Properties

Label 6019.2.a.e
Level 6019
Weight 2
Character orbit 6019.a
Self dual yes
Analytic conductor 48.062
Analytic rank 0
Dimension 130
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: \(0\)
Dimension: \(130\)
Coefficient ring index: multiple of None
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.

\(\operatorname{Tr}(f)(q) = \) \( 130q + 10q^{2} + 11q^{3} + 146q^{4} + 40q^{5} + 4q^{6} + 8q^{7} + 24q^{8} + 181q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 130q + 10q^{2} + 11q^{3} + 146q^{4} + 40q^{5} + 4q^{6} + 8q^{7} + 24q^{8} + 181q^{9} + 5q^{10} + 43q^{11} + 28q^{12} + 130q^{13} + 47q^{14} + 29q^{15} + 170q^{16} + 85q^{17} + 20q^{18} + 3q^{19} + 73q^{20} + 62q^{21} + 12q^{22} + 62q^{23} - 5q^{24} + 178q^{25} + 10q^{26} + 35q^{27} - q^{28} + 134q^{29} + 24q^{30} + 14q^{31} + 48q^{32} + 4q^{33} + 4q^{34} + 50q^{35} + 244q^{36} + 32q^{37} + 76q^{38} + 11q^{39} - 6q^{40} + 48q^{41} + 9q^{42} + 34q^{43} + 123q^{44} + 115q^{45} + 5q^{46} + 25q^{47} + 35q^{48} + 210q^{49} + 24q^{50} + 20q^{51} + 146q^{52} + 193q^{53} - 39q^{54} + 32q^{55} + 122q^{56} + 7q^{57} - 4q^{58} + 50q^{59} + 42q^{60} + 57q^{61} + 51q^{62} + 8q^{63} + 172q^{64} + 40q^{65} - 4q^{66} + 21q^{67} + 132q^{68} + 92q^{69} - 46q^{70} + 58q^{71} - 26q^{72} + 15q^{73} + 120q^{74} + 23q^{75} - 65q^{76} + 192q^{77} + 4q^{78} + 32q^{79} + 66q^{80} + 326q^{81} + 11q^{82} + 33q^{83} + 5q^{84} + 43q^{85} + 105q^{86} + 31q^{87} - 17q^{88} + 84q^{89} - 73q^{90} + 8q^{91} + 161q^{92} + 52q^{93} + 4q^{94} + 59q^{95} - 77q^{96} + 9q^{97} - 61q^{98} + 100q^{99} + O(q^{100}) \)

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 −2.80453 3.24972 5.86540 2.53460 −9.11395 2.92678 −10.8406 7.56069 −7.10835
1.2 −2.76072 1.85217 5.62158 −1.74367 −5.11334 −4.49860 −9.99819 0.430551 4.81380
1.3 −2.70229 −1.73872 5.30239 −0.220244 4.69853 −4.26508 −8.92402 0.0231491 0.595165
1.4 −2.65690 −1.17656 5.05912 −3.97344 3.12601 −1.98444 −8.12779 −1.61571 10.5570
1.5 −2.57909 0.0546080 4.65172 2.10708 −0.140839 −1.58025 −6.83904 −2.99702 −5.43435
1.6 −2.55222 −2.23917 4.51381 1.89858 5.71484 −3.17598 −6.41579 2.01387 −4.84558
1.7 −2.52323 3.28941 4.36670 3.66616 −8.29994 −5.12423 −5.97175 7.82019 −9.25058
1.8 −2.52101 −1.65021 4.35552 2.33988 4.16020 4.41588 −5.93829 −0.276814 −5.89887
1.9 −2.51967 −3.32656 4.34873 −0.493062 8.38182 −0.741150 −5.91802 8.06597 1.24235
1.10 −2.50771 −1.46096 4.28860 1.53494 3.66367 0.422474 −5.73914 −0.865591 −3.84918
1.11 −2.49834 2.94692 4.24169 −1.72770 −7.36239 −2.26517 −5.60049 5.68431 4.31639
1.12 −2.49278 −3.38832 4.21397 3.98474 8.44636 1.44276 −5.51896 8.48073 −9.93310
1.13 −2.48853 0.814378 4.19279 −1.02272 −2.02661 0.518159 −5.45682 −2.33679 2.54508
1.14 −2.40942 1.96845 3.80532 3.79888 −4.74282 2.98166 −4.34977 0.874791 −9.15310
1.15 −2.39514 1.83196 3.73671 3.10935 −4.38781 4.25584 −4.15967 0.356083 −7.44733
1.16 −2.34374 2.49578 3.49312 −2.30500 −5.84945 0.790647 −3.49949 3.22890 5.40232
1.17 −2.33535 −1.90450 3.45386 −1.81837 4.44767 2.51906 −3.39528 0.627108 4.24653
1.18 −2.28421 0.124993 3.21761 −2.44620 −0.285511 −2.39008 −2.78127 −2.98438 5.58762
1.19 −2.17988 −0.326610 2.75186 0.291618 0.711970 2.70764 −1.63895 −2.89333 −0.635691
1.20 −2.07170 0.913939 2.29195 −0.284252 −1.89341 −4.46498 −0.604826 −2.16472 0.588884
See next 80 embeddings (of 130 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.130
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 6019.2.a.e 130
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6019.2.a.e 130 1.a even 1 1 trivial

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{130} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\).