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Properties

Label 95.5.d.e
Level $95$
Weight $5$
Character orbit 95.d
Analytic conductor $9.820$
Analytic rank $0$
Dimension $28$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,5,Mod(94,95)]
 
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([1, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.94");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.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: \(9.82014649297\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 160 q^{4} - 42 q^{5} - 104 q^{6} + 428 q^{9} - 356 q^{11} - 552 q^{16} - 988 q^{19} - 1652 q^{20} - 8040 q^{24} - 5058 q^{25} - 696 q^{26} + 3784 q^{30} - 2490 q^{35} + 3864 q^{36} + 4024 q^{39}+ \cdots - 44764 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
94.1 −7.11740 7.28479 34.6574 1.40879 − 24.9603i −51.8488 − 62.0168i −132.792 −27.9318 −10.0269 + 177.652i
94.2 −7.11740 7.28479 34.6574 1.40879 + 24.9603i −51.8488 62.0168i −132.792 −27.9318 −10.0269 − 177.652i
94.3 −6.11453 11.8086 21.3875 −14.6232 − 20.2771i −72.2040 81.6457i −32.9421 58.4427 89.4141 + 123.985i
94.4 −6.11453 11.8086 21.3875 −14.6232 + 20.2771i −72.2040 − 81.6457i −32.9421 58.4427 89.4141 − 123.985i
94.5 −5.60144 −13.7439 15.3761 −1.78135 − 24.9365i 76.9855 40.3374i 3.49448 107.894 9.97810 + 139.680i
94.6 −5.60144 −13.7439 15.3761 −1.78135 + 24.9365i 76.9855 − 40.3374i 3.49448 107.894 9.97810 − 139.680i
94.7 −3.99503 −2.13646 −0.0397685 −21.8919 − 12.0726i 8.53521 − 58.2329i 64.0793 −76.4355 87.4585 + 48.2302i
94.8 −3.99503 −2.13646 −0.0397685 −21.8919 + 12.0726i 8.53521 58.2329i 64.0793 −76.4355 87.4585 − 48.2302i
94.9 −3.44072 4.95866 −4.16145 16.9001 − 18.4225i −17.0613 3.69804i 69.3699 −56.4117 −58.1484 + 63.3865i
94.10 −3.44072 4.95866 −4.16145 16.9001 + 18.4225i −17.0613 − 3.69804i 69.3699 −56.4117 −58.1484 − 63.3865i
94.11 −2.18180 −12.9286 −11.2398 20.9669 − 13.6157i 28.2076 − 93.9000i 59.4316 86.1488 −45.7455 + 29.7067i
94.12 −2.18180 −12.9286 −11.2398 20.9669 + 13.6157i 28.2076 93.9000i 59.4316 86.1488 −45.7455 − 29.7067i
94.13 −0.141230 −9.81294 −15.9801 −11.4794 − 22.2086i 1.38588 7.99045i 4.51655 15.2937 1.62123 + 3.13653i
94.14 −0.141230 −9.81294 −15.9801 −11.4794 + 22.2086i 1.38588 − 7.99045i 4.51655 15.2937 1.62123 − 3.13653i
94.15 0.141230 9.81294 −15.9801 −11.4794 − 22.2086i 1.38588 7.99045i −4.51655 15.2937 −1.62123 − 3.13653i
94.16 0.141230 9.81294 −15.9801 −11.4794 + 22.2086i 1.38588 − 7.99045i −4.51655 15.2937 −1.62123 + 3.13653i
94.17 2.18180 12.9286 −11.2398 20.9669 − 13.6157i 28.2076 − 93.9000i −59.4316 86.1488 45.7455 − 29.7067i
94.18 2.18180 12.9286 −11.2398 20.9669 + 13.6157i 28.2076 93.9000i −59.4316 86.1488 45.7455 + 29.7067i
94.19 3.44072 −4.95866 −4.16145 16.9001 − 18.4225i −17.0613 3.69804i −69.3699 −56.4117 58.1484 − 63.3865i
94.20 3.44072 −4.95866 −4.16145 16.9001 + 18.4225i −17.0613 − 3.69804i −69.3699 −56.4117 58.1484 + 63.3865i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 94.28
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.b odd 2 1 inner
95.d 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.d.e ✓ 28
5.b even 2 1 inner 95.5.d.e ✓ 28
19.b odd 2 1 inner 95.5.d.e ✓ 28
95.d odd 2 1 inner 95.5.d.e ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.d.e ✓ 28 1.a even 1 1 trivial
95.5.d.e ✓ 28 5.b even 2 1 inner
95.5.d.e ✓ 28 19.b odd 2 1 inner
95.5.d.e ✓ 28 95.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{14} - 152 T_{2}^{12} + 8869 T_{2}^{10} - 250478 T_{2}^{8} + 3543224 T_{2}^{6} - 23350448 T_{2}^{4} + \cdots - 1066080 \) acting on \(S_{5}^{\mathrm{new}}(95, [\chi])\). Copy content Toggle raw display