Properties

Label 4015.2.a.b
Level 4015
Weight 2
Character orbit 4015.a
Self dual yes
Analytic conductor 32.060
Analytic rank 1
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(1\)
Dimension: \(23\)
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.

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

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 −2.71506 1.57103 5.37156 1.00000 −4.26545 1.27925 −9.15401 −0.531858 −2.71506
1.2 −2.35657 2.73189 3.55343 1.00000 −6.43790 −2.31150 −3.66076 4.46323 −2.35657
1.3 −2.32698 −0.285099 3.41485 1.00000 0.663421 −4.31195 −3.29232 −2.91872 −2.32698
1.4 −2.28085 −0.867872 3.20226 1.00000 1.97948 0.729352 −2.74217 −2.24680 −2.28085
1.5 −2.06292 0.357225 2.25565 1.00000 −0.736927 1.84250 −0.527390 −2.87239 −2.06292
1.6 −1.83447 −2.15866 1.36527 1.00000 3.95999 0.444043 1.16439 1.65981 −1.83447
1.7 −1.19799 1.69638 −0.564821 1.00000 −2.03224 −2.11615 3.07263 −0.122309 −1.19799
1.8 −1.16229 1.36223 −0.649085 1.00000 −1.58330 3.38995 3.07900 −1.14434 −1.16229
1.9 −1.09501 −2.94583 −0.800943 1.00000 3.22573 2.47152 3.06707 5.67794 −1.09501
1.10 −1.08357 −1.29689 −0.825886 1.00000 1.40527 −5.06508 3.06203 −1.31806 −1.08357
1.11 −0.654679 2.96699 −1.57140 1.00000 −1.94243 −1.18438 2.33812 5.80304 −0.654679
1.12 −0.182665 1.60195 −1.96663 1.00000 −0.292620 −3.46851 0.724566 −0.433762 −0.182665
1.13 0.152616 −0.242697 −1.97671 1.00000 −0.0370393 2.57515 −0.606909 −2.94110 0.152616
1.14 0.152825 −1.31847 −1.97664 1.00000 −0.201495 −0.959999 −0.607731 −1.26164 0.152825
1.15 0.430868 −1.25921 −1.81435 1.00000 −0.542554 4.34543 −1.64348 −1.41438 0.430868
1.16 0.772478 −3.03398 −1.40328 1.00000 −2.34368 1.44909 −2.62896 6.20504 0.772478
1.17 1.18208 −1.23608 −0.602686 1.00000 −1.46115 −1.06876 −3.07658 −1.47210 1.18208
1.18 1.32991 2.72450 −0.231346 1.00000 3.62333 −4.53918 −2.96748 4.42288 1.32991
1.19 1.55677 0.976240 0.423526 1.00000 1.51978 −0.0535957 −2.45420 −2.04696 1.55677
1.20 1.79465 0.618778 1.22075 1.00000 1.11049 1.73339 −1.39847 −2.61711 1.79465
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
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 4015.2.a.b 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4015.2.a.b 23 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(11\) \(-1\)
\(73\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{23} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database