Properties

Label 5635.2.a.j
Level $5635$
Weight $2$
Character orbit 5635.a
Self dual yes
Analytic conductor $44.996$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5635 = 5 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5635.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9957015390\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} + 2 q^{4} + q^{5} - 3 q^{9} + O(q^{10}) \) \( q + 2 q^{2} + 2 q^{4} + q^{5} - 3 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{13} - 4 q^{16} - 3 q^{17} - 6 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{22} + q^{23} + q^{25} + 4 q^{26} + 7 q^{29} + 5 q^{31} - 8 q^{32} - 6 q^{34} - 6 q^{36} + 11 q^{37} + 4 q^{38} - q^{41} + 4 q^{44} - 3 q^{45} + 2 q^{46} + 2 q^{50} + 4 q^{52} + 11 q^{53} + 2 q^{55} + 14 q^{58} + 13 q^{59} + 8 q^{61} + 10 q^{62} - 8 q^{64} + 2 q^{65} + 5 q^{67} - 6 q^{68} + 5 q^{71} - 6 q^{73} + 22 q^{74} + 4 q^{76} - 12 q^{79} - 4 q^{80} + 9 q^{81} - 2 q^{82} - 9 q^{83} - 3 q^{85} - 4 q^{89} - 6 q^{90} + 2 q^{92} + 2 q^{95} + 14 q^{97} - 6 q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(-1\)
\(23\) \(-1\)

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 5635.2.a.j 1
7.b odd 2 1 115.2.a.a 1
21.c even 2 1 1035.2.a.b 1
28.d even 2 1 1840.2.a.d 1
35.c odd 2 1 575.2.a.b 1
35.f even 4 2 575.2.b.a 2
56.e even 2 1 7360.2.a.n 1
56.h odd 2 1 7360.2.a.q 1
105.g even 2 1 5175.2.a.y 1
140.c even 2 1 9200.2.a.t 1
161.c even 2 1 2645.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.2.a.a 1 7.b odd 2 1
575.2.a.b 1 35.c odd 2 1
575.2.b.a 2 35.f even 4 2
1035.2.a.b 1 21.c even 2 1
1840.2.a.d 1 28.d even 2 1
2645.2.a.c 1 161.c even 2 1
5175.2.a.y 1 105.g even 2 1
5635.2.a.j 1 1.a even 1 1 trivial
7360.2.a.n 1 56.e even 2 1
7360.2.a.q 1 56.h odd 2 1
9200.2.a.t 1 140.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5635))\):

\( T_{2} - 2 \)
\( T_{3} \)
\( T_{11} - 2 \)
\( T_{17} + 3 \)

Hecke characteristic polynomials

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