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Properties

Label 95.5.f.a
Level $95$
Weight $5$
Character orbit 95.f
Analytic conductor $9.820$
Analytic rank $0$
Dimension $72$
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(58,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.58");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.f (of order \(4\), 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: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 20 q^{3} - 66 q^{5} - 128 q^{6} + 130 q^{7} + 16 q^{10} + 312 q^{11} - 80 q^{12} - 760 q^{13} + 1184 q^{15} - 3504 q^{16} + 1110 q^{17} + 960 q^{20} - 2840 q^{21} + 720 q^{22} + 300 q^{23} - 2322 q^{25}+ \cdots - 31440 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
58.1 −5.30665 + 5.30665i 2.41397 + 2.41397i − 40.3212i −2.18828 + 24.9040i −25.6202 −42.3343 + 42.3343i 129.064 + 129.064i − 69.3455i −120.545 − 143.770i
58.2 −5.12256 + 5.12256i −5.46800 − 5.46800i − 36.4812i −11.8750 − 21.9996i 56.0203 25.9577 − 25.9577i 104.916 + 104.916i − 21.2020i 173.525 + 51.8639i
58.3 −4.90994 + 4.90994i 8.46078 + 8.46078i − 32.2150i −23.3481 − 8.93675i −83.0838 42.1265 − 42.1265i 79.6148 + 79.6148i 62.1695i 158.517 − 70.7589i
58.4 −4.79384 + 4.79384i 5.53698 + 5.53698i − 29.9618i 14.7652 − 20.1740i −53.0868 −23.2725 + 23.2725i 66.9306 + 66.9306i − 19.6836i 25.9287 + 167.493i
58.5 −4.78039 + 4.78039i −9.05561 − 9.05561i − 29.7042i 24.9964 + 0.425630i 86.5786 −15.8565 + 15.8565i 65.5112 + 65.5112i 83.0080i −121.527 + 117.458i
58.6 −4.23855 + 4.23855i −4.93728 − 4.93728i − 19.9307i −13.0941 + 21.2966i 41.8539 40.2634 − 40.2634i 16.6604 + 16.6604i − 32.2465i −34.7665 − 145.767i
58.7 −4.16421 + 4.16421i 12.0620 + 12.0620i − 18.6813i 16.7563 + 18.5533i −100.457 20.5817 − 20.5817i 11.1654 + 11.1654i 209.983i −147.037 − 7.48303i
58.8 −3.39342 + 3.39342i −5.31605 − 5.31605i − 7.03062i −22.3933 − 11.1148i 36.0792 −55.1321 + 55.1321i −30.4369 − 30.4369i − 24.4792i 113.707 − 38.2728i
58.9 −3.28518 + 3.28518i 4.14472 + 4.14472i − 5.58480i 14.5751 − 20.3118i −27.2323 −2.29458 + 2.29458i −34.2158 − 34.2158i − 46.6426i 18.8460 + 114.609i
58.10 −3.11698 + 3.11698i −0.688627 − 0.688627i − 3.43115i 22.0384 + 11.8030i 4.29288 37.9639 − 37.9639i −39.1769 − 39.1769i − 80.0516i −105.483 + 31.9037i
58.11 −2.75499 + 2.75499i 5.87847 + 5.87847i 0.820023i −23.5841 + 8.29401i −32.3903 −5.74658 + 5.74658i −46.3391 − 46.3391i − 11.8872i 42.1241 − 87.8240i
58.12 −2.51989 + 2.51989i −12.1685 − 12.1685i 3.30029i −4.70504 + 24.5533i 61.3266 −17.9310 + 17.9310i −48.6346 − 48.6346i 215.145i −50.0154 − 73.7277i
58.13 −2.19355 + 2.19355i −10.8006 − 10.8006i 6.37670i −2.80757 − 24.8419i 47.3831 47.9842 − 47.9842i −49.0844 − 49.0844i 152.305i 60.6503 + 48.3332i
58.14 −1.77561 + 1.77561i 5.55126 + 5.55126i 9.69442i 12.8047 + 21.4719i −19.7137 −61.7979 + 61.7979i −45.6233 − 45.6233i − 19.3671i −60.8617 − 15.3896i
58.15 −1.29380 + 1.29380i 12.6620 + 12.6620i 12.6522i −5.24005 − 24.4447i −32.7642 −35.2660 + 35.2660i −37.0701 − 37.0701i 239.653i 38.4060 + 24.8469i
58.16 −1.16294 + 1.16294i 3.01850 + 3.01850i 13.2951i −12.2952 − 21.7676i −7.02068 55.8545 − 55.8545i −34.0685 − 34.0685i − 62.7773i 39.6130 + 11.0159i
58.17 −0.248255 + 0.248255i −4.68699 − 4.68699i 15.8767i −20.9216 + 13.6853i 2.32714 9.28930 − 9.28930i −7.91356 − 7.91356i − 37.0643i 1.79645 − 8.59133i
58.18 −0.229865 + 0.229865i −3.27734 − 3.27734i 15.8943i 7.94023 + 23.7055i 1.50669 −1.23879 + 1.23879i −7.33139 − 7.33139i − 59.5181i −7.27426 − 3.62390i
58.19 0.246555 − 0.246555i 8.34670 + 8.34670i 15.8784i 24.9735 − 1.15071i 4.11585 47.6422 − 47.6422i 7.85980 + 7.85980i 58.3348i 5.87364 − 6.44106i
58.20 0.664466 − 0.664466i 8.70016 + 8.70016i 15.1170i −12.3025 + 21.7635i 11.5619 22.4410 − 22.4410i 20.6762 + 20.6762i 70.3857i 6.28653 + 22.6357i
See all 72 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 58.36
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.5.f.a ✓ 72
5.c odd 4 1 inner 95.5.f.a ✓ 72
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.f.a ✓ 72 1.a even 1 1 trivial
95.5.f.a ✓ 72 5.c odd 4 1 inner

Hecke kernels

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