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Properties

Label 1190.2.p.e
Level $1190$
Weight $2$
Character orbit 1190.p
Analytic conductor $9.502$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1190,2,Mod(421,1190)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1190, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1190.421");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1190.p (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: \(9.50219784053\)
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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} - 24 q^{4} - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} - 24 q^{4} - 4 q^{6} - 4 q^{11} + 4 q^{12} - 4 q^{13} + 24 q^{16} + 12 q^{17} + 32 q^{18} - 8 q^{21} + 4 q^{22} + 4 q^{24} + 32 q^{27} - 12 q^{29} - 8 q^{30} + 32 q^{31} + 16 q^{33} + 24 q^{35} - 8 q^{37} - 8 q^{38} + 44 q^{39} - 28 q^{41} + 4 q^{44} + 8 q^{45} - 56 q^{47} - 4 q^{48} + 24 q^{50} + 24 q^{51} + 4 q^{52} - 32 q^{54} - 12 q^{55} - 12 q^{57} - 12 q^{58} + 32 q^{61} + 32 q^{62} - 8 q^{63} - 24 q^{64} + 8 q^{65} + 44 q^{67} - 12 q^{68} - 84 q^{69} + 12 q^{71} - 32 q^{72} + 28 q^{73} - 8 q^{74} + 4 q^{75} + 44 q^{78} - 4 q^{79} - 144 q^{81} + 28 q^{82} + 8 q^{84} + 20 q^{86} - 4 q^{88} - 20 q^{89} - 8 q^{90} + 8 q^{91} + 12 q^{95} - 4 q^{96} - 24 q^{97} - 24 q^{98} + 36 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
421.1 − 1.00000i −2.39678 − 2.39678i −1.00000 0.707107 + 0.707107i −2.39678 + 2.39678i 0.707107 − 0.707107i 1.00000i 8.48912i 0.707107 − 0.707107i
421.2 − 1.00000i −2.35600 − 2.35600i −1.00000 −0.707107 − 0.707107i −2.35600 + 2.35600i −0.707107 + 0.707107i 1.00000i 8.10143i −0.707107 + 0.707107i
421.3 − 1.00000i −1.67959 − 1.67959i −1.00000 0.707107 + 0.707107i −1.67959 + 1.67959i 0.707107 − 0.707107i 1.00000i 2.64202i 0.707107 − 0.707107i
421.4 − 1.00000i −0.797871 − 0.797871i −1.00000 −0.707107 − 0.707107i −0.797871 + 0.797871i −0.707107 + 0.707107i 1.00000i − 1.72680i −0.707107 + 0.707107i
421.5 − 1.00000i −0.732199 − 0.732199i −1.00000 −0.707107 − 0.707107i −0.732199 + 0.732199i −0.707107 + 0.707107i 1.00000i − 1.92777i −0.707107 + 0.707107i
421.6 − 1.00000i −0.463969 − 0.463969i −1.00000 0.707107 + 0.707107i −0.463969 + 0.463969i 0.707107 − 0.707107i 1.00000i − 2.56947i 0.707107 − 0.707107i
421.7 − 1.00000i −0.175706 − 0.175706i −1.00000 0.707107 + 0.707107i −0.175706 + 0.175706i 0.707107 − 0.707107i 1.00000i − 2.93825i 0.707107 − 0.707107i
421.8 − 1.00000i 0.502009 + 0.502009i −1.00000 −0.707107 − 0.707107i 0.502009 − 0.502009i −0.707107 + 0.707107i 1.00000i − 2.49597i −0.707107 + 0.707107i
421.9 − 1.00000i 0.901045 + 0.901045i −1.00000 0.707107 + 0.707107i 0.901045 − 0.901045i 0.707107 − 0.707107i 1.00000i − 1.37624i 0.707107 − 0.707107i
421.10 − 1.00000i 1.40078 + 1.40078i −1.00000 0.707107 + 0.707107i 1.40078 − 1.40078i 0.707107 − 0.707107i 1.00000i 0.924392i 0.707107 − 0.707107i
421.11 − 1.00000i 1.56347 + 1.56347i −1.00000 −0.707107 − 0.707107i 1.56347 − 1.56347i −0.707107 + 0.707107i 1.00000i 1.88888i −0.707107 + 0.707107i
421.12 − 1.00000i 2.23480 + 2.23480i −1.00000 −0.707107 − 0.707107i 2.23480 − 2.23480i −0.707107 + 0.707107i 1.00000i 6.98867i −0.707107 + 0.707107i
701.1 1.00000i −2.39678 + 2.39678i −1.00000 0.707107 − 0.707107i −2.39678 − 2.39678i 0.707107 + 0.707107i − 1.00000i − 8.48912i 0.707107 + 0.707107i
701.2 1.00000i −2.35600 + 2.35600i −1.00000 −0.707107 + 0.707107i −2.35600 − 2.35600i −0.707107 − 0.707107i − 1.00000i − 8.10143i −0.707107 − 0.707107i
701.3 1.00000i −1.67959 + 1.67959i −1.00000 0.707107 − 0.707107i −1.67959 − 1.67959i 0.707107 + 0.707107i − 1.00000i − 2.64202i 0.707107 + 0.707107i
701.4 1.00000i −0.797871 + 0.797871i −1.00000 −0.707107 + 0.707107i −0.797871 − 0.797871i −0.707107 − 0.707107i − 1.00000i 1.72680i −0.707107 − 0.707107i
701.5 1.00000i −0.732199 + 0.732199i −1.00000 −0.707107 + 0.707107i −0.732199 − 0.732199i −0.707107 − 0.707107i − 1.00000i 1.92777i −0.707107 − 0.707107i
701.6 1.00000i −0.463969 + 0.463969i −1.00000 0.707107 − 0.707107i −0.463969 − 0.463969i 0.707107 + 0.707107i − 1.00000i 2.56947i 0.707107 + 0.707107i
701.7 1.00000i −0.175706 + 0.175706i −1.00000 0.707107 − 0.707107i −0.175706 − 0.175706i 0.707107 + 0.707107i − 1.00000i 2.93825i 0.707107 + 0.707107i
701.8 1.00000i 0.502009 − 0.502009i −1.00000 −0.707107 + 0.707107i 0.502009 + 0.502009i −0.707107 − 0.707107i − 1.00000i 2.49597i −0.707107 − 0.707107i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 421.12
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1190.2.p.e ✓ 24
17.c even 4 1 inner 1190.2.p.e ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1190.2.p.e ✓ 24 1.a even 1 1 trivial
1190.2.p.e ✓ 24 17.c even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 4 T_{3}^{23} + 8 T_{3}^{22} - 8 T_{3}^{21} + 152 T_{3}^{20} + 572 T_{3}^{19} + 1104 T_{3}^{18} + \cdots + 4096 \) acting on \(S_{2}^{\mathrm{new}}(1190, [\chi])\). Copy content Toggle raw display