Properties

Label 2925.2.a.o
Level $2925$
Weight $2$
Character orbit 2925.a
Self dual yes
Analytic conductor $23.356$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2925.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.3562425912\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 975)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - q^{4} + 3 q^{7} - 3 q^{8} + q^{11} - q^{13} + 3 q^{14} - q^{16} - 5 q^{17} - 8 q^{19} + q^{22} - q^{26} - 3 q^{28} - q^{29} + 3 q^{31} + 5 q^{32} - 5 q^{34} + 8 q^{37} - 8 q^{38} + 2 q^{41} - 8 q^{43} - q^{44} - 11 q^{47} + 2 q^{49} + q^{52} - 11 q^{53} - 9 q^{56} - q^{58} - 5 q^{59} + q^{61} + 3 q^{62} + 7 q^{64} - 3 q^{67} + 5 q^{68} - 16 q^{71} + 4 q^{73} + 8 q^{74} + 8 q^{76} + 3 q^{77} + 12 q^{79} + 2 q^{82} - 3 q^{83} - 8 q^{86} - 3 q^{88} - 3 q^{91} - 11 q^{94} + 2 q^{97} + 2 q^{98}+O(q^{100}) \) 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 3.00000 −3.00000 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(-1\)
\(13\) \(1\)

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 2925.2.a.o 1
3.b odd 2 1 975.2.a.d 1
5.b even 2 1 2925.2.a.b 1
5.c odd 4 2 2925.2.c.i 2
15.d odd 2 1 975.2.a.k yes 1
15.e even 4 2 975.2.c.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
975.2.a.d 1 3.b odd 2 1
975.2.a.k yes 1 15.d odd 2 1
975.2.c.g 2 15.e even 4 2
2925.2.a.b 1 5.b even 2 1
2925.2.a.o 1 1.a even 1 1 trivial
2925.2.c.i 2 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2925))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{7} - 3 \) Copy content Toggle raw display
\( T_{11} - 1 \) 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
$7$ \( T - 3 \) Copy content Toggle raw display
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T + 1 \) Copy content Toggle raw display
$17$ \( T + 5 \) Copy content Toggle raw display
$19$ \( T + 8 \) Copy content Toggle raw display
$23$ \( T \) Copy content Toggle raw display
$29$ \( T + 1 \) Copy content Toggle raw display
$31$ \( T - 3 \) Copy content Toggle raw display
$37$ \( T - 8 \) Copy content Toggle raw display
$41$ \( T - 2 \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T + 11 \) Copy content Toggle raw display
$53$ \( T + 11 \) Copy content Toggle raw display
$59$ \( T + 5 \) Copy content Toggle raw display
$61$ \( T - 1 \) Copy content Toggle raw display
$67$ \( T + 3 \) Copy content Toggle raw display
$71$ \( T + 16 \) Copy content Toggle raw display
$73$ \( T - 4 \) Copy content Toggle raw display
$79$ \( T - 12 \) Copy content Toggle raw display
$83$ \( T + 3 \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T - 2 \) Copy content Toggle raw display
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