# Properties

 Label 1849.4.a.h Level $1849$ Weight $4$ Character orbit 1849.a Self dual yes Analytic conductor $109.095$ Analytic rank $0$ Dimension $30$ CM no Inner twists $1$

# Related objects

## 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: $$0$$ 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 −5.24346 −0.263601 19.4939 17.3447 1.38218 −21.1320 −60.2678 −26.9305 −90.9462
1.2 −4.95333 −0.318435 16.5355 12.4187 1.57731 3.53619 −42.2793 −26.8986 −61.5142
1.3 −4.74854 2.44099 14.5486 −1.86645 −11.5911 5.76487 −31.0963 −21.0416 8.86289
1.4 −4.11874 6.75554 8.96404 −11.5913 −27.8243 18.3634 −3.97064 18.6373 47.7418
1.5 −4.08390 −9.96623 8.67820 12.0746 40.7010 17.5242 −2.76970 72.3258 −49.3113
1.6 −3.72135 5.79603 5.84847 −14.8139 −21.5691 −12.2090 8.00659 6.59399 55.1279
1.7 −3.68353 −8.25521 5.56841 −12.2925 30.4083 28.5576 8.95684 41.1485 45.2798
1.8 −3.12588 −4.83570 1.77114 −5.07243 15.1158 −2.39891 19.4707 −3.61601 15.8558
1.9 −1.99192 10.2076 −4.03226 −6.84373 −20.3326 −3.06785 23.9673 77.1944 13.6322
1.10 −1.84451 0.727573 −4.59779 12.1583 −1.34201 −17.8467 23.2367 −26.4706 −22.4260
1.11 −1.56619 −5.42418 −5.54704 8.12470 8.49531 −30.7370 21.2173 2.42171 −12.7249
1.12 −1.40131 7.71122 −6.03633 16.2919 −10.8058 16.8292 19.6692 32.4629 −22.8300
1.13 −1.32038 −4.35495 −6.25659 −15.6111 5.75020 4.97789 18.8242 −8.03441 20.6126
1.14 −0.830523 7.00735 −7.31023 4.56308 −5.81976 −20.3840 12.7155 22.1029 −3.78975
1.15 −0.188737 −1.07307 −7.96438 16.0623 0.202528 29.7402 3.01306 −25.8485 −3.03154
1.16 0.335126 −1.29157 −7.88769 −9.09411 −0.432838 17.7083 −5.32438 −25.3319 −3.04767
1.17 1.36355 −9.26361 −6.14074 −1.21569 −12.6314 −10.5300 −19.2815 58.8145 −1.65764
1.18 1.77522 4.21024 −4.84859 5.54921 7.47410 24.8990 −22.8091 −9.27388 9.85108
1.19 1.92929 5.16200 −4.27784 −3.37495 9.95900 −15.9770 −23.6875 −0.353756 −6.51127
1.20 1.94581 1.92433 −4.21381 −20.3652 3.74438 13.1013 −23.7658 −23.2970 −39.6269
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.h 30
43.b odd 2 1 1849.4.a.g 30
43.e even 7 2 43.4.e.a 60

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.4.e.a 60 43.e even 7 2
1849.4.a.g 30 43.b odd 2 1
1849.4.a.h 30 1.a even 1 1 trivial

## 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 $$S_{4}^{\mathrm{new}}(\Gamma_0(1849))$$.