# 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

## Newspace parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 43.d (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 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.

 $$\operatorname{Tr}(f)(q) =$$ $$28q + 6q^{3} - 234q^{4} - 3q^{5} + 15q^{6} + 129q^{7} + 534q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$28q + 6q^{3} - 234q^{4} - 3q^{5} + 15q^{6} + 129q^{7} + 534q^{9} + 91q^{10} - 376q^{11} - 1026q^{12} - 198q^{13} + 78q^{14} - 289q^{15} + 806q^{16} + 23q^{17} - 435q^{18} - 438q^{19} + 177q^{20} + 1684q^{21} - 214q^{23} + 1450q^{24} + 463q^{25} + 45q^{26} - 3828q^{28} + 1725q^{29} + 8127q^{30} + 2135q^{31} - 474q^{33} + 201q^{34} - 6882q^{35} - 12052q^{36} + 1638q^{37} - 2124q^{38} - 6721q^{40} + 3014q^{41} + 157q^{43} + 17162q^{44} - 6240q^{46} - 3670q^{47} + 11547q^{48} + 3085q^{49} + 9738q^{50} + 13746q^{52} + 1208q^{53} - 32416q^{54} - 11202q^{55} - 16245q^{56} + 6207q^{57} - 5756q^{58} - 8716q^{59} - 281q^{60} + 8382q^{61} - 25191q^{62} + 23625q^{63} + 17564q^{64} - 21909q^{66} - 9295q^{67} + 6758q^{68} + 30663q^{69} + 24828q^{71} + 46194q^{72} + 5307q^{73} + 13866q^{74} + 5178q^{76} - 27645q^{77} - 10592q^{78} - 24914q^{79} - 13683q^{80} - 43222q^{81} + 7010q^{83} - 21568q^{84} + 15366q^{86} + 57084q^{87} - 80787q^{89} + 114772q^{90} - 24438q^{91} + 22049q^{92} - 39723q^{93} + 29955q^{95} + 1378q^{96} - 12210q^{97} + 28845q^{98} - 49211q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
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 37.14 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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 $$S_{5}^{\mathrm{new}}(43, [\chi])$$.