↑

Properties

Label 190.3.l.c
Level $190$
Weight $3$
Character orbit 190.l
Analytic conductor $5.177$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [190,3,Mod(7,190)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(190, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("190.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 190.l (of order \(12\), 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: \(5.17712502285\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 18 q^{2} + 6 q^{3} - 10 q^{5} + 12 q^{6} - 28 q^{7} - 72 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 36 q - 18 q^{2} + 6 q^{3} - 10 q^{5} + 12 q^{6} - 28 q^{7} - 72 q^{8} - 16 q^{10} - 12 q^{11} - 24 q^{12} + 2 q^{15} + 72 q^{16} + 56 q^{17} + 148 q^{18} + 24 q^{20} + 104 q^{21} + 6 q^{22} - 22 q^{23} - 32 q^{25} + 180 q^{27} - 28 q^{28} + 28 q^{30} - 348 q^{31} + 72 q^{32} + 50 q^{33} - 184 q^{35} - 148 q^{36} - 60 q^{37} - 76 q^{38} + 8 q^{40} - 12 q^{41} + 104 q^{42} - 272 q^{43} + 400 q^{45} + 88 q^{46} - 94 q^{47} - 24 q^{48} + 128 q^{50} + 136 q^{51} - 128 q^{53} - 48 q^{55} + 112 q^{56} + 66 q^{57} - 100 q^{58} - 32 q^{60} - 34 q^{61} + 174 q^{62} - 22 q^{63} - 752 q^{65} + 100 q^{66} + 192 q^{67} + 224 q^{68} - 280 q^{70} + 26 q^{71} - 148 q^{72} + 186 q^{73} + 204 q^{75} + 148 q^{76} + 500 q^{77} - 512 q^{78} + 40 q^{80} + 414 q^{81} - 12 q^{82} - 360 q^{83} - 392 q^{85} - 544 q^{86} - 740 q^{87} + 24 q^{88} - 450 q^{90} + 284 q^{91} - 44 q^{92} + 370 q^{93} + 34 q^{95} + 96 q^{96} + 16 q^{97} + 170 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 0.366025 − 1.36603i −5.06796 − 1.35795i −1.73205 − 1.00000i −1.00987 − 4.89696i −3.71000 + 6.42591i −4.30335 − 4.30335i −2.00000 + 2.00000i 16.0459 + 9.26411i −7.05900 − 0.412907i
7.2 0.366025 − 1.36603i −3.08170 − 0.825740i −1.73205 − 1.00000i −4.74395 + 1.57954i −2.25596 + 3.90744i 3.30100 + 3.30100i −2.00000 + 2.00000i 1.02082 + 0.589373i 0.421289 + 7.05851i
7.3 0.366025 − 1.36603i −2.85314 − 0.764497i −1.73205 − 1.00000i 3.94944 + 3.06626i −2.08864 + 3.61764i −5.58717 − 5.58717i −2.00000 + 2.00000i −0.238275 − 0.137568i 5.63418 − 4.27270i
7.4 0.366025 − 1.36603i −0.417218 − 0.111793i −1.73205 − 1.00000i 2.51535 − 4.32123i −0.305425 + 0.529012i −0.608829 − 0.608829i −2.00000 + 2.00000i −7.63266 − 4.40672i −4.98222 − 5.01771i
7.5 0.366025 − 1.36603i 0.0364092 + 0.00975582i −1.73205 − 1.00000i −3.98152 + 3.02449i 0.0266534 − 0.0461650i 1.50004 + 1.50004i −2.00000 + 2.00000i −7.79300 − 4.49929i 2.67419 + 6.54589i
7.6 0.366025 − 1.36603i 2.25332 + 0.603775i −1.73205 − 1.00000i −4.51562 − 2.14689i 1.64954 − 2.85709i −6.75499 − 6.75499i −2.00000 + 2.00000i −3.08133 − 1.77901i −4.58554 + 5.38264i
7.7 0.366025 − 1.36603i 2.97773 + 0.797879i −1.73205 − 1.00000i 0.585242 + 4.96563i 2.17985 − 3.77560i 4.22403 + 4.22403i −2.00000 + 2.00000i 0.436008 + 0.251729i 6.99739 + 1.01809i
7.8 0.366025 − 1.36603i 4.88398 + 1.30866i −1.73205 − 1.00000i 4.99993 − 0.0258159i 3.57532 − 6.19263i −7.61700 − 7.61700i −2.00000 + 2.00000i 14.3464 + 8.28290i 1.79484 − 6.83949i
