Properties

 Label 1849.4.a.m Level $1849$ Weight $4$ Character orbit 1849.a Self dual yes Analytic conductor $109.095$ Analytic rank $0$ Dimension $110$ CM no Inner twists $2$

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: $$110$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$110q + 492q^{4} + 102q^{6} + 1234q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$110q + 492q^{4} + 102q^{6} + 1234q^{9} + 102q^{10} + 360q^{11} + 166q^{13} + 496q^{14} + 540q^{15} + 2204q^{16} + 610q^{17} + 896q^{21} + 1508q^{23} + 1086q^{24} + 3168q^{25} + 2312q^{31} + 2760q^{35} + 8334q^{36} + 3626q^{38} + 1462q^{40} + 3598q^{41} + 1596q^{44} + 4448q^{47} + 7194q^{49} + 3620q^{52} + 3818q^{53} - 2570q^{54} - 714q^{56} + 3236q^{57} + 3242q^{58} + 8556q^{59} + 178q^{60} + 7308q^{64} + 4202q^{66} + 1992q^{67} + 8994q^{68} + 8256q^{74} + 4784q^{78} + 13752q^{79} + 19678q^{81} + 7620q^{83} + 11390q^{84} + 6012q^{87} - 476q^{90} + 8022q^{92} + 7392q^{95} + 16760q^{96} - 1186q^{97} + 11068q^{99} + O(q^{100})$$

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 −5.53180 −6.46364 22.6009 8.28125 35.7556 −25.9073 −80.7691 14.7786 −45.8102
1.2 −5.51127 1.26223 22.3741 19.4467 −6.95647 10.3981 −79.2194 −25.4068 −107.176
1.3 −5.49399 −8.55746 22.1840 6.67475 47.0146 12.2751 −77.9266 46.2301 −36.6710
1.4 −5.36605 6.88924 20.7944 −18.7139 −36.9680 −7.67108 −68.6556 20.4617 100.419
1.5 −5.23595 −2.93512 19.4152 0.131108 15.3681 −16.0025 −59.7695 −18.3851 −0.686473
1.6 −5.18193 −8.74912 18.8524 −11.4363 45.3373 14.1176 −56.2363 49.5471 59.2620
1.7 −5.17162 3.79592 18.7457 1.41868 −19.6311 25.9835 −55.5726 −12.5910 −7.33688
1.8 −5.08007 −3.35274 17.8071 −16.0526 17.0322 17.0633 −49.8208 −15.7591 81.5484
1.9 −5.06596 8.82751 17.6640 −4.85016 −44.7198 30.6269 −48.9575 50.9249 24.5707
1.10 −4.92230 9.67693 16.2290 −12.1144 −47.6328 −16.5271 −40.5059 66.6431 59.6309
1.11 −4.86125 −9.74641 15.6317 4.01387 47.3797 −30.3164 −37.0997 67.9924 −19.5124
1.12 −4.78359 8.84041 14.8827 13.5668 −42.2888 6.63547 −32.9240 51.1528 −64.8979
1.13 −4.73977 5.14067 14.4654 17.6318 −24.3656 −24.5187 −30.6444 −0.573505 −83.5706
1.14 −4.62802 −8.10864 13.4186 −17.9110 37.5270 −27.1680 −25.0774 38.7501 82.8927
1.15 −4.51768 −4.91857 12.4095 −20.1547 22.2205 −14.7467 −19.9206 −2.80772 91.0526
1.16 −4.51685 5.52727 12.4019 −4.13127 −24.9658 −3.02277 −19.8829 3.55067 18.6603
1.17 −4.50695 −7.50413 12.3126 8.17365 33.8208 30.0213 −19.4369 29.3120 −36.8383
1.18 −4.38832 2.26695 11.2573 −13.4262 −9.94809 4.85010 −14.2943 −21.8610 58.9185
1.19 −4.20768 −0.654616 9.70454 13.9092 2.75441 32.2423 −7.17215 −26.5715 −58.5253
1.20 −4.17102 −0.918823 9.39743 −18.4602 3.83243 −23.0342 −5.82873 −26.1558 76.9977
See next 80 embeddings (of 110 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.110 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

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

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.b odd 2 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1849.4.a.m 110
43.b odd 2 1 inner 1849.4.a.m 110

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1849.4.a.m 110 1.a even 1 1 trivial
1849.4.a.m 110 43.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{110} - \cdots$$ acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(1849))$$.