↑

Properties

Label 145.3.r.a
Level $145$
Weight $3$
Character orbit 145.r
Analytic conductor $3.951$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [145,3,Mod(11,145)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(145, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([0, 25]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("145.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 145 = 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 145.r (of order \(28\), degree \(12\), 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: \(3.95096383322\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(20\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 240 q + 4 q^{2} - 72 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 240 q + 4 q^{2} - 72 q^{8} - 20 q^{11} + 60 q^{12} - 36 q^{14} - 20 q^{15} + 120 q^{16} + 36 q^{17} + 24 q^{18} + 12 q^{19} - 188 q^{21} - 336 q^{22} - 132 q^{23} - 216 q^{24} + 200 q^{25} - 160 q^{26} - 228 q^{27} + 104 q^{29} + 144 q^{31} + 304 q^{32} + 420 q^{33} + 456 q^{36} + 208 q^{37} + 560 q^{38} + 124 q^{39} - 32 q^{41} - 120 q^{43} - 144 q^{44} - 1480 q^{46} - 464 q^{47} - 40 q^{48} - 848 q^{49} - 20 q^{50} - 672 q^{51} - 1064 q^{52} + 368 q^{53} - 508 q^{54} + 80 q^{55} - 256 q^{56} + 216 q^{58} - 48 q^{59} - 160 q^{60} + 232 q^{61} + 980 q^{62} + 1764 q^{64} + 1496 q^{66} + 1120 q^{67} - 288 q^{68} + 1704 q^{69} + 784 q^{71} - 1264 q^{72} - 440 q^{73} - 1068 q^{74} + 668 q^{76} - 640 q^{77} - 1400 q^{78} - 748 q^{79} - 80 q^{81} + 200 q^{83} - 1544 q^{84} - 120 q^{85} + 176 q^{87} - 464 q^{88} + 260 q^{89} + 20 q^{90} + 2016 q^{92} + 784 q^{93} + 768 q^{94} - 40 q^{95} - 1596 q^{96} + 704 q^{97} + 524 q^{98} + 792 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −3.67917 + 1.28740i −0.371125 − 3.29382i 8.75159 − 6.97916i 0.970194 − 2.01463i 5.60589 + 11.6408i 6.78274 − 8.50528i −14.9184 + 23.7425i −1.93718 + 0.442149i −0.975882 + 8.66119i
11.2 −3.65949 + 1.28051i 0.637245 + 5.65571i 8.62481 − 6.87806i −0.970194 + 2.01463i −9.57418 − 19.8810i −0.186554 + 0.233931i −14.5041 + 23.0832i −22.8066 + 5.20546i 0.970660 − 8.61485i
11.3 −3.28978 + 1.15114i −0.224484 − 1.99235i 6.37017 − 5.08004i −0.970194 + 2.01463i 3.03199 + 6.29598i −5.26622 + 6.60363i −7.69129 + 12.2406i 4.85527 − 1.10818i 0.872596 − 7.74451i
11.4 −3.00340 + 1.05093i 0.134469 + 1.19344i 4.78860 − 3.81878i 0.970194 − 2.01463i −1.65809 − 3.44307i −6.02342 + 7.55313i −3.59717 + 5.72487i 7.36813 − 1.68173i −0.796636 + 7.07034i
11.5 −2.65819 + 0.930141i 0.364223 + 3.23257i 3.07349 − 2.45103i 0.970194 − 2.01463i −3.97492 − 8.25401i 6.09124 − 7.63818i 0.103170 − 0.164194i −1.54250 + 0.352065i −0.705071 + 6.25768i
11.6 −2.27711 + 0.796796i −0.416714 − 3.69844i 1.42303 − 1.13482i −0.970194 + 2.01463i 3.89580 + 8.08972i 3.53697 − 4.43522i 2.79793 − 4.45288i −4.73045 + 1.07970i 0.603992 − 5.36058i
11.7 −1.14472 + 0.400555i 0.422482 + 3.74963i −1.97739 + 1.57691i −0.970194 + 2.01463i −1.98556 − 4.12305i −4.04573 + 5.07318i 4.21286 − 6.70472i −5.10691 + 1.16562i 0.303631 − 2.69480i
