Properties

Label 4015.2.a.a
Level 4015
Weight 2
Character orbit 4015.a
Self dual yes
Analytic conductor 32.060
Analytic rank 1
Dimension 1
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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - 2q^{4} - q^{5} - 3q^{7} - 2q^{9} + O(q^{10}) \) \( q - q^{3} - 2q^{4} - q^{5} - 3q^{7} - 2q^{9} + q^{11} + 2q^{12} + q^{13} + q^{15} + 4q^{16} - 3q^{17} + 6q^{19} + 2q^{20} + 3q^{21} - 7q^{23} + q^{25} + 5q^{27} + 6q^{28} + 6q^{29} + 2q^{31} - q^{33} + 3q^{35} + 4q^{36} + 2q^{37} - q^{39} + 6q^{41} + 11q^{43} - 2q^{44} + 2q^{45} - 4q^{47} - 4q^{48} + 2q^{49} + 3q^{51} - 2q^{52} - 8q^{53} - q^{55} - 6q^{57} - 8q^{59} - 2q^{60} + 10q^{61} + 6q^{63} - 8q^{64} - q^{65} - 9q^{67} + 6q^{68} + 7q^{69} + q^{73} - q^{75} - 12q^{76} - 3q^{77} + 14q^{79} - 4q^{80} + q^{81} - 9q^{83} - 6q^{84} + 3q^{85} - 6q^{87} - 6q^{89} - 3q^{91} + 14q^{92} - 2q^{93} - 6q^{95} + 2q^{97} - 2q^{99} + O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 −1.00000 −2.00000 −1.00000 0 −3.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
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.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4015.2.a.a 1 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 \( T_{2} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\).

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ \( 1 + T + 3 T^{2} \)
$5$ \( 1 + T \)
$7$ \( 1 + 3 T + 7 T^{2} \)
$11$ \( 1 - T \)
$13$ \( 1 - T + 13 T^{2} \)
$17$ \( 1 + 3 T + 17 T^{2} \)
$19$ \( 1 - 6 T + 19 T^{2} \)
$23$ \( 1 + 7 T + 23 T^{2} \)
$29$ \( 1 - 6 T + 29 T^{2} \)
$31$ \( 1 - 2 T + 31 T^{2} \)
$37$ \( 1 - 2 T + 37 T^{2} \)
$41$ \( 1 - 6 T + 41 T^{2} \)
$43$ \( 1 - 11 T + 43 T^{2} \)
$47$ \( 1 + 4 T + 47 T^{2} \)
$53$ \( 1 + 8 T + 53 T^{2} \)
$59$ \( 1 + 8 T + 59 T^{2} \)
$61$ \( 1 - 10 T + 61 T^{2} \)
$67$ \( 1 + 9 T + 67 T^{2} \)
$71$ \( 1 + 71 T^{2} \)
$73$ \( 1 - T \)
$79$ \( 1 - 14 T + 79 T^{2} \)
$83$ \( 1 + 9 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 - 2 T + 97 T^{2} \)
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