Properties

Label 1849.4.a.l
Level 1849
Weight 4
Character orbit 1849.a
Self dual yes
Analytic conductor 109.095
Analytic rank 0
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: \(0\)
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 −5.54883 3.16072 22.7896 −0.181879 −17.5383 0.441468 −82.0648 −17.0098 1.00922
1.2 −4.87633 −2.05704 15.7786 −3.82460 10.0308 10.2100 −37.9309 −22.7686 18.6500
1.3 −4.73539 6.79195 14.4239 −5.40004 −32.1625 −14.4341 −30.4195 19.1306 25.5713
1.4 −4.73263 −0.112092 14.3978 9.26635 0.530489 −26.6989 −30.2784 −26.9874 −43.8542
1.5 −4.56753 −2.19336 12.8623 −3.47394 10.0182 19.6384 −22.2088 −22.1892 15.8673
1.6 −4.53463 3.33693 12.5629 −15.3423 −15.1318 −5.56073 −20.6909 −15.8649 69.5716
1.7 −4.52369 8.77561 12.4638 −8.38225 −39.6982 −31.9850 −20.1929 50.0114 37.9187
1.8 −4.51171 −4.95558 12.3555 1.01635 22.3581 6.42896 −19.6507 −2.44218 −4.58548
1.9 −4.02380 5.78552 8.19098 21.7212 −23.2798 5.74476 −0.768479 6.47225 −87.4016
1.10 −3.96613 −5.58493 7.73016 −7.81764 22.1506 27.2797 1.07022 4.19148 31.0057
1.11 −3.76599 −6.86945 6.18266 18.0611 25.8703 −6.19899 6.84408 20.1894 −68.0178
1.12 −3.46142 −6.83402 3.98140 1.69224 23.6554 −8.79957 13.9100 19.7039 −5.85755
1.13 −3.35944 9.40931 3.28580 13.8884 −31.6100 31.8219 15.8370 61.5352 −46.6572
1.14 −3.29999 5.03144 2.88991 8.27916 −16.6037 −12.1380 16.8632 −1.68463 −27.3211
1.15 −2.96101 −0.861620 0.767595 −10.7841 2.55127 −8.60318 21.4152 −26.2576 31.9318
1.16 −2.59936 7.01034 −1.24330 8.10615 −18.2224 33.0836 24.0267 22.1448 −21.0708
1.17 −2.55745 −7.55882 −1.45945 2.65059 19.3313 −19.9078 24.1921 30.1357 −6.77875
1.18 −2.21102 3.63995 −3.11137 17.7911 −8.04801 23.5136 24.5675 −13.7508 −39.3366
1.19 −2.06457 3.98114 −3.73756 17.7822 −8.21933 5.12480 24.2330 −11.1505 −36.7125
1.20 −1.82039 −6.70653 −4.68620 −11.7013 12.2085 −4.14681 23.0938 17.9776 21.3008
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.l 60
43.b odd 2 1 1849.4.a.k 60
43.g even 21 2 43.4.g.a 120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.4.g.a 120 43.g even 21 2
1849.4.a.k 60 43.b odd 2 1
1849.4.a.l 60 1.a even 1 1 trivial

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