↑

Properties

Label 95.5.c.a
Level $95$
Weight $5$
Character orbit 95.c
Analytic conductor $9.820$
Analytic rank $0$
Dimension $28$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,5,Mod(56,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, 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("95.56");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.c (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: \(9.82014649297\)
Analytic rank: \(0\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 284 q^{4} - 28 q^{6} - 100 q^{7} - 528 q^{9} + 192 q^{11} + 2532 q^{16} - 588 q^{17} - 168 q^{19} - 1092 q^{23} + 148 q^{24} + 3500 q^{25} - 2820 q^{26} + 892 q^{28} + 1400 q^{30} - 1200 q^{35} + 11248 q^{36}+ \cdots - 39240 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
56.1 − 7.92395i − 5.43565i −46.7890 11.1803 −43.0718 −60.1635 243.970i 51.4538 − 88.5925i
56.2 − 7.45519i 11.0671i −39.5799 −11.1803 82.5076 21.0582 175.793i −41.4815 83.3516i
56.3 − 6.90314i − 16.4787i −31.6533 −11.1803 −113.755 57.7266 108.057i −190.547 77.1794i
56.4 − 6.39140i − 4.27611i −24.8500 −11.1803 −27.3303 −38.7085 56.5639i 62.7149 71.4580i
56.5 − 6.32523i 3.88173i −24.0086 11.1803 24.5529 86.4193 50.6561i 65.9322 − 70.7183i
56.6 − 5.90838i 15.4645i −18.9089 11.1803 91.3703 −35.5188 17.1871i −158.152 − 66.0577i
56.7 − 4.90974i 9.78357i −8.10557 −11.1803 48.0348 −28.2223 − 38.7596i −14.7183 54.8926i
56.8 − 4.66049i − 13.7041i −5.72016 11.1803 −63.8680 −20.1107 − 47.9091i −106.804 − 52.1059i
56.9 − 4.17612i 4.97310i −1.43996 11.1803 20.7682 −77.5528 − 60.8044i 56.2683 − 46.6904i
56.10 − 2.69165i − 5.53366i 8.75502 −11.1803 −14.8947 68.1779 − 66.6319i 50.3786 30.0936i
56.11 − 2.13541i 5.20668i 11.4400 −11.1803 11.1184 −3.77875 − 58.5956i 53.8905 23.8746i
56.12 − 1.97674i − 8.87634i 12.0925 11.1803 −17.5462 40.4386 − 55.5315i 2.21056 − 22.1006i
56.13 − 1.73387i − 13.8338i 12.9937 −11.1803 −23.9861 −74.4203 − 50.2714i −110.374 19.3853i
56.14 − 1.49194i 8.10997i 13.7741 11.1803 12.0996 14.6549 − 44.4211i 15.2284 − 16.6803i
56.15 1.49194i − 8.10997i 13.7741 11.1803 12.0996 14.6549 44.4211i 15.2284 16.6803i
56.16 1.73387i 13.8338i 12.9937 −11.1803 −23.9861 −74.4203 50.2714i −110.374 − 19.3853i
56.17 1.97674i 8.87634i 12.0925 11.1803 −17.5462 40.4386 55.5315i 2.21056 22.1006i
56.18 2.13541i − 5.20668i 11.4400 −11.1803 11.1184 −3.77875 58.5956i 53.8905 − 23.8746i
56.19 2.69165i 5.53366i 8.75502 −11.1803 −14.8947 68.1779 66.6319i 50.3786 − 30.0936i
56.20 4.17612i − 4.97310i −1.43996 11.1803 20.7682 −77.5528 60.8044i 56.2683 46.6904i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 56.28
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.5.c.a ✓ 28
19.b odd 2 1 inner 95.5.c.a ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.c.a ✓ 28 1.a even 1 1 trivial
95.5.c.a ✓ 28 19.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(95, [\chi])\).