11.8 −0.899641 + 0.314798i −0.132544 − 1.17636i −2.41707 + 1.92755i 0.970194 − 2.01463i 0.489559 + 1.01658i −2.69867 + 3.38402i 3.59608 − 5.72314i 7.40809 − 1.69085i −0.238625 + 2.11786i
11.9 −0.716575 + 0.250740i −0.0792832 − 0.703658i −2.67672 + 2.13461i 0.970194 − 2.01463i 0.233248 + 0.484344i 0.469225 − 0.588389i 2.99846 − 4.77203i 8.28550 − 1.89111i −0.190068 + 1.68690i
11.10 −0.249202 + 0.0871997i −0.176309 − 1.56478i −3.07283 + 2.45050i −0.970194 + 2.01463i 0.180385 + 0.374574i 6.74755 − 8.46116i 1.11394 − 1.77282i 6.35688 − 1.45092i 0.0660996 − 0.586651i
11.11 0.215381 − 0.0753650i −0.443468 − 3.93589i −3.08662 + 2.46149i −0.970194 + 2.01463i −0.392143 − 0.814293i −6.33962 + 7.94963i −0.964897 + 1.53562i −6.52018 + 1.48819i −0.0571287 + 0.507031i
11.12 0.849547 − 0.297269i −0.626590 − 5.56114i −2.49397 + 1.98887i 0.970194 − 2.01463i −2.18547 − 4.53818i 4.45604 − 5.58770i −3.44294 + 5.47941i −21.7593 + 4.96641i 0.225338 − 1.99993i
11.13 1.28226 − 0.448682i 0.350681 + 3.11238i −1.68445 + 1.34331i 0.970194 − 2.01463i 1.84613 + 3.83353i −7.66503 + 9.61164i −4.44824 + 7.07933i −0.789576 + 0.180215i 0.340113 − 3.01858i
11.14 1.53363 − 0.536642i 0.214695 + 1.90547i −1.06327 + 0.847933i −0.970194 + 2.01463i 1.35182 + 2.80708i −2.07199 + 2.59820i −4.63345 + 7.37410i 5.18963 − 1.18450i −0.406789 + 3.61035i
11.15 2.23557 − 0.782260i 0.0394068 + 0.349745i 1.25852 − 1.00364i 0.970194 − 2.01463i 0.361688 + 0.751053i 6.59781 − 8.27339i −3.01203 + 4.79361i 8.65358 − 1.97512i 0.592974 − 5.26279i
11.16 2.38293 − 0.833825i 0.631477 + 5.60452i 1.85579 − 1.47994i −0.970194 + 2.01463i 6.17795 + 12.8287i 4.75993 − 5.96876i −2.18448 + 3.47658i −22.2375 + 5.07556i −0.632061 + 5.60970i
11.17 2.89645 − 1.01351i −0.474571 − 4.21194i 4.23491 − 3.37723i −0.970194 + 2.01463i −5.64343 − 11.7187i 3.27903 − 4.11177i 2.31287 − 3.68091i −8.74084 + 1.99504i −0.768270 + 6.81858i
11.18 3.09898 − 1.08438i −0.396336 − 3.51758i 5.30048 − 4.22699i 0.970194 − 2.01463i −5.04264 − 10.4711i −5.55101 + 6.96075i 4.85530 − 7.72716i −3.44195 + 0.785603i 0.821989 − 7.29535i
11.19 3.27926 − 1.14746i 0.450699 + 4.00007i 6.30952 − 5.03168i 0.970194 − 2.01463i 6.06788 + 12.6001i −1.83847 + 2.30536i 7.52330 − 11.9733i −7.02305 + 1.60297i 0.869806 − 7.71974i
11.20 3.38053 − 1.18290i 0.0960459 + 0.852431i 6.90140 − 5.50368i −0.970194 + 2.01463i 1.33302 + 2.76805i −1.03383 + 1.29638i 9.19817 − 14.6388i 8.05694 − 1.83894i −0.896668 + 7.95815i
See next 80 embeddings (of 240 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 11.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.f odd 28 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 145.3.r.a ✓ 240
29.f odd 28 1 inner 145.3.r.a ✓ 240
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
145.3.r.a ✓ 240 1.a even 1 1 trivial
145.3.r.a ✓ 240 29.f odd 28 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(145, [\chi])\).