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Properties

Label 95.5.m.a
Level $95$
Weight $5$
Character orbit 95.m
Analytic conductor $9.820$
Analytic rank $0$
Dimension $152$
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(7,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.m (of order \(12\), degree \(4\), 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: \(152\)
Relative dimension: \(38\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 152 q - 2 q^{2} - 2 q^{3} - 20 q^{5} - 40 q^{6} + 52 q^{7} + 108 q^{8} - 2 q^{10} - 304 q^{11} - 268 q^{12} + 198 q^{13} + 172 q^{15} + 4064 q^{16} + 238 q^{17} + 3792 q^{18} + 528 q^{20} - 796 q^{21} - 2774 q^{22}+ \cdots + 15572 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 −2.00464 + 7.48144i −6.02777 − 1.61514i −38.0969 − 21.9952i 19.2366 − 15.9672i 24.1671 − 41.8586i 42.6172 + 42.6172i 153.298 − 153.298i −36.4228 − 21.0287i 80.8950 + 175.926i
7.2 −1.89126 + 7.05826i 11.6064 + 3.10992i −32.3858 − 18.6980i −4.12336 − 24.6576i −43.9013 + 76.0393i −48.0202 − 48.0202i 110.553 − 110.553i 54.8888 + 31.6900i 181.838 + 17.5301i
7.3 −1.88699 + 7.04235i −13.1788 − 3.53124i −32.1775 − 18.5777i −19.4346 + 15.7257i 49.7365 − 86.1461i −26.0222 − 26.0222i 109.064 − 109.064i 91.0624 + 52.5749i −74.0727 − 166.539i
7.4 −1.79516 + 6.69961i 11.7300 + 3.14304i −27.8058 − 16.0537i −11.9846 + 21.9401i −42.1143 + 72.9441i 38.4526 + 38.4526i 78.9982 − 78.9982i 57.5657 + 33.2356i −125.476 − 119.678i
7.5 −1.62018 + 6.04660i −1.59130 − 0.426387i −20.0800 − 11.5932i 13.7862 + 20.8552i 5.15639 − 8.93113i −37.0362 − 37.0362i 31.8101 − 31.8101i −67.7976 − 39.1430i −148.440 + 49.5703i
7.6 −1.61465 + 6.02596i −1.21021 − 0.324275i −19.8487 − 11.4597i −24.9326 − 1.83423i 3.90814 − 6.76910i −1.87404 − 1.87404i 30.5232 − 30.5232i −68.7886 − 39.7151i 51.3105 − 147.281i
7.7 −1.51945 + 5.67065i 9.44369 + 2.53043i −15.9912 − 9.23250i 24.9954 − 0.479005i −28.6984 + 49.7070i 5.19577 + 5.19577i 10.2327 − 10.2327i 12.6322 + 7.29322i −35.2629 + 142.468i
7.8 −1.31890 + 4.92220i −13.1586 − 3.52583i −8.63218 − 4.98379i −3.81213 − 24.7076i 34.7097 − 60.1189i −13.9598 − 13.9598i −21.7366 + 21.7366i 90.5683 + 52.2897i 126.644 + 13.8228i
7.9 −1.24227 + 4.63620i 1.40001 + 0.375131i −6.09471 − 3.51878i −20.0801 − 14.8926i −3.47837 + 6.02471i 55.0876 + 55.0876i −30.4179 + 30.4179i −68.3288 − 39.4496i 93.9898 − 74.5949i
7.10 −1.19472 + 4.45875i −12.4417 − 3.33374i −4.59673 − 2.65392i 16.0067 + 19.2038i 29.7287 − 51.4916i 56.2139 + 56.2139i −34.8996 + 34.8996i 73.5339 + 42.4548i −104.749 + 48.4267i
7.11 −0.984813 + 3.67537i −2.95944 − 0.792981i 1.31790 + 0.760891i 18.4338 − 16.8878i 5.82900 − 10.0961i −28.1313 − 28.1313i −47.1434 + 47.1434i −62.0186 − 35.8064i 43.9150 + 84.3822i
7.12 −0.871340 + 3.25189i 13.0769 + 3.50396i 4.04087 + 2.33300i −1.89394 − 24.9282i −22.7889 + 39.4716i 21.4417 + 21.4417i −49.1964 + 49.1964i 88.5806 + 51.1420i 82.7138 + 15.5620i
7.13 −0.786289 + 2.93447i 8.03815 + 2.15382i 5.86353 + 3.38531i −24.4263 + 5.32520i −12.6406 + 21.8942i −67.8037 − 67.8037i −48.9155 + 48.9155i −10.1751 − 5.87458i 3.57947 − 75.8653i
7.14 −0.773143 + 2.88541i 14.8770 + 3.98627i 6.12857 + 3.53833i 15.7790 + 19.3913i −23.0040 + 39.8442i −13.4027 − 13.4027i −48.7441 + 48.7441i 135.286 + 78.1072i −68.1513 + 30.5366i
7.15 −0.631286 + 2.35599i 2.59409 + 0.695085i 8.70424 + 5.02539i −9.35720 + 23.1828i −3.27523 + 5.67286i 15.8569 + 15.8569i −44.9299 + 44.9299i −63.9019 − 36.8938i −48.7114 − 36.6805i
7.16 −0.548107 + 2.04556i −12.0367 − 3.22523i 9.97251 + 5.75763i −20.7755 + 13.9060i 13.1948 − 22.8541i −5.69349 − 5.69349i −41.2029 + 41.2029i 64.3327 + 37.1425i −17.0584 − 50.1196i
7.17 −0.225771 + 0.842589i 1.59816 + 0.428224i 13.1974 + 7.61954i 23.5944 − 8.26459i −0.721634 + 1.24991i 34.1318 + 34.1318i −19.2688 + 19.2688i −67.7773 − 39.1313i 1.63672 + 21.7463i
7.18 −0.203075 + 0.757886i −12.0551 − 3.23014i 13.3233 + 7.69218i 22.9592 + 9.89314i 4.89616 − 8.48040i −50.6680 − 50.6680i −17.4124 + 17.4124i 64.7425 + 37.3791i −12.1603 + 15.3914i
7.19 0.125844 − 0.469657i −7.83458 − 2.09927i 13.6517 + 7.88179i −19.5139 − 15.6271i −1.97187 + 3.41539i 24.5781 + 24.5781i 10.9207 − 10.9207i −13.1743 − 7.60620i −9.79510 + 7.19827i
7.20 0.183856 − 0.686162i 3.57524 + 0.957982i 13.4194 + 7.74769i 14.5673 + 20.3174i 1.31466 − 2.27706i 38.3696 + 38.3696i 15.8203 − 15.8203i −58.2835 − 33.6500i 16.6193 − 6.26002i
See next 80 embeddings (of 152 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.38
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
19.c even 3 1 inner
95.m odd 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.5.m.a ✓ 152
5.c odd 4 1 inner 95.5.m.a ✓ 152
19.c even 3 1 inner 95.5.m.a ✓ 152
95.m odd 12 1 inner 95.5.m.a ✓ 152
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.m.a ✓ 152 1.a even 1 1 trivial
95.5.m.a ✓ 152 5.c odd 4 1 inner
95.5.m.a ✓ 152 19.c even 3 1 inner
95.5.m.a ✓ 152 95.m odd 12 1 inner

Hecke kernels

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