Properties

Label 4025.2.a.e
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 161)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - q^{4} - q^{7} - 3 q^{8} - 3 q^{9} + 4 q^{11} - 6 q^{13} - q^{14} - q^{16} + 2 q^{17} - 3 q^{18} + 4 q^{19} + 4 q^{22} + q^{23} - 6 q^{26} + q^{28} - 2 q^{29} - 4 q^{31} + 5 q^{32} + 2 q^{34} + 3 q^{36} + 2 q^{37} + 4 q^{38} - 6 q^{41} - 12 q^{43} - 4 q^{44} + q^{46} + 12 q^{47} + q^{49} + 6 q^{52} + 10 q^{53} + 3 q^{56} - 2 q^{58} + 2 q^{61} - 4 q^{62} + 3 q^{63} + 7 q^{64} - 12 q^{67} - 2 q^{68} + 8 q^{71} + 9 q^{72} + 14 q^{73} + 2 q^{74} - 4 q^{76} - 4 q^{77} + 8 q^{79} + 9 q^{81} - 6 q^{82} + 4 q^{83} - 12 q^{86} - 12 q^{88} + 6 q^{89} + 6 q^{91} - q^{92} + 12 q^{94} + 10 q^{97} + q^{98} - 12 q^{99}+O(q^{100}) \) 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
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.e 1
5.b even 2 1 161.2.a.a 1
15.d odd 2 1 1449.2.a.d 1
20.d odd 2 1 2576.2.a.j 1
35.c odd 2 1 1127.2.a.a 1
115.c odd 2 1 3703.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
161.2.a.a 1 5.b even 2 1
1127.2.a.a 1 35.c odd 2 1
1449.2.a.d 1 15.d odd 2 1
2576.2.a.j 1 20.d odd 2 1
3703.2.a.a 1 115.c odd 2 1
4025.2.a.e 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{3} \) Copy content Toggle raw display
\( T_{11} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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