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Properties

Label 105.3.l.a
Level $105$
Weight $3$
Character orbit 105.l
Analytic conductor $2.861$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(22,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.22");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), 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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31}+ \cdots - 56 q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1 −2.72310 − 2.72310i −1.22474 + 1.22474i 10.8306i 4.39513 − 2.38387i 6.67022 −1.87083 − 1.87083i 18.6004 − 18.6004i − 3.00000i −18.4599 − 5.47689i
22.2 −1.59930 − 1.59930i −1.22474 + 1.22474i 1.11554i −1.35929 − 4.81169i 3.91747 1.87083 + 1.87083i −4.61313 + 4.61313i − 3.00000i −5.52142 + 9.86926i
22.3 −1.36784 − 1.36784i −1.22474 + 1.22474i − 0.258033i 3.39663 + 3.66919i 3.35051 1.87083 + 1.87083i −5.82430 + 5.82430i − 3.00000i 0.372817 − 9.66489i
22.4 −1.01289 − 1.01289i 1.22474 − 1.22474i − 1.94811i 3.97454 − 3.03365i −2.48106 1.87083 + 1.87083i −6.02478 + 6.02478i − 3.00000i −7.09851 − 0.953024i
22.5 −0.867675 − 0.867675i 1.22474 − 1.22474i − 2.49428i −4.93004 − 0.833478i −2.12536 −1.87083 − 1.87083i −5.63493 + 5.63493i − 3.00000i 3.55449 + 5.00086i
22.6 0.408558 + 0.408558i −1.22474 + 1.22474i − 3.66616i 0.563288 − 4.96817i −1.00076 −1.87083 − 1.87083i 3.13207 − 3.13207i − 3.00000i 2.25992 − 1.79965i
22.7 0.675544 + 0.675544i 1.22474 − 1.22474i − 3.08728i 3.39488 + 3.67080i 1.65474 −1.87083 − 1.87083i 4.78777 − 4.78777i − 3.00000i −0.186396 + 4.77318i
22.8 0.992944 + 0.992944i 1.22474 − 1.22474i − 2.02813i −2.01954 − 4.57400i 2.43221 1.87083 + 1.87083i 5.98559 − 5.98559i − 3.00000i 2.53644 − 6.54701i
22.9 2.08980 + 2.08980i −1.22474 + 1.22474i 4.73454i 0.137153 + 4.99812i −5.11895 −1.87083 − 1.87083i −1.53505 + 1.53505i − 3.00000i −10.1585 + 10.7317i
22.10 2.24469 + 2.24469i 1.22474 − 1.22474i 6.07726i −3.05058 + 3.96156i 5.49834 1.87083 + 1.87083i −4.66280 + 4.66280i − 3.00000i −15.7401 + 2.04487i
22.11 2.41688 + 2.41688i 1.22474 − 1.22474i 7.68258i 4.18124 − 2.74175i 5.92011 −1.87083 − 1.87083i −8.90034 + 8.90034i − 3.00000i 16.7320 + 3.47908i
22.12 2.74240 + 2.74240i −1.22474 + 1.22474i 11.0415i −0.683416 − 4.95307i −6.71747 1.87083 + 1.87083i −19.3105 + 19.3105i − 3.00000i 11.7091 − 15.4575i
43.1 −2.72310 + 2.72310i −1.22474 − 1.22474i − 10.8306i 4.39513 + 2.38387i 6.67022 −1.87083 + 1.87083i 18.6004 + 18.6004i 3.00000i −18.4599 + 5.47689i
43.2 −1.59930 + 1.59930i −1.22474 − 1.22474i − 1.11554i −1.35929 + 4.81169i 3.91747 1.87083 − 1.87083i −4.61313 − 4.61313i 3.00000i −5.52142 − 9.86926i
43.3 −1.36784 + 1.36784i −1.22474 − 1.22474i 0.258033i 3.39663 − 3.66919i 3.35051 1.87083 − 1.87083i −5.82430 − 5.82430i 3.00000i 0.372817 + 9.66489i
43.4 −1.01289 + 1.01289i 1.22474 + 1.22474i 1.94811i 3.97454 + 3.03365i −2.48106 1.87083 − 1.87083i −6.02478 − 6.02478i 3.00000i −7.09851 + 0.953024i
43.5 −0.867675 + 0.867675i 1.22474 + 1.22474i 2.49428i −4.93004 + 0.833478i −2.12536 −1.87083 + 1.87083i −5.63493 − 5.63493i 3.00000i 3.55449 − 5.00086i
43.6 0.408558 − 0.408558i −1.22474 − 1.22474i 3.66616i 0.563288 + 4.96817i −1.00076 −1.87083 + 1.87083i 3.13207 + 3.13207i 3.00000i 2.25992 + 1.79965i
43.7 0.675544 − 0.675544i 1.22474 + 1.22474i 3.08728i 3.39488 − 3.67080i 1.65474 −1.87083 + 1.87083i 4.78777 + 4.78777i 3.00000i −0.186396 − 4.77318i
43.8 0.992944 − 0.992944i 1.22474 + 1.22474i 2.02813i −2.01954 + 4.57400i 2.43221 1.87083 − 1.87083i 5.98559 + 5.98559i 3.00000i 2.53644 + 6.54701i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 22.12
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.l.a ✓ 24
3.b odd 2 1 315.3.o.b 24
5.b even 2 1 525.3.l.e 24
5.c odd 4 1 inner 105.3.l.a ✓ 24
5.c odd 4 1 525.3.l.e 24
15.e even 4 1 315.3.o.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.l.a ✓ 24 1.a even 1 1 trivial
105.3.l.a ✓ 24 5.c odd 4 1 inner
315.3.o.b 24 3.b odd 2 1
315.3.o.b 24 15.e even 4 1
525.3.l.e 24 5.b even 2 1
525.3.l.e 24 5.c odd 4 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(105, [\chi])\).