# Properties

 Label 1849.4.a.g Level $1849$ Weight $4$ Character orbit 1849.a Self dual yes Analytic conductor $109.095$ Analytic rank $1$ Dimension $30$ CM no Inner twists $1$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1849 = 43^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1849.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$109.094531601$$ Analytic rank: $$1$$ Dimension: $$30$$ Twist minimal: no (minimal twist has level 43) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} - 27q^{10} + 80q^{11} + 36q^{12} - 13q^{13} + 36q^{14} + 16q^{15} + 318q^{16} + 66q^{17} - 80q^{18} - 254q^{19} - 312q^{20} - 548q^{21} - 305q^{22} - 105q^{23} + 123q^{24} + 523q^{25} - 549q^{26} + 10q^{27} - 578q^{28} - 793q^{29} - 1560q^{30} - 359q^{31} - 676q^{32} - 208q^{33} - 1007q^{34} - 514q^{35} + 776q^{36} - 510q^{37} - 2066q^{38} - 898q^{39} - 1248q^{40} - 270q^{41} + 915q^{42} + 3256q^{44} - 807q^{45} - 1960q^{46} + 1421q^{47} + 632q^{48} + 386q^{49} + 141q^{50} - 209q^{51} + 2825q^{52} - 21q^{53} + 2368q^{54} - 2258q^{55} + 2521q^{56} - 1723q^{57} - 347q^{58} + 1752q^{59} + 2711q^{60} - 1759q^{61} - 395q^{62} - 2204q^{63} + 222q^{64} - 1151q^{65} + 160q^{66} - 3001q^{67} + 1921q^{68} - 1660q^{69} - 1597q^{70} - 727q^{71} - 9100q^{72} - 4623q^{73} - 2649q^{74} - 1027q^{75} - 874q^{76} - 3556q^{77} - 4979q^{78} + 546q^{79} - 5809q^{80} - 410q^{81} + 4397q^{82} - 492q^{83} - 10611q^{84} + 1723q^{85} + 5937q^{87} - 3974q^{88} - 5218q^{89} + 10492q^{90} - 1104q^{91} + 1060q^{92} - 1997q^{93} + 2134q^{94} + 6346q^{95} - 11984q^{96} + 2590q^{97} - 6270q^{98} - 2693q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1 −5.55308 6.73841 22.8367 8.33670 −37.4189 −27.2593 −82.3895 18.4062 −46.2944
1.2 −5.07016 5.26544 17.7066 3.42027 −26.6966 −25.1802 −49.2138 0.724844 −17.3413
1.3 −5.00294 −7.79914 17.0294 −17.6229 39.0186 25.3356 −45.1735 33.8266 88.1665
1.4 −4.74823 −6.58177 14.5457 −7.24018 31.2517 −6.49418 −31.0804 16.3197 34.3780
1.5 −4.39566 −7.85436 11.3218 −5.85216 34.5251 −12.3980 −14.6016 34.6910 25.7241
1.6 −4.36589 4.55814 11.0610 9.21441 −19.9004 12.2688 −13.3641 −6.22333 −40.2291
1.7 −3.60614 0.812227 5.00427 −5.99647 −2.92901 26.3629 10.8030 −26.3403 21.6241
1.8 −3.54418 −3.02897 4.56122 20.5936 10.7352 15.8438 12.1877 −17.8253 −72.9874
1.9 −2.89826 6.20542 0.399940 −21.5042 −17.9850 −25.5918 22.0270 11.5073 62.3249
1.10 −2.28876 6.58088 −2.76159 −7.90295 −15.0620 15.8319 24.6307 16.3080 18.0879
1.11 −1.94581 −1.92433 −4.21381 20.3652 3.74438 −13.1013 23.7658 −23.2970 −39.6269
1.12 −1.92929 −5.16200 −4.27784 3.37495 9.95900 15.9770 23.6875 −0.353756 −6.51127
1.13 −1.77522 −4.21024 −4.84859 −5.54921 7.47410 −24.8990 22.8091 −9.27388 9.85108
1.14 −1.36355 9.26361 −6.14074 1.21569 −12.6314 10.5300 19.2815 58.8145 −1.65764
1.15 −0.335126 1.29157 −7.88769 9.09411 −0.432838 −17.7083 5.32438 −25.3319 −3.04767
1.16 0.188737 1.07307 −7.96438 −16.0623 0.202528 −29.7402 −3.01306 −25.8485 −3.03154
1.17 0.830523 −7.00735 −7.31023 −4.56308 −5.81976 20.3840 −12.7155 22.1029 −3.78975
1.18 1.32038 4.35495 −6.25659 15.6111 5.75020 −4.97789 −18.8242 −8.03441 20.6126
1.19 1.40131 −7.71122 −6.03633 −16.2919 −10.8058 −16.8292 −19.6692 32.4629 −22.8300
1.20 1.56619 5.42418 −5.54704 −8.12470 8.49531 30.7370 −21.2173 2.42171 −12.7249
See all 30 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.30 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$43$$ $$-1$$

## Inner twists

This newform does not admit any (nontrivial) inner twists.

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1849.4.a.g 30
43.b odd 2 1 1849.4.a.h 30
43.f odd 14 2 43.4.e.a 60

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.4.e.a 60 43.f odd 14 2
1849.4.a.g 30 1.a even 1 1 trivial
1849.4.a.h 30 43.b odd 2 1

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$10\!\cdots\!23$$$$T_{2}^{13} - 769892821768 T_{2}^{12} -$$$$44\!\cdots\!43$$$$T_{2}^{11} +$$$$26\!\cdots\!44$$$$T_{2}^{10} +$$$$13\!\cdots\!85$$$$T_{2}^{9} -$$$$67\!\cdots\!70$$$$T_{2}^{8} -$$$$24\!\cdots\!72$$$$T_{2}^{7} +$$$$12\!\cdots\!84$$$$T_{2}^{6} +$$$$27\!\cdots\!28$$$$T_{2}^{5} -$$$$13\!\cdots\!52$$$$T_{2}^{4} -$$$$14\!\cdots\!68$$$$T_{2}^{3} +$$$$72\!\cdots\!76$$$$T_{2}^{2} +$$$$18\!\cdots\!32$$$$T_{2} - 491617257984$$">$$T_{2}^{30} + \cdots$$ acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(1849))$$.