Properties

Label 190.3.o.a
Level $190$
Weight $3$
Character orbit 190.o
Analytic conductor $5.177$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [190,3,Mod(29,190)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(190, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 17]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("190.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 190.o (of order \(18\), degree \(6\), 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: \(5.17712502285\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 120 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 120 q - 60 q^{11} + 48 q^{14} + 78 q^{15} - 48 q^{19} - 24 q^{20} + 144 q^{21} - 156 q^{25} + 48 q^{26} - 120 q^{29} - 198 q^{35} - 48 q^{39} - 12 q^{41} - 24 q^{44} - 252 q^{45} + 720 q^{46} + 720 q^{49} - 432 q^{50} + 504 q^{51} + 360 q^{54} - 150 q^{55} - 240 q^{59} + 204 q^{60} - 792 q^{61} - 480 q^{64} + 810 q^{65} - 624 q^{66} + 144 q^{70} - 1560 q^{71} + 144 q^{74} + 72 q^{76} - 984 q^{79} - 336 q^{81} - 1080 q^{84} - 708 q^{85} - 192 q^{86} - 528 q^{89} - 576 q^{90} + 312 q^{91} + 114 q^{95} + 1836 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 −0.245576 1.39273i −3.99079 + 3.34867i −1.87939 + 0.684040i 2.53312 4.31083i 5.64382 + 4.73573i −8.01154 4.62547i 1.41421 + 2.44949i 3.14997 17.8644i −6.62589 2.46931i
29.2 −0.245576 1.39273i −3.88588 + 3.26064i −1.87939 + 0.684040i −3.86795 + 3.16843i 5.49546 + 4.61124i 3.11910 + 1.80081i 1.41421 + 2.44949i 2.90545 16.4776i 5.36264 + 4.60892i
29.3 −0.245576 1.39273i −2.27829 + 1.91171i −1.87939 + 0.684040i 3.94596 + 3.07073i 3.22199 + 2.70357i −5.25836 3.03592i 1.41421 + 2.44949i −0.0268715 + 0.152396i 3.30766 6.24975i
29.4 −0.245576 1.39273i −1.00496 + 0.843264i −1.87939 + 0.684040i −4.42892 2.32048i 1.42123 + 1.19256i 5.78989 + 3.34280i 1.41421 + 2.44949i −1.26398 + 7.16837i −2.14417 + 6.73814i
29.5 −0.245576 1.39273i −0.344931 + 0.289432i −1.87939 + 0.684040i 4.98850 0.338993i 0.487806 + 0.409318i 3.92642 + 2.26692i 1.41421 + 2.44949i −1.52763 + 8.66360i −1.69718 6.86437i
29.6 −0.245576 1.39273i 0.718479 0.602876i −1.87939 + 0.684040i −2.46682 + 4.34911i −1.01608 0.852595i −5.60642 3.23687i 1.41421 + 2.44949i −1.41008 + 7.99696i 6.66293 + 2.36758i
29.7 −0.245576 1.39273i 1.55916 1.30829i −1.87939 + 0.684040i 1.56822 4.74770i −2.20498 1.85020i −7.83152 4.52153i 1.41421 + 2.44949i −0.843479 + 4.78361i −6.99738 1.01818i
29.8 −0.245576 1.39273i 2.03549 1.70798i −1.87939 + 0.684040i 1.01591 + 4.89571i −2.87862 2.41545i 10.4469 + 6.03154i 1.41421 + 2.44949i −0.336806 + 1.91012i 6.56891 2.61715i
29.9 −0.245576 1.39273i 3.34876 2.80994i −1.87939 + 0.684040i −4.92535 + 0.860784i −4.73586 3.97386i −1.74818 1.00931i 1.41421 + 2.44949i 1.75558 9.95640i 2.40838 + 6.64828i
29.10 −0.245576 1.39273i 3.84296 3.22462i −1.87939 + 0.684040i 2.57704 4.28473i −5.43476 4.56031i 6.84923 + 3.95441i 1.41421 + 2.44949i 2.80729 15.9209i −6.60032 2.53689i
29.11 0.245576 + 1.39273i −3.84296 + 3.22462i −1.87939 + 0.684040i −0.780045 + 4.93878i −5.43476 4.56031i −6.84923 3.95441i −1.41421 2.44949i 2.80729 15.9209i −7.06994 + 0.126453i
29.12 0.245576 + 1.39273i −3.34876 + 2.80994i −1.87939 + 0.684040i −3.21973 3.82535i −4.73586 3.97386i 1.74818 + 1.00931i −1.41421 2.44949i 1.75558 9.95640i 4.53699 5.42363i
29.13 0.245576 + 1.39273i −2.03549 + 1.70798i −1.87939 + 0.684040i 3.92513 3.09732i −2.87862 2.41545i −10.4469 6.03154i −1.41421 2.44949i −0.336806 + 1.91012i 5.27764 + 4.70601i
29.14 0.245576 + 1.39273i −1.55916 + 1.30829i −1.87939 + 0.684040i −1.85044 + 4.64498i −2.20498 1.85020i 7.83152 + 4.52153i −1.41421 2.44949i −0.843479 + 4.78361i −6.92362 1.43647i
29.15 0.245576 + 1.39273i −0.718479 + 0.602876i −1.87939 + 0.684040i 0.905861 4.91726i −1.01608 0.852595i 5.60642 + 3.23687i −1.41421 2.44949i −1.41008 + 7.99696i 7.07086 + 0.0540596i
29.16 0.245576 + 1.39273i 0.344931 0.289432i −1.87939 + 0.684040i 3.60351 + 3.46623i 0.487806 + 0.409318i −3.92642 2.26692i −1.41421 2.44949i −1.52763 + 8.66360i −3.94258 + 5.86993i
29.17 0.245576 + 1.39273i 1.00496 0.843264i −1.87939 + 0.684040i −4.88433 1.06926i 1.42123 + 1.19256i −5.78989 3.34280i −1.41421 2.44949i −1.26398 + 7.16837i 0.289722 7.06513i
29.18 0.245576 + 1.39273i 2.27829 1.91171i −1.87939 + 0.684040i 4.99661 + 0.184101i 3.22199 + 2.70357i 5.25836 + 3.03592i −1.41421 2.44949i −0.0268715 + 0.152396i 0.970642 + 7.00413i
29.19 0.245576 + 1.39273i 3.88588 3.26064i −1.87939 + 0.684040i −0.926396 4.91343i 5.49546 + 4.61124i −3.11910 1.80081i −1.41421 2.44949i 2.90545 16.4776i 6.61557 2.49684i
29.20 0.245576 + 1.39273i 3.99079 3.34867i −1.87939 + 0.684040i −0.830467 + 4.93055i 5.64382 + 4.73573i 8.01154 + 4.62547i −1.41421 2.44949i 3.14997 17.8644i −7.07086 + 0.0542075i
See next 80 embeddings (of 120 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.f odd 18 1 inner
95.o odd 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 190.3.o.a 120
5.b even 2 1 inner 190.3.o.a 120
19.f odd 18 1 inner 190.3.o.a 120
95.o odd 18 1 inner 190.3.o.a 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.3.o.a 120 1.a even 1 1 trivial
190.3.o.a 120 5.b even 2 1 inner
190.3.o.a 120 19.f odd 18 1 inner
190.3.o.a 120 95.o odd 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(190, [\chi])\).