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Properties

Label 1100.2.q.b
Level $1100$
Weight $2$
Character orbit 1100.q
Analytic conductor $8.784$
Analytic rank $0$
Dimension $52$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1100,2,Mod(221,1100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1100, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1100.221");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.q (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.78354422234\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(13\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52 q - 3 q^{5} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43} - 7 q^{45} + 19 q^{47} + 68 q^{49} + 34 q^{51} + 3 q^{53} - 2 q^{55} - 24 q^{57} - 37 q^{59} + 10 q^{61} - 8 q^{63} + 12 q^{65} + 2 q^{67} + 27 q^{69} - 3 q^{71} + 4 q^{73} + 68 q^{75} - 17 q^{79} - 39 q^{81} + 78 q^{83} + 13 q^{85} + 13 q^{87} - 7 q^{89} - 2 q^{91} - 94 q^{93} + 18 q^{95} + 15 q^{97} - 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
221.1 0 −2.46992 − 1.79450i 0 −0.932128 − 2.03252i 0 4.85051 0 1.95322 + 6.01139i 0
221.2 0 −1.98827 − 1.44456i 0 1.83057 + 1.28413i 0 0.715669 0 0.939404 + 2.89119i 0
221.3 0 −1.84339 − 1.33930i 0 0.702061 + 2.12300i 0 −3.98140 0 0.677309 + 2.08454i 0
221.4 0 −1.67142 − 1.21436i 0 −1.73889 + 1.40580i 0 1.74835 0 0.391935 + 1.20625i 0
221.5 0 −1.19952 − 0.871501i 0 1.53725 − 1.62384i 0 0.464093 0 −0.247722 − 0.762409i 0
221.6 0 −0.463412 − 0.336688i 0 −1.34725 − 1.78463i 0 −3.78473 0 −0.825660 − 2.54112i 0
221.7 0 0.287074 + 0.208571i 0 1.90283 − 1.17441i 0 −3.22759 0 −0.888142 − 2.73342i 0
221.8 0 0.722709 + 0.525079i 0 1.39423 + 1.74818i 0 1.78111 0 −0.680451 − 2.09421i 0
221.9 0 0.921658 + 0.669624i 0 −1.47725 + 1.67861i 0 −4.58549 0 −0.525993 − 1.61884i 0
221.10 0 1.10560 + 0.803263i 0 0.235915 − 2.22359i 0 3.63293 0 −0.349938 − 1.07700i 0
221.11 0 1.36589 + 0.992379i 0 −2.23514 − 0.0642463i 0 0.0719347 0 −0.0462056 − 0.142206i 0
221.12 0 2.51887 + 1.83006i 0 1.68514 + 1.46980i 0 1.24095 0 2.06850 + 6.36620i 0
221.13 0 2.71414 + 1.97194i 0 −1.74832 − 1.39405i 0 1.07366 0 2.55096 + 7.85106i 0
441.1 0 −0.994170 − 3.05974i 0 0.246812 − 2.22240i 0 3.71818 0 −5.94659 + 4.32045i 0
441.2 0 −0.885916 − 2.72657i 0 −2.22917 − 0.175548i 0 −1.14570 0 −4.22229 + 3.06767i 0
441.3 0 −0.631762 − 1.94436i 0 1.75484 + 1.38583i 0 1.39297 0 −0.954372 + 0.693392i 0
441.4 0 −0.611345 − 1.88153i 0 −0.0494719 + 2.23552i 0 −3.07794 0 −0.739349 + 0.537169i 0
441.5 0 −0.183465 − 0.564647i 0 −1.90569 + 1.16976i 0 −0.847663 0 2.14188 − 1.55617i 0
441.6 0 −0.0542729 − 0.167035i 0 −1.54766 − 1.61392i 0 3.08318 0 2.40210 − 1.74522i 0
441.7 0 −0.0181419 − 0.0558349i 0 −0.144597 − 2.23139i 0 −1.97462 0 2.42426 − 1.76133i 0
See all 52 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 221.13
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
25.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1100.2.q.b ✓ 52
25.d even 5 1 inner 1100.2.q.b ✓ 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1100.2.q.b ✓ 52 1.a even 1 1 trivial
1100.2.q.b ✓ 52 25.d even 5 1 inner