# Properties

 Label 143.4.n.a Level $143$ Weight $4$ Character orbit 143.n Analytic conductor $8.437$ Analytic rank $0$ Dimension $160$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$143 = 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 143.n (of order $$10$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.43727313082$$ Analytic rank: $$0$$ Dimension: $$160$$ Relative dimension: $$40$$ over $$\Q(\zeta_{10})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10})$$ 160 * q - 6 * q^3 + 146 * q^4 - 426 * q^9 $$\operatorname{Tr}(f)(q) =$$ $$160 q - 6 q^{3} + 146 q^{4} - 426 q^{9} + 184 q^{10} + 84 q^{12} - 39 q^{13} - 158 q^{14} - 634 q^{16} - 116 q^{17} - 1026 q^{22} + 184 q^{23} + 506 q^{25} - 450 q^{26} - 210 q^{27} + 188 q^{29} - 1424 q^{30} + 1762 q^{35} + 1086 q^{36} - 418 q^{38} + 529 q^{39} - 1190 q^{40} + 1444 q^{42} + 4288 q^{43} - 2128 q^{48} + 902 q^{49} + 350 q^{51} - 1746 q^{52} - 2866 q^{53} + 486 q^{55} - 6436 q^{56} + 570 q^{61} + 1702 q^{62} + 5834 q^{64} + 810 q^{65} + 3954 q^{66} - 3112 q^{68} + 4656 q^{69} + 5140 q^{74} - 854 q^{75} - 144 q^{77} - 4904 q^{78} - 1730 q^{79} + 1622 q^{81} + 5578 q^{82} - 8556 q^{87} - 3538 q^{88} - 12996 q^{90} + 5315 q^{91} + 9394 q^{92} + 4646 q^{94} + 1922 q^{95}+O(q^{100})$$ 160 * q - 6 * q^3 + 146 * q^4 - 426 * q^9 + 184 * q^10 + 84 * q^12 - 39 * q^13 - 158 * q^14 - 634 * q^16 - 116 * q^17 - 1026 * q^22 + 184 * q^23 + 506 * q^25 - 450 * q^26 - 210 * q^27 + 188 * q^29 - 1424 * q^30 + 1762 * q^35 + 1086 * q^36 - 418 * q^38 + 529 * q^39 - 1190 * q^40 + 1444 * q^42 + 4288 * q^43 - 2128 * q^48 + 902 * q^49 + 350 * q^51 - 1746 * q^52 - 2866 * q^53 + 486 * q^55 - 6436 * q^56 + 570 * q^61 + 1702 * q^62 + 5834 * q^64 + 810 * q^65 + 3954 * q^66 - 3112 * q^68 + 4656 * q^69 + 5140 * q^74 - 854 * q^75 - 144 * q^77 - 4904 * q^78 - 1730 * q^79 + 1622 * q^81 + 5578 * q^82 - 8556 * q^87 - 3538 * q^88 - 12996 * q^90 + 5315 * q^91 + 9394 * q^92 + 4646 * q^94 + 1922 * q^95

