Properties

Label 1849.4.a.k
Level 1849
Weight 4
Character orbit 1849.a
Self dual yes
Analytic conductor 109.095
Analytic rank 1
Dimension 60
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: \(60\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 60q - 15q^{2} - 37q^{3} + 213q^{4} - 51q^{5} + 22q^{6} - 54q^{7} - 204q^{8} + 387q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 60q - 15q^{2} - 37q^{3} + 213q^{4} - 51q^{5} + 22q^{6} - 54q^{7} - 204q^{8} + 387q^{9} + 27q^{10} + 43q^{11} - 432q^{12} + 13q^{13} + 96q^{14} + 65q^{15} + 717q^{16} - 138q^{17} - 625q^{18} - 610q^{19} - 345q^{20} + 611q^{21} - 118q^{22} - 243q^{23} + 258q^{24} + 899q^{25} - 1071q^{26} - 1609q^{27} - 46q^{28} - 773q^{29} - 375q^{30} - 97q^{31} - 1967q^{32} - 500q^{33} - 217q^{34} + 247q^{35} + 175q^{36} - 228q^{37} + 1253q^{38} - 1493q^{39} + 2220q^{40} - 951q^{41} - 2643q^{42} - 1378q^{44} - 1086q^{45} + 565q^{46} - 2q^{47} - 2303q^{48} + 1264q^{49} - 3273q^{50} - 3076q^{51} - 2825q^{52} - 39q^{53} + 5201q^{54} - 1306q^{55} + 3683q^{56} + 1342q^{57} + 2588q^{58} - 1065q^{59} + 2803q^{60} - 2999q^{61} - 5569q^{62} - 2377q^{63} + 2082q^{64} - 5578q^{65} + 3338q^{66} + 961q^{67} - 3754q^{68} - 1817q^{69} - 2738q^{70} - 8003q^{71} - 1412q^{72} + 1011q^{73} - 1413q^{74} - 7457q^{75} - 5516q^{76} - 4052q^{77} + 1091q^{78} - 4422q^{79} - 1610q^{80} + 2108q^{81} - 4676q^{82} - 297q^{83} - 54q^{84} - 4333q^{85} + 1377q^{87} - 3652q^{88} - 2480q^{89} - 1414q^{90} - 4551q^{91} - 3286q^{92} - 4q^{93} - 4609q^{94} - 835q^{95} + 5864q^{96} + 3785q^{97} - 753q^{98} + 5072q^{99} + O(q^{100}) \)

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 −5.51648 0.947128 22.4316 −12.1331 −5.22481 14.8097 −79.6117 −26.1029 66.9318
1.2 −5.45533 −5.87893 21.7606 −15.7772 32.0715 −10.5901 −75.0688 7.56187 86.0700
1.3 −5.29884 2.87298 20.0777 −16.9175 −15.2234 −23.6451 −63.9980 −18.7460 89.6431
1.4 −5.27638 −1.62592 19.8401 9.68193 8.57899 −2.56298 −62.4730 −24.3564 −51.0855
1.5 −5.24990 −9.69865 19.5614 −5.59920 50.9169 0.820208 −60.6963 67.0638 29.3952
1.6 −4.92818 1.20886 16.2870 −11.7477 −5.95749 −36.0345 −40.8396 −25.5387 57.8946
1.7 −4.89580 −8.83989 15.9689 20.6381 43.2783 −10.5375 −39.0140 51.1436 −101.040
1.8 −4.85348 5.30735 15.5563 16.1569 −25.7591 27.9534 −36.6742 1.16797 −78.4173
1.9 −4.40707 −0.148254 11.4223 15.4121 0.653363 27.6883 −15.0821 −26.9780 −67.9222
1.10 −4.22240 5.78517 9.82864 5.96613 −24.4273 −8.16125 −7.72124 6.46824 −25.1914
1.11 −4.01034 9.44314 8.08281 −4.71622 −37.8702 23.9018 −0.332104 62.1728 18.9136
1.12 −3.61784 0.230904 5.08877 16.9044 −0.835373 −0.941277 10.5324 −26.9467 −61.1575
1.13 −3.57276 1.25498 4.76459 −8.29511 −4.48372 −13.8938 11.5593 −25.4250 29.6364
1.14 −3.46218 −10.0163 3.98667 −19.0537 34.6782 3.52814 13.8949 73.3264 65.9672
1.15 −3.42085 −8.07188 3.70224 −8.16009 27.6127 −23.9507 14.7020 38.1553 27.9145
1.16 −3.40283 5.79667 3.57928 10.2155 −19.7251 9.81633 15.0430 6.60143 −34.7615
1.17 −3.39478 −9.53108 3.52451 −2.38295 32.3559 −2.00316 15.1933 63.8414 8.08958
1.18 −3.00899 1.07669 1.05404 −2.94077 −3.23974 −27.1168 20.9004 −25.8407 8.84876
1.19 −2.74329 8.71284 −0.474355 −4.82785 −23.9019 0.994355 23.2476 48.9136 13.2442
1.20 −2.61993 −5.66517 −1.13597 −13.7987 14.8423 18.6959 23.9356 5.09416 36.1517
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.60
Significant digits:
Format:

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.k 60
43.b odd 2 1 1849.4.a.l 60
43.h odd 42 2 43.4.g.a 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.4.g.a 120 43.h odd 42 2
1849.4.a.k 60 1.a even 1 1 trivial
1849.4.a.l 60 43.b odd 2 1

Atkin-Lehner signs

\( p \) Sign
\(43\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{60} + \cdots\) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database