{3}^{18} + 8621 T_{3}^{16} + 52677 T_{3}^{14} + 199183 T_{3}^{12} + \cdots + 324 \) acting on \(S_{2}^{\mathrm{new}}(1166, [\chi])\). Copy content Toggle raw display