Properties

Label 4018.2.a.s
Level $4018$
Weight $2$
Character orbit 4018.a
Self dual yes
Analytic conductor $32.084$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0838915322\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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
1.00000 3.00000 1.00000 1.00000 3.00000 0 1.00000 6.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(-1\)
\(41\) \(-1\)

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 4018.2.a.s 1
7.b odd 2 1 574.2.a.g 1
21.c even 2 1 5166.2.a.o 1
28.d even 2 1 4592.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.a.g 1 7.b odd 2 1
4018.2.a.s 1 1.a even 1 1 trivial
4592.2.a.l 1 28.d even 2 1
5166.2.a.o 1 21.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\):

\( T_{3} - 3 \)
\( T_{5} - 1 \)
\( T_{11} + 2 \)

Hecke characteristic polynomials

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