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Properties

Label 25.4.d.a
Level $25$
Weight $4$
Character orbit 25.d
Analytic conductor $1.475$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,4,Mod(6,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.6");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 25.d (of order \(5\), 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: \(1.47504775014\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
6.1 −1.57739 − 4.85470i 6.28151 − 4.56378i −14.6078 + 10.6132i 6.03231 + 9.41335i −32.0642 − 23.2960i −5.45530 41.5290 + 30.1725i 10.2858 − 31.6563i 36.1837 − 44.1336i
6.2 −1.41896 − 4.36711i −7.07217 + 5.13823i −10.5860 + 7.69120i 1.19043 − 11.1168i 32.4743 + 23.5940i −20.8866 18.8904 + 13.7247i 15.2707 − 46.9983i −50.2373 + 10.5755i
6.3 −0.624983 − 1.92350i 1.69858 − 1.23409i 3.16288 − 2.29797i −9.66664 − 5.61749i −3.43535 − 2.49593i 24.6755 −19.4867 − 14.1579i −6.98127 + 21.4861i −4.76375 + 22.1046i
6.4 −0.132779 − 0.408651i 0.0617670 − 0.0448763i 6.32277 − 4.59376i 11.1601 + 0.672002i −0.0265401 − 0.0192825i −16.1597 −5.49773 − 3.99433i −8.34166 + 25.6730i −1.20721 − 4.64982i
6.5 0.591509 + 1.82048i −7.58563 + 5.51128i 3.50788 − 2.54862i −4.63720 + 10.1733i −14.5201 − 10.5495i 14.5331 19.1034 + 13.8794i 18.8241 − 57.9345i −21.2632 − 2.42430i
6.6 0.906232 + 2.78910i 5.49244 − 3.99049i −0.485661 + 0.352853i −10.1222 + 4.74784i 16.1073 + 11.7026i −23.0864 17.5561 + 12.7553i 5.89942 − 18.1565i −22.4152 − 23.9290i
6.7 1.44735 + 4.45449i −1.18551 + 0.861326i −11.2755 + 8.19213i 5.51525 − 9.72533i −5.55262 − 4.03421i 13.4350 −22.4976 − 16.3455i −7.67990 + 23.6363i 51.3039 + 10.4917i
11.1 −4.11746 + 2.99151i −1.18297 + 3.64082i 5.53220 − 17.0263i −10.3703 − 4.17822i −6.02069 − 18.5298i −12.1888 15.5740 + 47.9320i 9.98733 + 7.25622i 55.1983 − 13.8191i
11.2 −2.81638 + 2.04622i 2.63646 − 8.11420i 1.27284 − 3.91740i 9.28856 − 6.22275i 9.17815 + 28.2474i 12.5082 −4.17503 − 12.8494i −37.0458 − 26.9153i −13.4270 + 36.5321i
11.3 −1.51671 + 1.10196i −0.496278 + 1.52739i −1.38603 + 4.26575i 2.00572 + 10.9990i −0.930402 − 2.86348i −5.91678 −7.23313 − 22.2613i 19.7568 + 14.3542i −15.1625 − 14.4720i
11.4 0.269925 − 0.196112i −2.60870 + 8.02875i −2.43774 + 7.50258i −0.131697 − 11.1796i 0.870380 + 2.67876i 30.0089 1.63816 + 5.04172i −35.8121 − 26.0190i −2.22799 − 2.99181i
11.5 1.92104 − 1.39571i 1.98691 − 6.11509i −0.729774 + 2.24601i −10.2730 + 4.41186i −4.71799 − 14.5205i 25.3460 7.60304 + 23.3997i −11.6030 − 8.43010i −13.5772 + 22.8136i
11.6 2.27143 − 1.65029i 0.411392 − 1.26614i −0.0362106 + 0.111445i 9.59405 − 5.74058i −1.15504 − 3.55485i −35.1773 7.04252 + 21.6747i 20.4096 + 14.8284i 12.3186 − 28.8722i
11.7 4.29718 − 3.12208i −1.93780 + 5.96393i 6.24620 − 19.2238i −9.58545 + 5.75493i 10.2928 + 31.6780i −9.63602 −20.0464 − 61.6963i −9.96993 − 7.24358i −23.2230 + 54.6565i
16.1 −4.11746 − 2.99151i −1.18297 − 3.64082i 5.53220 + 17.0263i −10.3703 + 4.17822i −6.02069 + 18.5298i −12.1888 15.5740 − 47.9320i 9.98733 − 7.25622i 55.1983 + 13.8191i
16.2 −2.81638 − 2.04622i 2.63646 + 8.11420i 1.27284 + 3.91740i 9.28856 + 6.22275i 9.17815 − 28.2474i 12.5082 −4.17503 + 12.8494i −37.0458 + 26.9153i −13.4270 − 36.5321i
16.3 −1.51671 − 1.10196i −0.496278 − 1.52739i −1.38603 − 4.26575i 2.00572 − 10.9990i −0.930402 + 2.86348i −5.91678 −7.23313 + 22.2613i 19.7568 − 14.3542i −15.1625 + 14.4720i
16.4 0.269925 + 0.196112i −2.60870 − 8.02875i −2.43774 − 7.50258i −0.131697 + 11.1796i 0.870380 − 2.67876i 30.0089 1.63816 − 5.04172i −35.8121 + 26.0190i −2.22799 + 2.99181i
16.5 1.92104 + 1.39571i 1.98691 + 6.11509i −0.729774 − 2.24601i −10.2730 − 4.41186i −4.71799 + 14.5205i 25.3460 7.60304 − 23.3997i −11.6030 + 8.43010i −13.5772 − 22.8136i
16.6 2.27143 + 1.65029i 0.411392 + 1.26614i −0.0362106 − 0.111445i 9.59405 + 5.74058i −1.15504 + 3.55485i −35.1773 7.04252 − 21.6747i 20.4096 − 14.8284i 12.3186 + 28.8722i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 6.7
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
25.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 25.4.d.a ✓ 28
3.b odd 2 1 225.4.h.b 28
5.b even 2 1 125.4.d.a 28
5.c odd 4 2 125.4.e.b 56
25.d even 5 1 inner 25.4.d.a ✓ 28
25.d even 5 1 625.4.a.c 14
25.e even 10 1 125.4.d.a 28
25.e even 10 1 625.4.a.d 14
25.f odd 20 2 125.4.e.b 56
75.j odd 10 1 225.4.h.b 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
25.4.d.a ✓ 28 1.a even 1 1 trivial
25.4.d.a ✓ 28 25.d even 5 1 inner
125.4.d.a 28 5.b even 2 1
125.4.d.a 28 25.e even 10 1
125.4.e.b 56 5.c odd 4 2
125.4.e.b 56 25.f odd 20 2
225.4.h.b 28 3.b odd 2 1
225.4.h.b 28 75.j odd 10 1
625.4.a.c 14 25.d even 5 1
625.4.a.d 14 25.e even 10 1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(25, [\chi])\).