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

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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:

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 \(T_{2}^{50} - \cdots\) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database