Properties

Label 495.2.a.a
Level $495$
Weight $2$
Character orbit 495.a
Self dual yes
Analytic conductor $3.953$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.95259490005\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{4} - q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} + q^{11} + 2 q^{13} - q^{16} - 6 q^{17} - 4 q^{19} + q^{20} - q^{22} - 4 q^{23} + q^{25} - 2 q^{26} - 6 q^{29} - 8 q^{31} - 5 q^{32} + 6 q^{34} - 2 q^{37} + 4 q^{38} - 3 q^{40} - 2 q^{41} + 4 q^{43} - q^{44} + 4 q^{46} + 12 q^{47} - 7 q^{49} - q^{50} - 2 q^{52} + 2 q^{53} - q^{55} + 6 q^{58} - 4 q^{59} - 10 q^{61} + 8 q^{62} + 7 q^{64} - 2 q^{65} - 16 q^{67} + 6 q^{68} - 8 q^{71} + 14 q^{73} + 2 q^{74} + 4 q^{76} + 8 q^{79} + q^{80} + 2 q^{82} + 4 q^{83} + 6 q^{85} - 4 q^{86} + 3 q^{88} - 10 q^{89} + 4 q^{92} - 12 q^{94} + 4 q^{95} + 10 q^{97} + 7 q^{98}+O(q^{100}) \) 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 −1.00000 0 0 3.00000 0 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(1\)
\(11\) \(-1\)

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 495.2.a.a 1
3.b odd 2 1 55.2.a.a 1
4.b odd 2 1 7920.2.a.i 1
5.b even 2 1 2475.2.a.i 1
5.c odd 4 2 2475.2.c.f 2
11.b odd 2 1 5445.2.a.i 1
12.b even 2 1 880.2.a.h 1
15.d odd 2 1 275.2.a.a 1
15.e even 4 2 275.2.b.b 2
21.c even 2 1 2695.2.a.c 1
24.f even 2 1 3520.2.a.n 1
24.h odd 2 1 3520.2.a.p 1
33.d even 2 1 605.2.a.b 1
33.f even 10 4 605.2.g.c 4
33.h odd 10 4 605.2.g.a 4
39.d odd 2 1 9295.2.a.b 1
60.h even 2 1 4400.2.a.p 1
60.l odd 4 2 4400.2.b.n 2
132.d odd 2 1 9680.2.a.r 1
165.d even 2 1 3025.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.2.a.a 1 3.b odd 2 1
275.2.a.a 1 15.d odd 2 1
275.2.b.b 2 15.e even 4 2
495.2.a.a 1 1.a even 1 1 trivial
605.2.a.b 1 33.d even 2 1
605.2.g.a 4 33.h odd 10 4
605.2.g.c 4 33.f even 10 4
880.2.a.h 1 12.b even 2 1
2475.2.a.i 1 5.b even 2 1
2475.2.c.f 2 5.c odd 4 2
2695.2.a.c 1 21.c even 2 1
3025.2.a.f 1 165.d even 2 1
3520.2.a.n 1 24.f even 2 1
3520.2.a.p 1 24.h odd 2 1
4400.2.a.p 1 60.h even 2 1
4400.2.b.n 2 60.l odd 4 2
5445.2.a.i 1 11.b odd 2 1
7920.2.a.i 1 4.b odd 2 1
9295.2.a.b 1 39.d odd 2 1
9680.2.a.r 1 132.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(495))\). 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
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T + 6 \) Copy content Toggle raw display
$19$ \( T + 4 \) Copy content Toggle raw display
$23$ \( T + 4 \) Copy content Toggle raw display
$29$ \( T + 6 \) Copy content Toggle raw display
$31$ \( T + 8 \) Copy content Toggle raw display
$37$ \( T + 2 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T - 4 \) Copy content Toggle raw display
$47$ \( T - 12 \) Copy content Toggle raw display
$53$ \( T - 2 \) Copy content Toggle raw display
$59$ \( T + 4 \) Copy content Toggle raw display
$61$ \( T + 10 \) Copy content Toggle raw display
$67$ \( T + 16 \) 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
$89$ \( T + 10 \) Copy content Toggle raw display
$97$ \( T - 10 \) Copy content Toggle raw display
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