Properties

Label 2535.2.a.h
Level $2535$
Weight $2$
Character orbit 2535.a
Self dual yes
Analytic conductor $20.242$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2535.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.2420769124\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + q^{3} - 2 q^{4} - q^{5} - q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{3} - 2 q^{4} - q^{5} - q^{7} + q^{9} + 6 q^{11} - 2 q^{12} - q^{15} + 4 q^{16} - 4 q^{19} + 2 q^{20} - q^{21} - 6 q^{23} + q^{25} + q^{27} + 2 q^{28} - 6 q^{29} + 5 q^{31} + 6 q^{33} + q^{35} - 2 q^{36} + 2 q^{37} + 11 q^{43} - 12 q^{44} - q^{45} + 6 q^{47} + 4 q^{48} - 6 q^{49} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{60} - q^{61} - q^{63} - 8 q^{64} + 11 q^{67} - 6 q^{69} - 6 q^{71} + 5 q^{73} + q^{75} + 8 q^{76} - 6 q^{77} + 11 q^{79} - 4 q^{80} + q^{81} + 12 q^{83} + 2 q^{84} - 6 q^{87} + 12 q^{89} + 12 q^{92} + 5 q^{93} + 4 q^{95} + 17 q^{97} + 6 q^{99}+O(q^{100}) \) 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
0 1.00000 −2.00000 −1.00000 0 −1.00000 0 1.00000 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 2535.2.a.h 1
3.b odd 2 1 7605.2.a.l 1
13.b even 2 1 2535.2.a.i 1
13.c even 3 2 195.2.i.b 2
39.d odd 2 1 7605.2.a.k 1
39.i odd 6 2 585.2.j.a 2
65.n even 6 2 975.2.i.d 2
65.q odd 12 4 975.2.bb.b 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
195.2.i.b 2 13.c even 3 2
585.2.j.a 2 39.i odd 6 2
975.2.i.d 2 65.n even 6 2
975.2.bb.b 4 65.q odd 12 4
2535.2.a.h 1 1.a even 1 1 trivial
2535.2.a.i 1 13.b even 2 1
7605.2.a.k 1 39.d odd 2 1
7605.2.a.l 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2535))\):

\( T_{2} \) Copy content Toggle raw display
\( T_{7} + 1 \) Copy content Toggle raw display
\( T_{11} - 6 \) Copy content Toggle raw display

Hecke characteristic polynomials

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