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Properties

Label 95.5.j.a
Level $95$
Weight $5$
Character orbit 95.j
Analytic conductor $9.820$
Analytic rank $0$
Dimension $56$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,5,Mod(31,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.31");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.j (of order \(6\), degree \(2\), 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: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 24 q^{3} + 242 q^{4} - 14 q^{6} + 100 q^{7} + 1032 q^{9} + 150 q^{10} - 192 q^{11} + 1242 q^{13} + 288 q^{14} - 2574 q^{16} - 78 q^{17} - 954 q^{19} - 1620 q^{21} - 1440 q^{22} + 462 q^{23} + 1292 q^{24}+ \cdots + 11706 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 −6.63719 + 3.83198i −10.1475 + 5.85866i 21.3682 − 37.0108i −5.59017 − 9.68246i 44.9006 − 77.7701i −16.0703 204.906i 28.1478 − 48.7534i 74.2060 + 42.8429i
31.2 −6.61086 + 3.81678i 13.0881 − 7.55645i 21.1356 − 36.6080i −5.59017 − 9.68246i −57.6826 + 99.9092i 85.5785 200.544i 73.6998 − 127.652i 73.9117 + 42.6729i
31.3 −6.23297 + 3.59860i −2.94312 + 1.69921i 17.8999 − 31.0036i 5.59017 + 9.68246i 12.2296 − 21.1822i 29.5142 142.503i −34.7254 + 60.1461i −69.6867 − 40.2336i
31.4 −5.88213 + 3.39605i 8.65585 − 4.99746i 15.0663 − 26.0956i 5.59017 + 9.68246i −33.9432 + 58.7914i −67.3617 95.9901i 9.44913 − 16.3664i −65.7642 − 37.9690i
31.5 −4.60508 + 2.65874i 4.43762 − 2.56206i 6.13782 − 10.6310i −5.59017 − 9.68246i −13.6237 + 23.5970i −5.72487 − 19.8042i −27.3717 + 47.4092i 51.4863 + 29.7256i
31.6 −4.58234 + 2.64562i −13.8097 + 7.97306i 5.99857 − 10.3898i 5.59017 + 9.68246i 42.1873 − 73.0706i −82.6679 − 21.1801i 86.6394 − 150.064i −51.2321 − 29.5789i
31.7 −4.11184 + 2.37397i −7.95849 + 4.59484i 3.27149 − 5.66639i 5.59017 + 9.68246i 21.8160 − 37.7865i 82.5345 − 44.9014i 1.72504 − 2.98786i −45.9718 − 26.5418i
31.8 −3.83785 + 2.21578i −13.8578 + 8.00083i 1.81940 − 3.15129i −5.59017 − 9.68246i 35.4562 − 61.4120i 71.1453 − 54.7795i 87.5266 − 151.600i 42.9085 + 24.7732i
31.9 −2.65653 + 1.53375i 14.4814 − 8.36083i −3.29525 + 5.70754i −5.59017 − 9.68246i −25.6468 + 44.4215i −75.8112 − 69.2962i 99.3068 − 172.004i 29.7009 + 17.1478i
31.10 −2.57403 + 1.48612i −6.17418 + 3.56466i −3.58290 + 6.20577i −5.59017 − 9.68246i 10.5950 − 18.3511i −49.4906 − 68.8543i −15.0863 + 26.1303i 28.7786 + 16.6153i
31.11 −2.10496 + 1.21530i −2.40033 + 1.38583i −5.04610 + 8.74011i 5.59017 + 9.68246i 3.36839 − 5.83422i −44.6809 − 63.4196i −36.6590 + 63.4952i −23.5341 − 13.5874i
31.12 −2.01601 + 1.16394i 6.47528 − 3.73850i −5.29048 + 9.16338i 5.59017 + 9.68246i −8.70280 + 15.0737i 63.8069 − 61.8774i −12.5472 + 21.7324i −22.5396 − 13.0133i
31.13 −0.846897 + 0.488956i 9.17027 − 5.29446i −7.52184 + 13.0282i −5.59017 − 9.68246i −5.17752 + 8.96773i 35.9556 − 30.3580i 15.5626 − 26.9552i 9.46860 + 5.46670i
31.14 −0.316593 + 0.182785i −1.25869 + 0.726703i −7.93318 + 13.7407i −5.59017 − 9.68246i 0.265661 − 0.460139i 60.5460 − 11.6494i −39.4438 + 68.3187i 3.53962 + 2.04360i
31.15 0.0632355 − 0.0365090i 6.72433 − 3.88229i −7.99733 + 13.8518i 5.59017 + 9.68246i 0.283477 − 0.490997i −69.9052 2.33619i −10.3556 + 17.9365i 0.706994 + 0.408183i
31.16 1.29179 − 0.745814i −11.0696 + 6.39105i −6.88752 + 11.9295i 5.59017 + 9.68246i −9.53307 + 16.5118i 25.4753 44.4133i 41.1910 − 71.3450i 14.4426 + 8.33845i
31.17 1.69789 − 0.980275i 15.1828 − 8.76580i −6.07812 + 10.5276i 5.59017 + 9.68246i 17.1858 − 29.7667i 13.8465 55.2017i 113.179 − 196.031i 18.9829 + 10.9598i
31.18 1.71500 − 0.990155i −13.9891 + 8.07663i −6.03919 + 10.4602i −5.59017 − 9.68246i −15.9942 + 27.7028i −45.3022 55.6039i 89.9638 − 155.822i −19.1743 − 11.0703i
31.19 2.23216 − 1.28874i 2.68098 − 1.54786i −4.67831 + 8.10308i −5.59017 − 9.68246i 3.98958 − 6.91015i −75.7762 65.3561i −35.7082 + 61.8485i −24.9563 − 14.4085i
31.20 3.00735 − 1.73629i 0.820719 − 0.473842i −1.97058 + 3.41314i 5.59017 + 9.68246i 1.64546 − 2.85002i 15.1496 69.2473i −40.0509 + 69.3703i 33.6232 + 19.4123i
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.28
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.5.j.a ✓ 56
19.d odd 6 1 inner 95.5.j.a ✓ 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.j.a ✓ 56 1.a even 1 1 trivial
95.5.j.a ✓ 56 19.d odd 6 1 inner

Hecke kernels

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