Properties

Label 2093.2.a.c
Level $2093$
Weight $2$
Character orbit 2093.a
Self dual yes
Analytic conductor $16.713$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2093 = 7 \cdot 13 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2093.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.7126891431\)
Analytic rank: \(0\)
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

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

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
−2.00000 3.00000 2.00000 3.00000 −6.00000 −1.00000 0 6.00000 −6.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)
\(13\) \(1\)
\(23\) \(-1\)

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 2093.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2093.2.a.c 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2093))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( -3 + T \)
$5$ \( -3 + T \)
$7$ \( 1 + T \)
$11$ \( -3 + T \)
$13$ \( 1 + T \)
$17$ \( -4 + T \)
$19$ \( -5 + T \)
$23$ \( -1 + T \)
$29$ \( 2 + T \)
$31$ \( 6 + T \)
$37$ \( 10 + T \)
$41$ \( -6 + T \)
$43$ \( 4 + T \)
$47$ \( -10 + T \)
$53$ \( 12 + T \)
$59$ \( 10 + T \)
$61$ \( -2 + T \)
$67$ \( -3 + T \)
$71$ \( 2 + T \)
$73$ \( -2 + T \)
$79$ \( 12 + T \)
$83$ \( -9 + T \)
$89$ \( -6 + T \)
$97$ \( -13 + T \)
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