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Properties

Label 190.2.m.b
Level $190$
Weight $2$
Character orbit 190.m
Analytic conductor $1.517$
Analytic rank $0$
Dimension $32$
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] = [190,2,Mod(27,190)]
 
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, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("190.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 190.m (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: \(1.51715763840\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 12 q^{3} + 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 12 q^{3} + 24 q^{7} - 12 q^{10} - 16 q^{11} + 24 q^{13} + 12 q^{15} + 16 q^{16} - 8 q^{17} + 8 q^{20} - 12 q^{22} + 4 q^{23} + 4 q^{25} - 16 q^{26} - 12 q^{28} - 40 q^{30} - 24 q^{33} - 20 q^{35} - 8 q^{36} + 16 q^{38} + 24 q^{41} + 20 q^{42} - 24 q^{43} - 80 q^{45} - 36 q^{47} - 12 q^{48} + 24 q^{51} + 24 q^{52} - 72 q^{53} - 24 q^{57} + 24 q^{58} - 48 q^{60} - 48 q^{61} - 4 q^{62} + 16 q^{63} + 32 q^{66} + 36 q^{67} + 16 q^{68} + 12 q^{70} + 24 q^{71} + 8 q^{73} - 24 q^{77} - 24 q^{78} + 56 q^{81} + 8 q^{82} + 24 q^{83} + 52 q^{85} + 104 q^{87} + 12 q^{90} - 24 q^{91} - 4 q^{92} + 52 q^{93} + 36 q^{95} - 24 q^{97} + 72 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
27.1 −0.258819 − 0.965926i −3.24379 + 0.869171i −0.866025 + 0.500000i −1.39667 − 1.74623i 1.67911 + 2.90830i 2.68888 + 2.68888i 0.707107 + 0.707107i 7.16865 − 4.13882i −1.32524 + 1.80104i
27.2 −0.258819 − 0.965926i −0.405580 + 0.108675i −0.866025 + 0.500000i 0.295440 + 2.21646i 0.209944 + 0.363633i 2.14890 + 2.14890i 0.707107 + 0.707107i −2.44539 + 1.41185i 2.06447 − 0.859036i
27.3 −0.258819 − 0.965926i −0.239238 + 0.0641036i −0.866025 + 0.500000i −1.90126 − 1.17696i 0.123839 + 0.214495i −2.17543 − 2.17543i 0.707107 + 0.707107i −2.54495 + 1.46933i −0.644773 + 2.14109i
27.4 −0.258819 − 0.965926i 1.52258 − 0.407975i −0.866025 + 0.500000i 1.68817 − 1.46631i −0.788148 − 1.36511i 2.78714 + 2.78714i 0.707107 + 0.707107i −0.446257 + 0.257647i −1.85328 − 1.25114i
27.5 0.258819 + 0.965926i −2.53935 + 0.680416i −0.866025 + 0.500000i 0.379052 − 2.20371i −1.31446 − 2.27672i −2.47691 − 2.47691i −0.707107 − 0.707107i 3.38724 − 1.95563i 2.22672 − 0.204225i
27.6 0.258819 + 0.965926i −1.26216 + 0.338196i −0.866025 + 0.500000i −2.22692 + 0.202078i −0.653344 − 1.13162i 1.48691 + 1.48691i −0.707107 − 0.707107i −1.11940 + 0.646284i −0.771561 − 2.09874i
27.7 0.258819 + 0.965926i −0.694795 + 0.186170i −0.866025 + 0.500000i 1.99447 + 1.01098i −0.359652 − 0.622936i 1.01416 + 1.01416i −0.707107 − 0.707107i −2.15000 + 1.24130i −0.460324 + 2.18817i
27.8 0.258819 + 0.965926i 2.13028 − 0.570807i −0.866025 + 0.500000i −0.564344 + 2.16368i 1.10271 + 1.90996i 0.526345 + 0.526345i −0.707107 − 0.707107i 1.61420 − 0.931958i −2.23602 + 0.0148872i
103.1 −0.965926 + 0.258819i −0.869171 − 3.24379i 0.866025 − 0.500000i 2.21061 + 0.336439i 1.67911 + 2.90830i 2.68888 − 2.68888i −0.707107 + 0.707107i −7.16865 + 4.13882i −2.22236 + 0.247174i
