Properties

Label 4025.2.a.g
Level $4025$
Weight $2$
Character orbit 4025.a
Self dual yes
Analytic conductor $32.140$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 805)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + q^{7} - 3 q^{8} - 3 q^{9} + O(q^{10}) \) \( q + q^{2} - q^{4} + q^{7} - 3 q^{8} - 3 q^{9} + 2 q^{11} - 4 q^{13} + q^{14} - q^{16} + 6 q^{17} - 3 q^{18} - 8 q^{19} + 2 q^{22} - q^{23} - 4 q^{26} - q^{28} + 10 q^{29} + 10 q^{31} + 5 q^{32} + 6 q^{34} + 3 q^{36} - 8 q^{37} - 8 q^{38} - 2 q^{41} - 2 q^{44} - q^{46} - 12 q^{47} + q^{49} + 4 q^{52} + 4 q^{53} - 3 q^{56} + 10 q^{58} + 14 q^{59} - 2 q^{61} + 10 q^{62} - 3 q^{63} + 7 q^{64} + 4 q^{67} - 6 q^{68} + 8 q^{71} + 9 q^{72} - 8 q^{74} + 8 q^{76} + 2 q^{77} + 6 q^{79} + 9 q^{81} - 2 q^{82} + 12 q^{83} - 6 q^{88} + 10 q^{89} - 4 q^{91} + q^{92} - 12 q^{94} + 2 q^{97} + q^{98} - 6 q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(-1\)
\(23\) \(1\)

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 4025.2.a.g 1
5.b even 2 1 805.2.a.b 1
15.d odd 2 1 7245.2.a.p 1
35.c odd 2 1 5635.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.a.b 1 5.b even 2 1
4025.2.a.g 1 1.a even 1 1 trivial
5635.2.a.c 1 35.c odd 2 1
7245.2.a.p 1 15.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\):

\( T_{2} - 1 \)
\( T_{3} \)
\( T_{11} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( -2 + T \)
$13$ \( 4 + T \)
$17$ \( -6 + T \)
$19$ \( 8 + T \)
$23$ \( 1 + T \)
$29$ \( -10 + T \)
$31$ \( -10 + T \)
$37$ \( 8 + T \)
$41$ \( 2 + T \)
$43$ \( T \)
$47$ \( 12 + T \)
$53$ \( -4 + T \)
$59$ \( -14 + T \)
$61$ \( 2 + T \)
$67$ \( -4 + T \)
$71$ \( -8 + T \)
$73$ \( T \)
$79$ \( -6 + T \)
$83$ \( -12 + T \)
$89$ \( -10 + T \)
$97$ \( -2 + T \)
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