Properties

Label 4025.2.a.b
Level $4025$
Weight $2$
Character orbit 4025.a
Self dual yes
Analytic conductor $32.140$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{7} - 2 q^{9} - 5 q^{11} + 2 q^{12} - 3 q^{13} - 2 q^{14} - 4 q^{16} + 5 q^{17} + 4 q^{18} + q^{21} + 10 q^{22} + q^{23} + 6 q^{26} - 5 q^{27} + 2 q^{28} + 3 q^{29} + 6 q^{31} + 8 q^{32} - 5 q^{33} - 10 q^{34} - 4 q^{36} + 4 q^{37} - 3 q^{39} - 2 q^{42} + 2 q^{43} - 10 q^{44} - 2 q^{46} + 9 q^{47} - 4 q^{48} + q^{49} + 5 q^{51} - 6 q^{52} + 6 q^{53} + 10 q^{54} - 6 q^{58} - 6 q^{59} + 10 q^{61} - 12 q^{62} - 2 q^{63} - 8 q^{64} + 10 q^{66} - 4 q^{67} + 10 q^{68} + q^{69} - 8 q^{71} - 10 q^{73} - 8 q^{74} - 5 q^{77} + 6 q^{78} - 15 q^{79} + q^{81} - 12 q^{83} + 2 q^{84} - 4 q^{86} + 3 q^{87} - 10 q^{89} - 3 q^{91} + 2 q^{92} + 6 q^{93} - 18 q^{94} + 8 q^{96} - 7 q^{97} - 2 q^{98} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 1.00000 2.00000 0 −2.00000 1.00000 0 −2.00000 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.b 1
5.b even 2 1 805.2.a.c 1
15.d odd 2 1 7245.2.a.d 1
35.c odd 2 1 5635.2.a.k 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.a.c 1 5.b even 2 1
4025.2.a.b 1 1.a even 1 1 trivial
5635.2.a.k 1 35.c odd 2 1
7245.2.a.d 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\):

\( T_{2} + 2 \) Copy content Toggle raw display
\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{11} + 5 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T - 1 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T + 5 \) Copy content Toggle raw display
$13$ \( T + 3 \) Copy content Toggle raw display
$17$ \( T - 5 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T - 1 \) Copy content Toggle raw display
$29$ \( T - 3 \) Copy content Toggle raw display
$31$ \( T - 6 \) Copy content Toggle raw display
$37$ \( T - 4 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T - 2 \) Copy content Toggle raw display
$47$ \( T - 9 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T + 6 \) Copy content Toggle raw display
$61$ \( T - 10 \) Copy content Toggle raw display
$67$ \( T + 4 \) Copy content Toggle raw display
$71$ \( T + 8 \) Copy content Toggle raw display
$73$ \( T + 10 \) Copy content Toggle raw display
$79$ \( T + 15 \) Copy content Toggle raw display
$83$ \( T + 12 \) Copy content Toggle raw display
$89$ \( T + 10 \) Copy content Toggle raw display
$97$ \( T + 7 \) Copy content Toggle raw display
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