Properties

Label 4015.2.a.e
Level 4015
Weight 2
Character orbit 4015.a
Self dual yes
Analytic conductor 32.060
Analytic rank 0
Dimension 27
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: \(0\)
Dimension: \(27\)
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.

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

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 −2.34661 2.98114 3.50659 −1.00000 −6.99558 0.286679 −3.53537 5.88720 2.34661
1.2 −2.33465 −0.983408 3.45061 −1.00000 2.29592 −2.48043 −3.38668 −2.03291 2.33465
1.3 −2.24746 1.22256 3.05108 −1.00000 −2.74765 −0.859995 −2.36225 −1.50535 2.24746
1.4 −2.19462 −2.47425 2.81638 −1.00000 5.43004 3.64013 −1.79164 3.12189 2.19462
1.5 −1.64001 1.19849 0.689644 −1.00000 −1.96554 −2.90687 2.14900 −1.56361 1.64001
1.6 −1.49741 2.11504 0.242240 −1.00000 −3.16709 4.23699 2.63209 1.47340 1.49741
1.7 −1.35811 0.129284 −0.155539 −1.00000 −0.175582 −0.681246 2.92746 −2.98329 1.35811
1.8 −1.32466 −2.16018 −0.245282 −1.00000 2.86150 −3.08475 2.97423 1.66638 1.32466
1.9 −0.788550 −0.398652 −1.37819 −1.00000 0.314357 4.29459 2.66387 −2.84108 0.788550
1.10 −0.590698 0.738483 −1.65108 −1.00000 −0.436221 −1.02669 2.15668 −2.45464 0.590698
1.11 −0.339834 2.87141 −1.88451 −1.00000 −0.975803 0.914353 1.32009 5.24498 0.339834
1.12 −0.0879542 −2.14989 −1.99226 −1.00000 0.189092 3.99167 0.351137 1.62202 0.0879542
1.13 −0.0560878 −2.46183 −1.99685 −1.00000 0.138079 −2.79584 0.224175 3.06062 0.0560878
1.14 0.0645883 −2.75103 −1.99583 −1.00000 −0.177684 0.602441 −0.258084 4.56815 −0.0645883
1.15 0.782969 −1.17473 −1.38696 −1.00000 −0.919776 1.16812 −2.65188 −1.62001 −0.782969
1.16 0.924358 1.45154 −1.14556 −1.00000 1.34174 3.41942 −2.90763 −0.893034 −0.924358
1.17 0.966384 2.94159 −1.06610 −1.00000 2.84271 −4.68182 −2.96303 5.65296 −0.966384
1.18 1.13591 3.01832 −0.709697 −1.00000 3.42856 3.60395 −3.07799 6.11027 −1.13591
1.19 1.36344 −0.755926 −0.141019 −1.00000 −1.03066 1.53902 −2.91916 −2.42858 −1.36344
1.20 1.39893 −0.528085 −0.0429944 −1.00000 −0.738755 −3.55790 −2.85801 −2.72113 −1.39893
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
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.e 27
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4015.2.a.e 27 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 \(T_{2}^{27} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database