## 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.

Label $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
25.1 −3.24066 4.46038i −2.34848 7.22789i −6.92102 + 21.3007i −7.96782 + 10.9668i −24.6285 + 33.8982i −23.0659 7.49455i 75.4900 24.5282i −24.8835 + 18.0789i 74.7369
25.2 −3.05502 4.20487i −0.605039 1.86212i −5.87568 + 18.0835i 6.52386 8.97932i −5.98157 + 8.23292i 15.3171 + 4.97683i 54.4441 17.6900i 18.7420 13.6169i −57.6874
25.3 −2.99746 4.12565i 2.67526 + 8.23360i −5.56408 + 17.1245i −11.3048 + 15.5597i 25.9500 35.7171i 1.89146 + 0.614574i 48.5278 15.7676i −38.7917 + 28.1838i 98.0794
25.4 −2.97823 4.09918i 1.04463 + 3.21504i −5.46131 + 16.8082i 2.66533 3.66851i 10.0679 13.8572i −6.84110 2.22281i 46.6138 15.1457i 12.5982 9.15316i −22.9758
25.5 −2.58109 3.55257i 2.03748 + 6.27072i −3.48657 + 10.7306i 5.87800 8.09037i 17.0182 23.4236i −2.32170 0.754367i 13.7098 4.45460i −13.3271 + 9.68270i −43.9133
25.6 −2.47563 3.40741i −1.83607 5.65083i −3.00956 + 9.26247i −5.13780 + 7.07158i −14.7093 + 20.2456i 23.0063 + 7.47520i 6.96637 2.26351i −6.71728 + 4.88039i 36.8150
25.7 −2.35953 3.24761i −3.09622 9.52919i −2.50747 + 7.71720i 8.33529 11.4725i −23.6415 + 32.5397i 7.59080 + 2.46640i 0.436537 0.141839i −59.3754 + 43.1388i −56.9257
25.8 −2.34047 3.22138i 0.168906 + 0.519839i −2.42734 + 7.47059i −6.24582 + 8.59663i 1.27928 1.76078i −28.0425 9.11157i −0.548925 + 0.178357i 21.6018 15.6946i 42.3111
25.9 −2.07518 2.85624i −1.29150 3.97482i −1.37961 + 4.24599i 2.94180 4.04904i −8.67296 + 11.9373i −10.2208 3.32095i −11.8712 + 3.85719i 7.71220 5.60324i −17.6698
25.10 −2.03051 2.79476i 0.161025 + 0.495585i −1.21557 + 3.74113i −8.96888 + 12.3446i 1.05808 1.45632i 16.3193 + 5.30246i −13.3597 + 4.34083i 21.6238 15.7106i 52.7116
25.11 −1.84899 2.54492i 2.52460 + 7.76993i −0.585700 + 1.80260i 2.53463 3.48862i 15.1059 20.7914i 31.9374 + 10.3771i −18.2634 + 5.93414i −32.1547 + 23.3618i −13.5647
25.12 −1.38497 1.90624i −0.928232 2.85681i 0.756503 2.32828i 7.86101 10.8197i −4.16020 + 5.72602i −12.3082 3.99917i −23.4134 + 7.60747i 14.5437 10.5666i −31.5123
25.13 −1.34014 1.84454i 1.90248 + 5.85523i 0.865771 2.66457i 10.8950 14.9957i 8.25063 11.3560i −23.1527 7.52276i −23.4223 + 7.61036i −8.82081 + 6.40869i −42.2611
25.14 −1.17535 1.61773i 1.36382 + 4.19741i 1.23654 3.80567i −5.85576 + 8.05976i 5.18729 7.13970i −0.00726186 0.00235952i −22.8239 + 7.41594i 6.08525 4.42119i 19.9210
25.15 −1.00857 1.38817i −2.62521 8.07958i 1.56232 4.80832i −2.93663 + 4.04193i −8.56815 + 11.7930i −18.0190 5.85473i −21.3057 + 6.92263i −36.5444 + 26.5511i 8.57268
25.16 −0.959626 1.32081i −0.156611 0.482000i 1.64847 5.07348i 11.1106 15.2925i −0.486343 + 0.669394i 30.6277 + 9.95155i −20.7047 + 6.72736i 21.6357 15.7192i −30.8606
25.17 −0.879569 1.21062i 3.03153 + 9.33009i 1.78017 5.47880i −4.73233 + 6.51349i 8.62878 11.8765i −22.9824 7.46744i −19.5839 + 6.36320i −56.0169 + 40.6986i 12.0478
25.18 −0.638353 0.878617i −2.31620 7.12853i 2.10766 6.48672i −10.7701 + 14.8238i −4.78470 + 6.58557i 6.75722 + 2.19555i −15.3078 + 4.97380i −23.6077 + 17.1520i 19.8996
25.19 −0.313996 0.432179i 1.17154 + 3.60564i 2.38395 7.33705i −4.60303 + 6.33553i 1.19042 1.63847i 4.31855 + 1.40318i −7.98392 + 2.59413i 10.2153 7.42187i 4.18341
25.20 −0.249988 0.344080i −1.06869 3.28909i 2.41624 7.43642i −0.222452 + 0.306179i −0.864547 + 1.18995i 24.1058 + 7.83243i −6.39867 + 2.07905i 12.1675 8.84018i 0.160960
See next 80 embeddings (of 160 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 103.40 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner
13.b even 2 1 inner
143.n even 10 1 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 143.4.n.a 160
11.c even 5 1 inner 143.4.n.a 160
13.b even 2 1 inner 143.4.n.a 160
143.n even 10 1 inner 143.4.n.a 160

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.n.a 160 1.a even 1 1 trivial
143.4.n.a 160 11.c even 5 1 inner
143.4.n.a 160 13.b even 2 1 inner
143.4.n.a 160 143.n even 10 1 inner

## Hecke kernels

This newform subspace is the entire newspace $$S_{4}^{\mathrm{new}}(143, [\chi])$$.