# Properties

 Label 1849.4.a.j Level $1849$ Weight $4$ Character orbit 1849.a Self dual yes Analytic conductor $109.095$ Analytic rank $1$ Dimension $50$ 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: $$1$$ Dimension: $$50$$ Twist minimal: yes 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.

 $$\operatorname{Tr}(f)(q) =$$ $$50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100})$$

## 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 −5.33237 5.38049 20.4342 1.13957 −28.6907 19.4433 −66.3036 1.94964 −6.07658
1.2 −5.20801 −5.00842 19.1234 13.8519 26.0839 26.6225 −57.9307 −1.91570 −72.1409
1.3 −4.80413 2.56623 15.0797 6.34124 −12.3285 −6.17767 −34.0117 −20.4145 −30.4642
1.4 −4.75171 7.02039 14.5788 4.22415 −33.3589 11.1787 −31.2605 22.2859 −20.0719
1.5 −4.55366 −4.29077 12.7358 −2.70051 19.5387 9.48123 −21.5655 −8.58929 12.2972
1.6 −4.32699 4.31725 10.7228 −7.58298 −18.6807 −15.1566 −11.7817 −8.36138 32.8115
1.7 −4.20684 −4.82832 9.69750 7.01067 20.3120 −27.8882 −7.14112 −3.68734 −29.4928
1.8 −4.15048 4.65912 9.22650 19.9023 −19.3376 −27.8552 −5.09055 −5.29261 −82.6043
1.9 −4.08033 −6.02226 8.64912 2.18258 24.5728 8.90728 −2.64861 9.26767 −8.90564
1.10 −3.88871 9.09520 7.12206 −19.0468 −35.3686 18.7927 3.41407 55.7226 74.0673
1.11 −3.61756 −2.47684 5.08677 −17.9947 8.96012 10.9253 10.5388 −20.8653 65.0971
1.12 −3.07922 −5.77516 1.48163 −13.4757 17.7830 34.2458 20.0715 6.35250 41.4947
1.13 −2.44476 −8.05562 −2.02317 −13.2954 19.6940 1.50720 24.5042 37.8930 32.5040
1.14 −2.34626 −7.09807 −2.49508 10.0323 16.6539 1.59249 24.6242 23.3826 −23.5383
1.15 −2.34509 2.42890 −2.50055 −18.7081 −5.69599 −0.512587 24.6247 −21.1004 43.8722
1.16 −2.12255 9.87196 −3.49478 −15.5747 −20.9537 −16.3831 24.3983 70.4556 33.0580
1.17 −1.89933 6.15189 −4.39254 1.87975 −11.6845 −2.77777 23.5375 10.8458 −3.57027
1.18 −1.84969 3.08645 −4.57866 18.1899 −5.70896 −24.2083 23.2666 −17.4738 −33.6456
1.19 −1.67189 −3.03153 −5.20480 19.6184 5.06836 −28.4637 22.0769 −17.8099 −32.7997
1.20 −1.29424 3.36009 −6.32495 −1.78174 −4.34876 27.5745 18.5399 −15.7098 2.30599
See all 50 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.50 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.j yes 50
43.b odd 2 1 1849.4.a.i 50

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1849.4.a.i 50 43.b odd 2 1
1849.4.a.j yes 50 1.a even 1 1 trivial

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$15\!\cdots\!82$$$$T_{2}^{37} - 153098536947 T_{2}^{36} +$$$$36\!\cdots\!46$$$$T_{2}^{35} -$$$$13\!\cdots\!65$$$$T_{2}^{34} -$$$$67\!\cdots\!06$$$$T_{2}^{33} +$$$$46\!\cdots\!17$$$$T_{2}^{32} +$$$$10\!\cdots\!63$$$$T_{2}^{31} -$$$$94\!\cdots\!79$$$$T_{2}^{30} -$$$$11\!\cdots\!60$$$$T_{2}^{29} +$$$$13\!\cdots\!37$$$$T_{2}^{28} +$$$$11\!\cdots\!44$$$$T_{2}^{27} -$$$$14\!\cdots\!34$$$$T_{2}^{26} -$$$$88\!\cdots\!16$$$$T_{2}^{25} +$$$$11\!\cdots\!01$$$$T_{2}^{24} +$$$$55\!\cdots\!27$$$$T_{2}^{23} -$$$$76\!\cdots\!44$$$$T_{2}^{22} -$$$$27\!\cdots\!74$$$$T_{2}^{21} +$$$$38\!\cdots\!51$$$$T_{2}^{20} +$$$$10\!\cdots\!46$$$$T_{2}^{19} -$$$$15\!\cdots\!42$$$$T_{2}^{18} -$$$$33\!\cdots\!08$$$$T_{2}^{17} +$$$$46\!\cdots\!86$$$$T_{2}^{16} +$$$$77\!\cdots\!77$$$$T_{2}^{15} -$$$$10\!\cdots\!20$$$$T_{2}^{14} -$$$$13\!\cdots\!64$$$$T_{2}^{13} +$$$$18\!\cdots\!08$$$$T_{2}^{12} +$$$$16\!\cdots\!32$$$$T_{2}^{11} -$$$$23\!\cdots\!88$$$$T_{2}^{10} -$$$$14\!\cdots\!80$$$$T_{2}^{9} +$$$$20\!\cdots\!08$$$$T_{2}^{8} +$$$$71\!\cdots\!88$$$$T_{2}^{7} -$$$$11\!\cdots\!52$$$$T_{2}^{6} -$$$$15\!\cdots\!00$$$$T_{2}^{5} +$$$$38\!\cdots\!20$$$$T_{2}^{4} -$$$$14\!\cdots\!04$$$$T_{2}^{3} -$$$$53\!\cdots\!20$$$$T_{2}^{2} +$$$$82\!\cdots\!40$$$$T_{2} +$$$$16\!\cdots\!28$$">$$T_{2}^{50} - \cdots$$ acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(1849))$$.