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Properties

Label 110.3.i.a
Level $110$
Weight $3$
Character orbit 110.i
Analytic conductor $2.997$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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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] = [110,3,Mod(19,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.19"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 110 = 2 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 110.i (of order \(10\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.99728290796\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 24 q^{4} - 10 q^{5} + 68 q^{9} + 12 q^{11} - 24 q^{14} - 38 q^{15} - 48 q^{16} - 20 q^{20} + 182 q^{25} - 32 q^{26} + 60 q^{30} - 164 q^{31} - 32 q^{34} - 70 q^{35} + 96 q^{36} + 80 q^{39} - 80 q^{40}+ \cdots - 1120 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1 −1.14412 + 0.831254i −4.66752 + 1.51657i 0.618034 − 1.90211i 0.639205 − 4.95897i 4.07956 − 5.61504i −0.907012 + 2.79150i 0.874032 + 2.68999i 12.2046 − 8.86717i 3.39084 + 6.20502i
19.2 −1.14412 + 0.831254i −2.80040 + 0.909907i 0.618034 − 1.90211i −3.44728 + 3.62164i 2.44764 − 3.36889i 2.91555 − 8.97315i 0.874032 + 2.68999i −0.266815 + 0.193853i 0.933611 − 7.00916i
19.3 −1.14412 + 0.831254i −2.20436 + 0.716242i 0.618034 − 1.90211i 4.07430 + 2.89829i 1.92669 − 2.65186i −0.355087 + 1.09285i 0.874032 + 2.68999i −2.93493 + 2.13235i −7.07071 + 0.0707788i
19.4 −1.14412 + 0.831254i 0.674730 − 0.219233i 0.618034 − 1.90211i −4.95548 − 0.665729i −0.589736 + 0.811701i −2.91352 + 8.96689i 0.874032 + 2.68999i −6.87396 + 4.99422i 6.22307 − 3.35759i
19.5 −1.14412 + 0.831254i 3.58330 − 1.16429i 0.618034 − 1.90211i −3.53138 − 3.53968i −3.13192 + 4.31072i 3.60989 − 11.1101i 0.874032 + 2.68999i 4.20335 − 3.05391i 6.98271 + 1.11436i
19.6 −1.14412 + 0.831254i 5.41426 − 1.75920i 0.618034 − 1.90211i 1.13131 + 4.87033i −4.73223 + 6.51336i −2.89000 + 8.89452i 0.874032 + 2.68999i 18.9382 − 13.7594i −5.34284 − 4.63185i
19.7 1.14412 − 0.831254i −5.41426 + 1.75920i 0.618034 − 1.90211i 4.98156 − 0.429077i −4.73223 + 6.51336i 2.89000 − 8.89452i −0.874032 − 2.68999i 18.9382 − 13.7594i 5.34284 − 4.63185i
19.8 1.14412 − 0.831254i −3.58330 + 1.16429i 0.618034 − 1.90211i −4.45770 − 2.26472i −3.13192 + 4.31072i −3.60989 + 11.1101i −0.874032 − 2.68999i 4.20335 − 3.05391i −6.98271 + 1.11436i
19.9 1.14412 − 0.831254i −0.674730 + 0.219233i 0.618034 − 1.90211i −2.16447 − 4.50722i −0.589736 + 0.811701i 2.91352 − 8.96689i −0.874032 − 2.68999i −6.87396 + 4.99422i −6.22307 − 3.35759i
19.10 1.14412 − 0.831254i 2.20436 − 0.716242i 0.618034 − 1.90211i 4.01546 + 2.97927i 1.92669 − 2.65186i 0.355087 − 1.09285i −0.874032 − 2.68999i −2.93493 + 2.13235i 7.07071 + 0.0707788i
19.11 1.14412 − 0.831254i 2.80040 − 0.909907i 0.618034 − 1.90211i 2.37911 − 4.39771i 2.44764 − 3.36889i −2.91555 + 8.97315i −0.874032 − 2.68999i −0.266815 + 0.193853i −0.933611 − 7.00916i
19.12 1.14412 − 0.831254i 4.66752 − 1.51657i 0.618034 − 1.90211i −4.51874 + 2.14033i 4.07956 − 5.61504i 0.907012 − 2.79150i −0.874032 − 2.68999i 12.2046 − 8.86717i −3.39084 + 6.20502i
29.1 −1.14412 − 0.831254i −4.66752 − 1.51657i 0.618034 + 1.90211i 0.639205 + 4.95897i 4.07956 + 5.61504i −0.907012 − 2.79150i 0.874032 − 2.68999i 12.2046 + 8.86717i 3.39084 − 6.20502i
29.2 −1.14412 − 0.831254i −2.80040 − 0.909907i 0.618034 + 1.90211i −3.44728 − 3.62164i 2.44764 + 3.36889i 2.91555 + 8.97315i 0.874032 − 2.68999i −0.266815 − 0.193853i 0.933611 + 7.00916i
29.3 −1.14412 − 0.831254i −2.20436 − 0.716242i 0.618034 + 1.90211i 4.07430 − 2.89829i 1.92669 + 2.65186i −0.355087 − 1.09285i 0.874032 − 2.68999i −2.93493 − 2.13235i −7.07071 − 0.0707788i
29.4 −1.14412 − 0.831254i 0.674730 + 0.219233i 0.618034 + 1.90211i −4.95548 + 0.665729i −0.589736 − 0.811701i −2.91352 − 8.96689i 0.874032 − 2.68999i −6.87396 − 4.99422i 6.22307 + 3.35759i
29.5 −1.14412 − 0.831254i 3.58330 + 1.16429i 0.618034 + 1.90211i −3.53138 + 3.53968i −3.13192 − 4.31072i 3.60989 + 11.1101i 0.874032 − 2.68999i 4.20335 + 3.05391i 6.98271 − 1.11436i
29.6 −1.14412 − 0.831254i 5.41426 + 1.75920i 0.618034 + 1.90211i 1.13131 − 4.87033i −4.73223 − 6.51336i −2.89000 − 8.89452i 0.874032 − 2.68999i 18.9382 + 13.7594i −5.34284 + 4.63185i
29.7 1.14412 + 0.831254i −5.41426 − 1.75920i 0.618034 + 1.90211i 4.98156 + 0.429077i −4.73223 − 6.51336i 2.89000 + 8.89452i −0.874032 + 2.68999i 18.9382 + 13.7594i 5.34284 + 4.63185i
29.8 1.14412 + 0.831254i −3.58330 − 1.16429i 0.618034 + 1.90211i −4.45770 + 2.26472i −3.13192 − 4.31072i −3.60989 − 11.1101i −0.874032 + 2.68999i 4.20335 + 3.05391i −6.98271 − 1.11436i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 19.12
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
11.d odd 10 1 inner
55.h odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 110.3.i.a ✓ 48
5.b even 2 1 inner 110.3.i.a ✓ 48
11.d odd 10 1 inner 110.3.i.a ✓ 48
55.h odd 10 1 inner 110.3.i.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
110.3.i.a ✓ 48 1.a even 1 1 trivial
110.3.i.a ✓ 48 5.b even 2 1 inner
110.3.i.a ✓ 48 11.d odd 10 1 inner
110.3.i.a ✓ 48 55.h odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(110, [\chi])\).