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Properties

Label 1.290.a.a
Level $1$
Weight $290$
Character orbit 1.a
Self dual yes
Analytic conductor $528.905$
Dimension $23$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1,290,Mod(1,1)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1, base_ring=CyclotomicField(1))
 
chi = DirichletCharacter(H, H._module([]))
 
N = Newforms(chi, 290, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1.1");
 
S:= CuspForms(chi, 290);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 290 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

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: yes
Analytic conductor: \(528.905022031\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 50\!\cdots\!68 q^{2}+ \cdots + 66\!\cdots\!79 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 23 q - 50\!\cdots\!68 q^{2}+ \cdots - 92\!\cdots\!32 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −5.94123e43 7.59130e68 2.53518e87 4.28191e100 −4.51017e112 −4.70987e121 −9.15264e130 −1.96478e137 −2.54398e144
1.2 −5.48207e43 −1.38141e69 2.01066e87 1.33294e101 7.57300e112 −9.98733e120 −5.56988e130 1.13554e138 −7.30727e144
1.3 −5.45130e43 −7.20355e68 1.97702e87 −1.86087e101 3.92688e112 1.35957e122 −5.35524e130 −2.53845e137 1.01441e145
1.4 −4.35939e43 −3.64199e68 9.05785e86 −2.41347e100 1.58769e112 −9.07756e121 3.87381e129 −6.40115e137 1.05213e144
1.5 −4.29810e43 1.22113e69 8.52717e86 −2.03941e100 −5.24853e112 2.27248e122 6.10028e129 7.18397e137 8.76560e143
1.6 −3.62259e43 1.53864e69 3.17671e86 −1.59896e101 −5.57387e112 −2.55521e122 2.45240e130 1.59466e138 5.79237e144
1.7 −3.27259e43 5.48575e68 7.63382e85 1.49451e101 −1.79526e112 −5.69165e121 3.00525e130 −4.71822e137 −4.89091e144
1.8 −2.69338e43 −8.10620e68 −2.69215e86 9.42484e100 2.18331e112 2.55569e122 3.40406e130 −1.15652e137 −2.53847e144
1.9 −2.15060e43 −1.48175e69 −5.32138e86 −5.84878e100 3.18664e112 −1.03571e122 3.28350e130 1.42281e138 1.25784e144
1.10 −1.29064e43 1.85758e68 −8.28071e86 −1.02208e101 −2.39746e111 2.00179e121 2.35247e130 −7.38251e137 1.31914e144
1.11 −5.08313e42 1.39918e69 −9.68808e86 1.03761e101 −7.11222e111 −1.23041e121 9.98050e129 1.18495e138 −5.27430e143
1.12 5.60133e42 −3.14807e68 −9.63272e86 1.00623e101 −1.76334e111 −2.24923e122 −1.09670e130 −6.73653e137 5.63623e143
1.13 6.30739e42 −9.90604e68 −9.54863e86 1.10261e101 −6.24812e111 7.41407e121 −1.22963e130 2.08539e137 6.95456e143
1.14 9.46958e42 8.35963e68 −9.04973e86 −7.59820e100 7.91622e111 9.75123e121 −1.79886e130 −7.39229e136 −7.19518e143
1.15 1.99387e43 −1.22289e69 −5.97096e86 −1.52923e101 −2.43827e112 1.75556e122 −3.17372e130 7.22699e137 −3.04909e144
1.16 2.92626e43 −9.62795e68 −1.38345e86 −5.33136e100 −2.81739e112 −1.00480e122 −3.31543e130 1.54218e137 −1.56010e144
1.17 3.08639e43 1.42187e69 −4.20657e85 8.41043e99 4.38844e112 −6.16222e121 −3.19970e130 1.24895e138 2.59579e143
1.18 3.52874e43 2.15811e68 2.50553e86 1.03960e101 7.61541e111 1.35922e122 −2.62571e130 −7.26182e137 3.66848e144
1.19 3.61003e43 4.02889e68 3.08585e86 −1.40948e101 1.45444e112 −2.16739e122 −2.47670e130 −6.10437e137 −5.08827e144
1.20 4.71267e43 −1.69535e69 1.22628e87 1.36810e101 −7.98965e112 −6.49457e121 1.09163e130 2.10147e138 6.44741e144
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1.290.a.a ✓ 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1.290.a.a ✓ 23 1.a even 1 1 trivial

Hecke kernels

This newform subspace is the entire newspace \(S_{290}^{\mathrm{new}}(\Gamma_0(1))\).