7.9 0.366025 − 1.36603i 5.36667 + 1.43799i −1.73205 − 1.00000i −2.89709 − 4.07516i 3.92867 − 6.80466i 8.84626 + 8.84626i −2.00000 + 2.00000i 18.9391 + 10.9345i −6.62717 + 2.46588i
83.1 −1.36603 − 0.366025i −1.43799 + 5.36667i 1.73205 + 1.00000i −2.08064 − 4.54653i 3.92867 − 6.80466i 8.84626 − 8.84626i −2.00000 − 2.00000i −18.9391 − 10.9345i 1.17807 + 6.97224i
83.2 −1.36603 − 0.366025i −1.30866 + 4.88398i 1.73205 + 1.00000i −2.52232 + 4.31716i 3.57532 − 6.19263i −7.61700 + 7.61700i −2.00000 − 2.00000i −14.3464 − 8.28290i 5.02575 − 4.97412i
83.3 −1.36603 − 0.366025i −0.797879 + 2.97773i 1.73205 + 1.00000i 4.00774 + 2.98965i 2.17985 − 3.77560i 4.22403 − 4.22403i −2.00000 − 2.00000i −0.436008 − 0.251729i −4.38039 − 5.55087i
83.4 −1.36603 − 0.366025i −0.603775 + 2.25332i 1.73205 + 1.00000i 0.398548 − 4.98409i 1.64954 − 2.85709i −6.75499 + 6.75499i −2.00000 − 2.00000i 3.08133 + 1.77901i −2.36873 + 6.66252i
83.5 −1.36603 − 0.366025i −0.00975582 + 0.0364092i 1.73205 + 1.00000i 4.61004 − 1.93585i 0.0266534 − 0.0461650i 1.50004 − 1.50004i −2.00000 − 2.00000i 7.79300 + 4.49929i −7.00600 + 0.957029i
83.6 −1.36603 − 0.366025i 0.111793 − 0.417218i 1.73205 + 1.00000i −4.99997 + 0.0177450i −0.305425 + 0.529012i −0.608829 + 0.608829i −2.00000 − 2.00000i 7.63266 + 4.40672i 6.83658 + 1.80588i
83.7 −1.36603 − 0.366025i 0.764497 − 2.85314i 1.73205 + 1.00000i 0.680740 + 4.95344i −2.08864 + 3.61764i −5.58717 + 5.58717i −2.00000 − 2.00000i 0.238275 + 0.137568i 0.883178 − 7.01570i
83.8 −1.36603 − 0.366025i 0.825740 − 3.08170i 1.73205 + 1.00000i 3.73990 − 3.31861i −2.25596 + 3.90744i 3.30100 − 3.30100i −2.00000 − 2.00000i −1.02082 − 0.589373i −6.32349 + 3.16441i
83.9 −1.36603 − 0.366025i 1.35795 − 5.06796i 1.73205 + 1.00000i −3.73595 − 3.32305i −3.71000 + 6.42591i −4.30335 + 4.30335i −2.00000 − 2.00000i −16.0459 − 9.26411i 3.88709 + 5.90682i
87.1 −1.36603 + 0.366025i −1.43799 − 5.36667i 1.73205 − 1.00000i −2.08064 + 4.54653i 3.92867 + 6.80466i 8.84626 + 8.84626i −2.00000 + 2.00000i −18.9391 + 10.9345i 1.17807 − 6.97224i
87.2 −1.36603 + 0.366025i −1.30866 − 4.88398i 1.73205 − 1.00000i −2.52232 − 4.31716i 3.57532 + 6.19263i −7.61700 − 7.61700i −2.00000 + 2.00000i −14.3464 + 8.28290i 5.02575 + 4.97412i
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.9
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
19.c even 3 1 inner
95.m odd 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 190.3.l.c ✓ 36
5.c odd 4 1 inner 190.3.l.c ✓ 36
19.c even 3 1 inner 190.3.l.c ✓ 36
95.m odd 12 1 inner 190.3.l.c ✓ 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.3.l.c ✓ 36 1.a even 1 1 trivial
190.3.l.c ✓ 36 5.c odd 4 1 inner
190.3.l.c ✓ 36 19.c even 3 1 inner
190.3.l.c ✓ 36 95.m odd 12 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{36} - 6 T_{3}^{35} + 18 T_{3}^{34} - 168 T_{3}^{33} - 486 T_{3}^{32} + 6800 T_{3}^{31} + \cdots + 699602500 \) acting on \(S_{3}^{\mathrm{new}}(190, [\chi])\). Copy content Toggle raw display