Properties

Label 9200.2.a.bd
Level $9200$
Weight $2$
Character orbit 9200.a
Self dual yes
Analytic conductor $73.462$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4600)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{3} - q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - q^{7} + q^{9} + 5q^{11} + q^{13} - 4q^{17} - 7q^{19} - 2q^{21} + q^{23} - 4q^{27} + 5q^{29} - 2q^{31} + 10q^{33} - 2q^{37} + 2q^{39} + 11q^{41} - q^{43} + 8q^{47} - 6q^{49} - 8q^{51} - 14q^{57} + 14q^{59} + 10q^{61} - q^{63} + 8q^{67} + 2q^{69} + 10q^{71} + 7q^{73} - 5q^{77} - 7q^{79} - 11q^{81} + 15q^{83} + 10q^{87} + 10q^{89} - q^{91} - 4q^{93} - 4q^{97} + 5q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(1\)
\(23\) \(-1\)

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 9200.2.a.bd 1
4.b odd 2 1 4600.2.a.c 1
5.b even 2 1 9200.2.a.i 1
20.d odd 2 1 4600.2.a.n yes 1
20.e even 4 2 4600.2.e.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4600.2.a.c 1 4.b odd 2 1
4600.2.a.n yes 1 20.d odd 2 1
4600.2.e.c 2 20.e even 4 2
9200.2.a.i 1 5.b even 2 1
9200.2.a.bd 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9200))\):

\( T_{3} - 2 \)
\( T_{7} + 1 \)
\( T_{11} - 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -2 + T \)
$5$ \( T \)
$7$ \( 1 + T \)
$11$ \( -5 + T \)
$13$ \( -1 + T \)
$17$ \( 4 + T \)
$19$ \( 7 + T \)
$23$ \( -1 + T \)
$29$ \( -5 + T \)
$31$ \( 2 + T \)
$37$ \( 2 + T \)
$41$ \( -11 + T \)
$43$ \( 1 + T \)
$47$ \( -8 + T \)
$53$ \( T \)
$59$ \( -14 + T \)
$61$ \( -10 + T \)
$67$ \( -8 + T \)
$71$ \( -10 + T \)
$73$ \( -7 + T \)
$79$ \( 7 + T \)
$83$ \( -15 + T \)
$89$ \( -10 + T \)
$97$ \( 4 + T \)
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