Properties

Label 2925.2.a.s
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 195)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{2} + 2 q^{4} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} + 2 q^{4} + q^{7} - 5 q^{11} + q^{13} + 2 q^{14} - 4 q^{16} - 7 q^{17} - 6 q^{19} - 10 q^{22} + 3 q^{23} + 2 q^{26} + 2 q^{28} - 2 q^{29} + 2 q^{31} - 8 q^{32} - 14 q^{34} - 7 q^{37} - 12 q^{38} - 9 q^{41} + 8 q^{43} - 10 q^{44} + 6 q^{46} + 10 q^{47} - 6 q^{49} + 2 q^{52} + 5 q^{53} - 4 q^{58} + 5 q^{61} + 4 q^{62} - 8 q^{64} + 4 q^{67} - 14 q^{68} - 9 q^{71} + 6 q^{73} - 14 q^{74} - 12 q^{76} - 5 q^{77} - 3 q^{79} - 18 q^{82} - 4 q^{83} + 16 q^{86} - 11 q^{89} + q^{91} + 6 q^{92} + 20 q^{94} + 11 q^{97} - 12 q^{98}+O(q^{100}) \) 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
2.00000 0 2.00000 0 0 1.00000 0 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.s 1
3.b odd 2 1 975.2.a.a 1
5.b even 2 1 585.2.a.c 1
5.c odd 4 2 2925.2.c.a 2
15.d odd 2 1 195.2.a.c 1
15.e even 4 2 975.2.c.c 2
20.d odd 2 1 9360.2.a.bv 1
60.h even 2 1 3120.2.a.d 1
65.d even 2 1 7605.2.a.t 1
105.g even 2 1 9555.2.a.u 1
195.e odd 2 1 2535.2.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
195.2.a.c 1 15.d odd 2 1
585.2.a.c 1 5.b even 2 1
975.2.a.a 1 3.b odd 2 1
975.2.c.c 2 15.e even 4 2
2535.2.a.d 1 195.e odd 2 1
2925.2.a.s 1 1.a even 1 1 trivial
2925.2.c.a 2 5.c odd 4 2
3120.2.a.d 1 60.h even 2 1
7605.2.a.t 1 65.d even 2 1
9360.2.a.bv 1 20.d odd 2 1
9555.2.a.u 1 105.g even 2 1

Hecke kernels

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

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