103.2 −0.965926 + 0.258819i −0.108675 − 0.405580i 0.866025 − 0.500000i −2.06723 + 0.852374i 0.209944 + 0.363633i 2.14890 − 2.14890i −0.707107 + 0.707107i 2.44539 − 1.41185i 1.77618 − 1.35837i
103.3 −0.965926 + 0.258819i −0.0641036 − 0.239238i 0.866025 − 0.500000i 1.96990 + 1.05806i 0.123839 + 0.214495i −2.17543 + 2.17543i −0.707107 + 0.707107i 2.54495 − 1.46933i −2.17663 − 0.512156i
103.4 −0.965926 + 0.258819i 0.407975 + 1.52258i 0.866025 − 0.500000i 0.425777 − 2.19516i −0.788148 − 1.36511i 2.78714 − 2.78714i −0.707107 + 0.707107i 0.446257 − 0.257647i 0.156879 + 2.23056i
103.5 0.965926 − 0.258819i −0.680416 − 2.53935i 0.866025 − 0.500000i 1.71894 − 1.43012i −1.31446 − 2.27672i −2.47691 + 2.47691i 0.707107 − 0.707107i −3.38724 + 1.95563i 1.29022 − 1.82629i
103.6 0.965926 − 0.258819i −0.338196 − 1.26216i 0.866025 − 0.500000i 0.938455 + 2.02961i −0.653344 − 1.13162i 1.48691 − 1.48691i 0.707107 − 0.707107i 1.11940 − 0.646284i 1.43178 + 1.71756i
103.7 0.965926 − 0.258819i −0.186170 − 0.694795i 0.866025 − 0.500000i −1.87277 − 1.22177i −0.359652 − 0.622936i 1.01416 − 1.01416i 0.707107 − 0.707107i 2.15000 − 1.24130i −2.12518 − 0.695434i
103.8 0.965926 − 0.258819i 0.570807 + 2.13028i 0.866025 − 0.500000i −1.59163 + 1.57058i 1.10271 + 1.90996i 0.526345 − 0.526345i 0.707107 − 0.707107i −1.61420 + 0.931958i −1.13090 + 1.92901i
107.1 −0.965926 − 0.258819i −0.869171 + 3.24379i 0.866025 + 0.500000i 2.21061 − 0.336439i 1.67911 − 2.90830i 2.68888 + 2.68888i −0.707107 − 0.707107i −7.16865 − 4.13882i −2.22236 − 0.247174i
107.2 −0.965926 − 0.258819i −0.108675 + 0.405580i 0.866025 + 0.500000i −2.06723 − 0.852374i 0.209944 − 0.363633i 2.14890 + 2.14890i −0.707107 − 0.707107i 2.44539 + 1.41185i 1.77618 + 1.35837i
107.3 −0.965926 − 0.258819i −0.0641036 + 0.239238i 0.866025 + 0.500000i 1.96990 − 1.05806i 0.123839 − 0.214495i −2.17543 − 2.17543i −0.707107 − 0.707107i 2.54495 + 1.46933i −2.17663 + 0.512156i
107.4 −0.965926 − 0.258819i 0.407975 − 1.52258i 0.866025 + 0.500000i 0.425777 + 2.19516i −0.788148 + 1.36511i 2.78714 + 2.78714i −0.707107 − 0.707107i 0.446257 + 0.257647i 0.156879 − 2.23056i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 27.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
19.d odd 6 1 inner
95.l even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 190.2.m.b ✓ 32
5.b even 2 1 950.2.q.g 32
5.c odd 4 1 inner 190.2.m.b ✓ 32
5.c odd 4 1 950.2.q.g 32
19.d odd 6 1 inner 190.2.m.b ✓ 32
95.h odd 6 1 950.2.q.g 32
95.l even 12 1 inner 190.2.m.b ✓ 32
95.l even 12 1 950.2.q.g 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.m.b ✓ 32 1.a even 1 1 trivial
190.2.m.b ✓ 32 5.c odd 4 1 inner
190.2.m.b ✓ 32 19.d odd 6 1 inner
190.2.m.b ✓ 32 95.l even 12 1 inner
950.2.q.g 32 5.b even 2 1
950.2.q.g 32 5.c odd 4 1
950.2.q.g 32 95.h odd 6 1
950.2.q.g 32 95.l even 12 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{32} + 12 T_{3}^{31} + 72 T_{3}^{30} + 288 T_{3}^{29} + 760 T_{3}^{28} + 1068 T_{3}^{27} + \cdots + 81 \) acting on \(S_{2}^{\mathrm{new}}(190, [\chi])\). Copy content Toggle raw display