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Properties

Label 1190.2.g.d
Level $1190$
Weight $2$
Character orbit 1190.g
Analytic conductor $9.502$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1190,2,Mod(169,1190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1190.169"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1190.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.50219784053\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 10 q^{3} - 24 q^{4} + 4 q^{5} + 24 q^{7} + 18 q^{9} + 4 q^{10} - 10 q^{12} - 6 q^{15} + 24 q^{16} - 16 q^{17} - 14 q^{19} - 4 q^{20} + 10 q^{21} - 2 q^{22} - 14 q^{23} + 16 q^{25} - 4 q^{26} + 52 q^{27}+ \cdots - 24 q^{97}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
169.1 − 1.00000i 3.27794 −1.00000 2.02001 − 0.958943i − 3.27794i 1.00000 1.00000i 7.74492 −0.958943 − 2.02001i
169.2 1.00000i 3.27794 −1.00000 2.02001 + 0.958943i 3.27794i 1.00000 − 1.00000i 7.74492 −0.958943 + 2.02001i
169.3 − 1.00000i −2.81638 −1.00000 1.66117 + 1.49684i 2.81638i 1.00000 1.00000i 4.93199 1.49684 − 1.66117i
169.4 1.00000i −2.81638 −1.00000 1.66117 − 1.49684i − 2.81638i 1.00000 − 1.00000i 4.93199 1.49684 + 1.66117i
169.5 − 1.00000i 1.54175 −1.00000 1.31588 − 1.80789i − 1.54175i 1.00000 1.00000i −0.623005 −1.80789 − 1.31588i
169.6 1.00000i 1.54175 −1.00000 1.31588 + 1.80789i 1.54175i 1.00000 − 1.00000i −0.623005 −1.80789 + 1.31588i
169.7 − 1.00000i −1.62649 −1.00000 2.16676 + 0.552397i 1.62649i 1.00000 1.00000i −0.354542 0.552397 − 2.16676i
169.8 1.00000i −1.62649 −1.00000 2.16676 − 0.552397i − 1.62649i 1.00000 − 1.00000i −0.354542 0.552397 + 2.16676i
169.9 − 1.00000i 3.07161 −1.00000 −1.96828 + 1.06107i − 3.07161i 1.00000 1.00000i 6.43479 1.06107 + 1.96828i
169.10 1.00000i 3.07161 −1.00000 −1.96828 − 1.06107i 3.07161i 1.00000 − 1.00000i 6.43479 1.06107 − 1.96828i
169.11 − 1.00000i −0.129014 −1.00000 2.23581 − 0.0342441i 0.129014i 1.00000 1.00000i −2.98336 −0.0342441 − 2.23581i
169.12 1.00000i −0.129014 −1.00000 2.23581 + 0.0342441i − 0.129014i 1.00000 − 1.00000i −2.98336 −0.0342441 + 2.23581i
169.13 − 1.00000i 1.13790 −1.00000 −1.14870 + 1.91846i − 1.13790i 1.00000 1.00000i −1.70517 1.91846 + 1.14870i
169.14 1.00000i 1.13790 −1.00000 −1.14870 − 1.91846i 1.13790i 1.00000 − 1.00000i −1.70517 1.91846 − 1.14870i
169.15 − 1.00000i −1.27851 −1.00000 0.138084 − 2.23180i 1.27851i 1.00000 1.00000i −1.36542 −2.23180 − 0.138084i
169.16 1.00000i −1.27851 −1.00000 0.138084 + 2.23180i − 1.27851i 1.00000 − 1.00000i −1.36542 −2.23180 + 0.138084i
169.17 − 1.00000i −0.432187 −1.00000 −1.67673 + 1.47938i 0.432187i 1.00000 1.00000i −2.81321 1.47938 + 1.67673i
169.18 1.00000i −0.432187 −1.00000 −1.67673 − 1.47938i − 0.432187i 1.00000 − 1.00000i −2.81321 1.47938 − 1.67673i
169.19 − 1.00000i −1.19927 −1.00000 −2.22599 + 0.212063i 1.19927i 1.00000 1.00000i −1.56176 0.212063 + 2.22599i
169.20 1.00000i −1.19927 −1.00000 −2.22599 − 0.212063i − 1.19927i 1.00000 − 1.00000i −1.56176 0.212063 − 2.22599i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 169.24
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
85.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1190.2.g.d yes 24
5.b even 2 1 1190.2.g.c ✓ 24
17.b even 2 1 1190.2.g.c ✓ 24
85.c even 2 1 inner 1190.2.g.d yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1190.2.g.c ✓ 24 5.b even 2 1
1190.2.g.c ✓ 24 17.b even 2 1
1190.2.g.d yes 24 1.a even 1 1 trivial
1190.2.g.d yes 24 85.c even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 5 T_{3}^{11} - 10 T_{3}^{10} + 73 T_{3}^{9} + 9 T_{3}^{8} - 340 T_{3}^{7} + 80 T_{3}^{6} + \cdots + 16 \) acting on \(S_{2}^{\mathrm{new}}(1190, [\chi])\). Copy content Toggle raw display