Properties

Label 9025.2.a.a
Level $9025$
Weight $2$
Character orbit 9025.a
Self dual yes
Analytic conductor $72.065$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.0649878242\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{2} + 2 q^{4} - 4 q^{7} - 3 q^{9} + O(q^{10}) \) \( q - 2 q^{2} + 2 q^{4} - 4 q^{7} - 3 q^{9} - q^{11} + 2 q^{13} + 8 q^{14} - 4 q^{16} - 2 q^{17} + 6 q^{18} + 2 q^{22} + 6 q^{23} - 4 q^{26} - 8 q^{28} - 9 q^{29} + 7 q^{31} + 8 q^{32} + 4 q^{34} - 6 q^{36} - 2 q^{37} - 2 q^{41} + 2 q^{43} - 2 q^{44} - 12 q^{46} + 6 q^{47} + 9 q^{49} + 4 q^{52} - 4 q^{53} + 18 q^{58} - 9 q^{59} - 7 q^{61} - 14 q^{62} + 12 q^{63} - 8 q^{64} + 10 q^{67} - 4 q^{68} - q^{71} + 10 q^{73} + 4 q^{74} + 4 q^{77} - q^{79} + 9 q^{81} + 4 q^{82} - 6 q^{83} - 4 q^{86} + 11 q^{89} - 8 q^{91} + 12 q^{92} - 12 q^{94} + 6 q^{97} - 18 q^{98} + 3 q^{99} + O(q^{100}) \)

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 0 2.00000 0 0 −4.00000 0 −3.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(19\) \(-1\)

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 9025.2.a.a 1
5.b even 2 1 9025.2.a.j 1
5.c odd 4 2 1805.2.b.a 2
19.b odd 2 1 9025.2.a.i 1
19.d odd 6 2 475.2.e.a 2
95.d odd 2 1 9025.2.a.b 1
95.g even 4 2 1805.2.b.b 2
95.h odd 6 2 475.2.e.c 2
95.l even 12 4 95.2.i.a 4
285.w odd 12 4 855.2.be.a 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.2.i.a 4 95.l even 12 4
475.2.e.a 2 19.d odd 6 2
475.2.e.c 2 95.h odd 6 2
855.2.be.a 4 285.w odd 12 4
1805.2.b.a 2 5.c odd 4 2
1805.2.b.b 2 95.g even 4 2
9025.2.a.a 1 1.a even 1 1 trivial
9025.2.a.b 1 95.d odd 2 1
9025.2.a.i 1 19.b odd 2 1
9025.2.a.j 1 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9025))\):

\( T_{2} + 2 \)
\( T_{3} \)
\( T_{7} + 4 \)
\( T_{11} + 1 \)
\( T_{29} + 9 \)

Hecke characteristic polynomials

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