Properties

Label 2205.2.a.g
Level $2205$
Weight $2$
Character orbit 2205.a
Self dual yes
Analytic conductor $17.607$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.6070136457\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - q^{5} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} - q^{5} - 3q^{8} - q^{10} - 2q^{11} - 6q^{13} - q^{16} + 6q^{17} + 6q^{19} + q^{20} - 2q^{22} - 4q^{23} + q^{25} - 6q^{26} + 8q^{29} + 6q^{31} + 5q^{32} + 6q^{34} - 6q^{37} + 6q^{38} + 3q^{40} + 6q^{41} + 2q^{44} - 4q^{46} + q^{50} + 6q^{52} + 2q^{53} + 2q^{55} + 8q^{58} + 12q^{59} + 6q^{62} + 7q^{64} + 6q^{65} + 4q^{67} - 6q^{68} - 14q^{71} + 6q^{73} - 6q^{74} - 6q^{76} + 8q^{79} + q^{80} + 6q^{82} + 12q^{83} - 6q^{85} + 6q^{88} - 6q^{89} + 4q^{92} - 6q^{95} - 6q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(5\) \(1\)
\(7\) \(-1\)

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 2205.2.a.g yes 1
3.b odd 2 1 2205.2.a.c yes 1
7.b odd 2 1 2205.2.a.h yes 1
21.c even 2 1 2205.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2205.2.a.a 1 21.c even 2 1
2205.2.a.c yes 1 3.b odd 2 1
2205.2.a.g yes 1 1.a even 1 1 trivial
2205.2.a.h yes 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\):

\( T_{2} - 1 \)
\( T_{11} + 2 \)
\( T_{13} + 6 \)
\( T_{17} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( 2 + T \)
$13$ \( 6 + T \)
$17$ \( -6 + T \)
$19$ \( -6 + T \)
$23$ \( 4 + T \)
$29$ \( -8 + T \)
$31$ \( -6 + T \)
$37$ \( 6 + T \)
$41$ \( -6 + T \)
$43$ \( T \)
$47$ \( T \)
$53$ \( -2 + T \)
$59$ \( -12 + T \)
$61$ \( T \)
$67$ \( -4 + T \)
$71$ \( 14 + T \)
$73$ \( -6 + T \)
$79$ \( -8 + T \)
$83$ \( -12 + T \)
$89$ \( 6 + T \)
$97$ \( 6 + T \)
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