Properties

Label 9025.2.a.c
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

\(f(q)\) \(=\) \( q - q^{2} - q^{4} - 2q^{7} + 3q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} - q^{4} - 2q^{7} + 3q^{8} - 3q^{9} - 4q^{11} - 2q^{13} + 2q^{14} - q^{16} - 4q^{17} + 3q^{18} + 4q^{22} + 6q^{23} + 2q^{26} + 2q^{28} + 6q^{29} + 4q^{31} - 5q^{32} + 4q^{34} + 3q^{36} - 10q^{37} + 10q^{41} - 2q^{43} + 4q^{44} - 6q^{46} + 6q^{47} - 3q^{49} + 2q^{52} + 10q^{53} - 6q^{56} - 6q^{58} + 2q^{61} - 4q^{62} + 6q^{63} + 7q^{64} + 8q^{67} + 4q^{68} - 4q^{71} - 9q^{72} - 4q^{73} + 10q^{74} + 8q^{77} - 4q^{79} + 9q^{81} - 10q^{82} + 18q^{83} + 2q^{86} - 12q^{88} + 2q^{89} + 4q^{91} - 6q^{92} - 6q^{94} + 6q^{97} + 3q^{98} + 12q^{99} + O(q^{100}) \)

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 0 −1.00000 0 0 −2.00000 3.00000 −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.c 1
5.b even 2 1 9025.2.a.h 1
5.c odd 4 2 1805.2.b.c 2
19.b odd 2 1 475.2.a.c 1
57.d even 2 1 4275.2.a.e 1
76.d even 2 1 7600.2.a.l 1
95.d odd 2 1 475.2.a.a 1
95.g even 4 2 95.2.b.a 2
285.b even 2 1 4275.2.a.p 1
285.j odd 4 2 855.2.c.b 2
380.d even 2 1 7600.2.a.i 1
380.j odd 4 2 1520.2.d.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.2.b.a 2 95.g even 4 2
475.2.a.a 1 95.d odd 2 1
475.2.a.c 1 19.b odd 2 1
855.2.c.b 2 285.j odd 4 2
1520.2.d.b 2 380.j odd 4 2
1805.2.b.c 2 5.c odd 4 2
4275.2.a.e 1 57.d even 2 1
4275.2.a.p 1 285.b even 2 1
7600.2.a.i 1 380.d even 2 1
7600.2.a.l 1 76.d even 2 1
9025.2.a.c 1 1.a even 1 1 trivial
9025.2.a.h 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9025))\):

\( T_{2} + 1 \)
\( T_{3} \)
\( T_{7} + 2 \)
\( T_{11} + 4 \)
\( T_{29} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( 2 + T \)
$11$ \( 4 + T \)
$13$ \( 2 + T \)
$17$ \( 4 + T \)
$19$ \( T \)
$23$ \( -6 + T \)
$29$ \( -6 + T \)
$31$ \( -4 + T \)
$37$ \( 10 + T \)
$41$ \( -10 + T \)
$43$ \( 2 + T \)
$47$ \( -6 + T \)
$53$ \( -10 + T \)
$59$ \( T \)
$61$ \( -2 + T \)
$67$ \( -8 + T \)
$71$ \( 4 + T \)
$73$ \( 4 + T \)
$79$ \( 4 + T \)
$83$ \( -18 + T \)
$89$ \( -2 + T \)
$97$ \( -6 + T \)
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