Properties

Label 6019.2.a.c
Level 6019
Weight 2
Character orbit 6019.a
Self dual yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6019 = 13 \cdot 463 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6019.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 108q - 11q^{2} + q^{3} + 95q^{4} - 40q^{5} - 10q^{6} - 8q^{7} - 33q^{8} + 79q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 108q - 11q^{2} + q^{3} + 95q^{4} - 40q^{5} - 10q^{6} - 8q^{7} - 33q^{8} + 79q^{9} - q^{10} - 45q^{11} - 6q^{12} - 108q^{13} - 31q^{14} - 39q^{15} + 73q^{16} + 21q^{17} - 35q^{18} - 19q^{19} - 79q^{20} - 72q^{21} - 26q^{23} - 23q^{24} + 92q^{25} + 11q^{26} + 7q^{27} - 21q^{28} - 94q^{29} - 24q^{30} - 36q^{31} - 77q^{32} - 32q^{33} - 58q^{34} - 10q^{35} + 17q^{36} - 54q^{37} - 12q^{38} - q^{39} - 4q^{40} - 68q^{41} - 11q^{42} - 32q^{43} - 151q^{44} - 121q^{45} - 33q^{46} - 51q^{47} - 27q^{48} + 72q^{49} - 45q^{50} - 24q^{51} - 95q^{52} - 81q^{53} - 29q^{54} + 4q^{55} - 68q^{56} - 45q^{57} - 30q^{58} - 94q^{59} - 108q^{60} - 39q^{61} - 9q^{62} - 52q^{63} + 31q^{64} + 40q^{65} - 40q^{66} - 47q^{67} + 24q^{68} - 60q^{69} - 66q^{70} - 86q^{71} - 91q^{72} - 51q^{73} - 110q^{74} - 7q^{75} - 51q^{76} - 96q^{77} + 10q^{78} - 18q^{79} - 136q^{80} - 24q^{81} - 33q^{82} - 77q^{83} - 113q^{84} - 95q^{85} - 137q^{86} + 23q^{87} + 19q^{88} - 112q^{89} - 19q^{90} + 8q^{91} - 111q^{92} - 124q^{93} - 20q^{94} - 73q^{95} - 77q^{96} - 41q^{97} - 80q^{98} - 154q^{99} + O(q^{100}) \)

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 −2.77848 2.29765 5.71995 2.18323 −6.38396 0.752947 −10.3358 2.27917 −6.06605
1.2 −2.73685 −2.13610 5.49032 −3.88543 5.84618 −1.04170 −9.55248 1.56292 10.6338
1.3 −2.64969 −0.413927 5.02086 −1.95969 1.09678 −0.899778 −8.00435 −2.82866 5.19257
1.4 −2.62932 0.928194 4.91333 1.81764 −2.44052 3.79843 −7.66009 −2.13846 −4.77917
1.5 −2.62196 −0.813055 4.87469 0.562087 2.13180 −5.01388 −7.53732 −2.33894 −1.47377
1.6 −2.61467 0.516414 4.83649 −3.96792 −1.35025 3.66433 −7.41648 −2.73332 10.3748
1.7 −2.60952 3.26666 4.80961 −2.76749 −8.52442 −0.615812 −7.33173 7.67107 7.22184
1.8 −2.59599 1.19783 4.73919 −2.90334 −3.10956 −3.26881 −7.11092 −1.56520 7.53704
1.9 −2.56322 −2.39331 4.57009 1.98047 6.13457 1.46442 −6.58772 2.72791 −5.07639
1.10 −2.51181 −2.99105 4.30921 1.76112 7.51295 3.89256 −5.80031 5.94635 −4.42360
1.11 −2.39631 −0.467815 3.74231 2.01057 1.12103 −2.84779 −4.17511 −2.78115 −4.81795
1.12 −2.34535 −1.65067 3.50065 −1.17678 3.87140 2.05341 −3.51955 −0.275278 2.75996
1.13 −2.34425 −1.25776 3.49550 −1.49624 2.94851 5.17811 −3.50582 −1.41803 3.50756
1.14 −2.26345 2.92995 3.12323 0.680242 −6.63181 −3.22192 −2.54237 5.58462 −1.53970
1.15 −2.25939 2.42736 3.10485 −0.500622 −5.48435 4.41326 −2.49629 2.89206 1.13110
1.16 −2.23728 2.31482 3.00542 −4.05108 −5.17891 −5.18040 −2.24940 2.35841 9.06339
1.17 −2.20802 −2.87685 2.87536 1.19118 6.35214 −0.105056 −1.93280 5.27625 −2.63016
1.18 −2.18373 2.09330 2.76866 2.17810 −4.57119 −2.34745 −1.67854 1.38190 −4.75637
1.19 −2.14163 −1.26927 2.58656 2.68002 2.71830 −0.999709 −1.25619 −1.38895 −5.73960
1.20 −2.12654 −0.167601 2.52216 −1.92531 0.356410 0.0410631 −1.11038 −2.97191 4.09424
See next 80 embeddings (of 108 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.108
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(13\) \(1\)
\(463\) \(1\)

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 6019.2.a.c 108
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6019.2.a.c 108 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{108} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database