Properties

Label 4021.2.a.b
Level 4021
Weight 2
Character orbit 4021.a
Self dual yes
Analytic conductor 32.108
Analytic rank 1
Dimension 151
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4021.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1078466528\)
Analytic rank: \(1\)
Dimension: \(151\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 151q - 16q^{2} - 29q^{3} + 120q^{4} - 27q^{5} - 18q^{6} - 18q^{7} - 48q^{8} + 98q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 151q - 16q^{2} - 29q^{3} + 120q^{4} - 27q^{5} - 18q^{6} - 18q^{7} - 48q^{8} + 98q^{9} - 7q^{10} - 126q^{11} - 47q^{12} - 10q^{13} - 58q^{14} - 50q^{15} + 74q^{16} - 39q^{17} - 47q^{18} - 48q^{19} - 64q^{20} - 50q^{21} - 7q^{22} - 91q^{23} - 44q^{24} + 102q^{25} - 94q^{26} - 92q^{27} - 27q^{28} - 79q^{29} - 12q^{30} - 33q^{31} - 102q^{32} - 7q^{33} - 17q^{34} - 183q^{35} - 6q^{36} - 24q^{37} - 77q^{38} - 81q^{39} - 37q^{40} - 62q^{41} + 4q^{42} - 74q^{43} - 209q^{44} - 35q^{45} - 37q^{46} - 127q^{47} - 59q^{48} + 75q^{49} - 79q^{50} - 138q^{51} - 12q^{52} - 104q^{53} - 43q^{54} - 49q^{55} - 167q^{56} - 19q^{57} - 32q^{58} - 207q^{59} - 94q^{60} - 57q^{61} - 69q^{62} - 49q^{63} - 4q^{64} - 78q^{65} - 51q^{66} - 92q^{67} - 80q^{68} - 84q^{69} + 5q^{70} - 217q^{71} - 79q^{72} + 2q^{73} - 113q^{74} - 173q^{75} - 70q^{76} - 85q^{77} - 46q^{78} - 70q^{79} - 95q^{80} - 49q^{81} - 12q^{82} - 109q^{83} - 114q^{84} - 25q^{85} - 136q^{86} - 60q^{87} - 2q^{88} - 144q^{89} - 55q^{90} - 62q^{91} - 175q^{92} - 42q^{93} - 15q^{94} - 189q^{95} - 64q^{96} - 24q^{97} - 37q^{98} - 293q^{99} + O(q^{100}) \)

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 −2.75476 1.58414 5.58872 −2.10175 −4.36394 2.25410 −9.88608 −0.490495 5.78981
1.2 −2.72951 0.628920 5.45022 1.83150 −1.71664 −2.53691 −9.41739 −2.60446 −4.99910
1.3 −2.70449 −0.271185 5.31424 −1.63010 0.733417 −2.12965 −8.96332 −2.92646 4.40858
1.4 −2.69273 1.85515 5.25082 1.44838 −4.99542 4.11859 −8.75359 0.441579 −3.90011
1.5 −2.69045 −2.62936 5.23855 −3.01308 7.07417 1.15272 −8.71316 3.91353 8.10656
1.6 −2.66021 −2.13808 5.07674 4.04432 5.68776 2.33919 −8.18478 1.57140 −10.7588
1.7 −2.64544 −1.40778 4.99834 −2.43306 3.72420 1.18791 −7.93191 −1.01815 6.43651
1.8 −2.64112 2.33893 4.97551 −1.70298 −6.17740 0.267464 −7.85867 2.47061 4.49778
1.9 −2.55186 −0.0699266 4.51199 −3.83680 0.178443 5.05477 −6.41025 −2.99511 9.79098
1.10 −2.54734 1.98068 4.48893 0.894542 −5.04546 −4.01929 −6.34013 0.923096 −2.27870
1.11 −2.52668 −3.06344 4.38409 0.824998 7.74031 3.92448 −6.02383 6.38463 −2.08450
1.12 −2.49227 −2.01078 4.21142 3.04731 5.01140 −1.48654 −5.51145 1.04322 −7.59472
1.13 −2.43685 −1.07161 3.93825 2.02983 2.61136 3.59143 −4.72324 −1.85165 −4.94641
1.14 −2.41856 −1.61942 3.84946 −1.02567 3.91668 2.10305 −4.47303 −0.377473 2.48065
1.15 −2.38084 2.66837 3.66838 −4.16670 −6.35294 0.560262 −3.97213 4.12018 9.92023
1.16 −2.37064 −0.181119 3.61993 1.77155 0.429369 −0.953276 −3.84026 −2.96720 −4.19971
1.17 −2.36898 2.54130 3.61208 1.21451 −6.02031 −1.53479 −3.81900 3.45822 −2.87715
1.18 −2.33695 0.0283872 3.46135 −2.49189 −0.0663397 4.25940 −3.41512 −2.99919 5.82343
1.19 −2.23472 −1.90948 2.99397 0.847533 4.26716 −4.08817 −2.22124 0.646133 −1.89400
1.20 −2.23064 −3.03788 2.97574 2.24920 6.77641 −3.34201 −2.17651 6.22873 −5.01714
See next 80 embeddings (of 151 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.151
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 4021.2.a.b 151
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4021.2.a.b 151 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(4021\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{151} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4021))\).