Properties

Label 2645.2.a.c
Level $2645$
Weight $2$
Character orbit 2645.a
Self dual yes
Analytic conductor $21.120$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2645 = 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2645.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.1204313346\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{2} + 2 q^{4} + q^{5} - q^{7} - 3 q^{9} + O(q^{10}) \) \( q + 2 q^{2} + 2 q^{4} + q^{5} - q^{7} - 3 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{13} - 2 q^{14} - 4 q^{16} - 3 q^{17} - 6 q^{18} + 2 q^{19} + 2 q^{20} - 4 q^{22} + q^{25} - 4 q^{26} - 2 q^{28} + 7 q^{29} - 5 q^{31} - 8 q^{32} - 6 q^{34} - q^{35} - 6 q^{36} - 11 q^{37} + 4 q^{38} + q^{41} - 4 q^{44} - 3 q^{45} - 6 q^{49} + 2 q^{50} - 4 q^{52} - 11 q^{53} - 2 q^{55} + 14 q^{58} - 13 q^{59} + 8 q^{61} - 10 q^{62} + 3 q^{63} - 8 q^{64} - 2 q^{65} - 5 q^{67} - 6 q^{68} - 2 q^{70} + 5 q^{71} + 6 q^{73} - 22 q^{74} + 4 q^{76} + 2 q^{77} + 12 q^{79} - 4 q^{80} + 9 q^{81} + 2 q^{82} - 9 q^{83} - 3 q^{85} - 4 q^{89} - 6 q^{90} + 2 q^{91} + 2 q^{95} + 14 q^{97} - 12 q^{98} + 6 q^{99} + O(q^{100}) \)

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 1.00000 0 −1.00000 0 −3.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(23\) \(-1\)

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 2645.2.a.c 1
23.b odd 2 1 115.2.a.a 1
69.c even 2 1 1035.2.a.b 1
92.b even 2 1 1840.2.a.d 1
115.c odd 2 1 575.2.a.b 1
115.e even 4 2 575.2.b.a 2
161.c even 2 1 5635.2.a.j 1
184.e odd 2 1 7360.2.a.q 1
184.h even 2 1 7360.2.a.n 1
345.h even 2 1 5175.2.a.y 1
460.g even 2 1 9200.2.a.t 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.2.a.a 1 23.b odd 2 1
575.2.a.b 1 115.c odd 2 1
575.2.b.a 2 115.e even 4 2
1035.2.a.b 1 69.c even 2 1
1840.2.a.d 1 92.b even 2 1
2645.2.a.c 1 1.a even 1 1 trivial
5175.2.a.y 1 345.h even 2 1
5635.2.a.j 1 161.c even 2 1
7360.2.a.n 1 184.h even 2 1
7360.2.a.q 1 184.e odd 2 1
9200.2.a.t 1 460.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\):

\( T_{2} - 2 \)
\( T_{7} + 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( T \)
$5$ \( -1 + T \)
$7$ \( 1 + T \)
$11$ \( 2 + T \)
$13$ \( 2 + T \)
$17$ \( 3 + T \)
$19$ \( -2 + T \)
$23$ \( T \)
$29$ \( -7 + T \)
$31$ \( 5 + T \)
$37$ \( 11 + T \)
$41$ \( -1 + T \)
$43$ \( T \)
$47$ \( T \)
$53$ \( 11 + T \)
$59$ \( 13 + T \)
$61$ \( -8 + T \)
$67$ \( 5 + T \)
$71$ \( -5 + T \)
$73$ \( -6 + T \)
$79$ \( -12 + T \)
$83$ \( 9 + T \)
$89$ \( 4 + T \)
$97$ \( -14 + T \)
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