↑

Properties

Label 43.5.d.a
Level $43$
Weight $5$
Character orbit 43.d
Analytic conductor $4.445$
Analytic rank $0$
Dimension $28$
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] = [43,5,Mod(7,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.d (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: \(4.44490841261\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9} + 91 q^{10} - 376 q^{11} - 1026 q^{12} - 198 q^{13} + 78 q^{14} - 289 q^{15} + 806 q^{16} + 23 q^{17} - 435 q^{18} - 438 q^{19} + 177 q^{20} + 1684 q^{21} - 214 q^{23} + 1450 q^{24} + 463 q^{25} + 45 q^{26} - 3828 q^{28} + 1725 q^{29} + 8127 q^{30} + 2135 q^{31} - 474 q^{33} + 201 q^{34} - 6882 q^{35} - 12052 q^{36} + 1638 q^{37} - 2124 q^{38} - 6721 q^{40} + 3014 q^{41} + 157 q^{43} + 17162 q^{44} - 6240 q^{46} - 3670 q^{47} + 11547 q^{48} + 3085 q^{49} + 9738 q^{50} + 13746 q^{52} + 1208 q^{53} - 32416 q^{54} - 11202 q^{55} - 16245 q^{56} + 6207 q^{57} - 5756 q^{58} - 8716 q^{59} - 281 q^{60} + 8382 q^{61} - 25191 q^{62} + 23625 q^{63} + 17564 q^{64} - 21909 q^{66} - 9295 q^{67} + 6758 q^{68} + 30663 q^{69} + 24828 q^{71} + 46194 q^{72} + 5307 q^{73} + 13866 q^{74} + 5178 q^{76} - 27645 q^{77} - 10592 q^{78} - 24914 q^{79} - 13683 q^{80} - 43222 q^{81} + 7010 q^{83} - 21568 q^{84} + 15366 q^{86} + 57084 q^{87} - 80787 q^{89} + 114772 q^{90} - 24438 q^{91} + 22049 q^{92} - 39723 q^{93} + 29955 q^{95} + 1378 q^{96} - 12210 q^{97} + 28845 q^{98} - 49211 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
7.1 − 7.38404i 15.2777 − 8.82059i −38.5241 −17.1186 + 9.88344i −65.1316 − 112.811i 36.3076 + 20.9622i 166.319i 115.106 − 199.369i 72.9798 + 126.405i
7.2 − 7.27000i −9.67914 + 5.58826i −36.8529 5.33236 − 3.07864i 40.6266 + 70.3674i 35.8849 + 20.7182i 151.601i 21.9572 − 38.0310i −22.3817 − 38.7662i
7.3 − 5.51064i −1.33569 + 0.771161i −14.3672 −29.9636 + 17.2995i 4.24959 + 7.36051i −50.7143 − 29.2799i − 8.99803i −39.3106 + 68.0880i 95.3312 + 165.119i
7.4 − 5.28884i 3.72701 − 2.15179i −11.9718 30.9460 − 17.8667i −11.3805 − 19.7116i −25.0066 − 14.4376i − 21.3046i −31.2396 + 54.1085i −94.4939 − 163.668i
7.5 − 2.95871i 6.98373 − 4.03206i 7.24603 4.46909 − 2.58023i −11.9297 − 20.6628i 37.3312 + 21.5532i − 68.7783i −7.98499 + 13.8304i −7.63415 − 13.2227i
7.6 − 2.55236i −13.8661 + 8.00559i 9.48548 27.9587 − 16.1420i 20.4331 + 35.3912i −55.0431 − 31.7792i − 65.0480i 87.6790 − 151.865i −41.2001 − 71.3606i
7.7 − 2.45393i −7.53154 + 4.34833i 9.97824 −12.0383 + 6.95034i 10.6705 + 18.4818i 83.6059 + 48.2699i − 63.7487i −2.68397 + 4.64877i 17.0556 + 29.5412i
7.8 0.411879i 10.8202 − 6.24704i 15.8304 −3.72754 + 2.15210i 2.57302 + 4.45661i −34.4055 − 19.8640i 13.1103i 37.5509 − 65.0401i −0.886404 − 1.53530i
7.9 1.02950i −6.61850 + 3.82119i 14.9401 −23.6208 + 13.6375i −3.93391 − 6.81373i −37.2107 − 21.4836i 31.8528i −11.2970 + 19.5669i −14.0398 − 24.3176i
7.10 2.98081i −1.27161 + 0.734162i 7.11478 26.8620 − 15.5088i −2.18840 − 3.79041i 15.5504 + 8.97804i 68.9007i −39.4220 + 68.2809i 46.2288 + 80.0706i
7.11 4.83828i 7.61693 − 4.39763i −7.40895 −37.8372 + 21.8453i 21.2770 + 36.8528i 66.6485 + 38.4795i 41.5659i −1.82162 + 3.15513i −105.694 − 183.067i
7.12 5.69416i −13.9948 + 8.07993i −16.4234 2.48060 − 1.43217i −46.0084 − 79.6889i 31.0431 + 17.9227i − 2.41117i 90.0705 − 156.007i 8.15502 + 14.1249i
7.13 6.51108i 13.8942 − 8.02184i −26.3942 31.7247 − 18.3162i 52.2308 + 90.4665i 5.86707 + 3.38735i − 67.6775i 88.1998 − 152.766i 119.259 + 206.562i
7.14 6.75666i −1.02237 + 0.590266i −29.6524 −6.96733 + 4.02259i −3.98823 − 6.90781i −45.3584 − 26.1877i − 92.2449i −39.8032 + 68.9411i −27.1793 − 47.0759i
37.1 − 6.75666i −1.02237 − 0.590266i −29.6524 −6.96733 − 4.02259i −3.98823 + 6.90781i −45.3584 + 26.1877i 92.2449i −39.8032 − 68.9411i −27.1793 + 47.0759i
37.2 − 6.51108i 13.8942 + 8.02184i −26.3942 31.7247 + 18.3162i 52.2308 − 90.4665i 5.86707 − 3.38735i 67.6775i 88.1998 + 152.766i 119.259 − 206.562i
37.3 − 5.69416i −13.9948 − 8.07993i −16.4234 2.48060 + 1.43217i −46.0084 + 79.6889i 31.0431 − 17.9227i 2.41117i 90.0705 + 156.007i 8.15502 − 14.1249i
37.4 − 4.83828i 7.61693 + 4.39763i −7.40895 −37.8372 − 21.8453i 21.2770 − 36.8528i 66.6485 − 38.4795i − 41.5659i −1.82162 − 3.15513i −105.694 + 183.067i
37.5 − 2.98081i −1.27161 − 0.734162i 7.11478 26.8620 + 15.5088i −2.18840 + 3.79041i 15.5504 − 8.97804i − 68.9007i −39.4220 − 68.2809i 46.2288 − 80.0706i
37.6 − 1.02950i −6.61850 − 3.82119i 14.9401 −23.6208 − 13.6375i −3.93391 + 6.81373i −37.2107 + 21.4836i − 31.8528i −11.2970 − 19.5669i −14.0398 + 24.3176i
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 7.14
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 43.5.d.a ✓ 28
43.d odd 6 1 inner 43.5.d.a ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.5.d.a ✓ 28 1.a even 1 1 trivial
43.5.d.a ✓ 28 43.d odd 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(43, [\chi])\).