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Properties

Label 230.5.d.a
Level $230$
Weight $5$
Character orbit 230.d
Analytic conductor $23.775$
Analytic rank $0$
Dimension $32$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [230,5,Mod(91,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.91");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), 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: \(23.7750915093\)
Analytic rank: \(0\)
Dimension: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39}+ \cdots + 43008 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
91.1 −2.82843 −5.93906 8.00000 − 11.1803i 16.7982 − 85.3294i −22.6274 −45.7275 31.6228i
91.2 −2.82843 −11.3966 8.00000 11.1803i 32.2344 − 85.1794i −22.6274 48.8818 − 31.6228i
91.3 −2.82843 7.33271 8.00000 11.1803i −20.7400 − 75.6542i −22.6274 −27.2314 − 31.6228i
91.4 −2.82843 15.6893 8.00000 11.1803i −44.3761 65.6030i −22.6274 165.154 − 31.6228i
91.5 −2.82843 −5.71864 8.00000 − 11.1803i 16.1747 − 36.1607i −22.6274 −48.2972 31.6228i
91.6 −2.82843 −14.3217 8.00000 11.1803i 40.5079 16.7293i −22.6274 124.111 − 31.6228i
91.7 −2.82843 0.828614 8.00000 − 11.1803i −2.34367 16.9191i −22.6274 −80.3134 31.6228i
91.8 −2.82843 7.86848 8.00000 − 11.1803i −22.2554 − 5.16947i −22.6274 −19.0870 31.6228i
91.9 −2.82843 7.86848 8.00000 11.1803i −22.2554 5.16947i −22.6274 −19.0870 − 31.6228i
91.10 −2.82843 0.828614 8.00000 11.1803i −2.34367 − 16.9191i −22.6274 −80.3134 − 31.6228i
91.11 −2.82843 −14.3217 8.00000 − 11.1803i 40.5079 − 16.7293i −22.6274 124.111 31.6228i
91.12 −2.82843 −5.71864 8.00000 11.1803i 16.1747 36.1607i −22.6274 −48.2972 − 31.6228i
91.13 −2.82843 15.6893 8.00000 − 11.1803i −44.3761 − 65.6030i −22.6274 165.154 31.6228i
91.14 −2.82843 7.33271 8.00000 − 11.1803i −20.7400 75.6542i −22.6274 −27.2314 31.6228i
91.15 −2.82843 −11.3966 8.00000 − 11.1803i 32.2344 85.1794i −22.6274 48.8818 31.6228i
91.16 −2.82843 −5.93906 8.00000 11.1803i 16.7982 85.3294i −22.6274 −45.7275 − 31.6228i
91.17 2.82843 17.4598 8.00000 11.1803i 49.3837 − 69.3646i 22.6274 223.844 31.6228i
91.18 2.82843 −0.0560696 8.00000 − 11.1803i −0.158589 58.4359i 22.6274 −80.9969 − 31.6228i
91.19 2.82843 11.3074 8.00000 − 11.1803i 31.9821 − 52.5241i 22.6274 46.8567 − 31.6228i
91.20 2.82843 −2.20532 8.00000 − 11.1803i −6.23758 − 53.7736i 22.6274 −76.1366 − 31.6228i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 91.32
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 230.5.d.a ✓ 32
23.b odd 2 1 inner 230.5.d.a ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
230.5.d.a ✓ 32 1.a even 1 1 trivial
230.5.d.a ✓ 32 23.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(230, [\chi])\).