Properties

Label 4410.2.a.bd
Level $4410$
Weight $2$
Character orbit 4410.a
Self dual yes
Analytic conductor $35.214$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4410.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.2140272914\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - q^{5} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 6q^{11} + 4q^{13} + q^{16} - 2q^{19} - q^{20} + 6q^{22} + 3q^{23} + q^{25} + 4q^{26} + 3q^{29} - 8q^{31} + q^{32} - 4q^{37} - 2q^{38} - q^{40} + 9q^{41} - 7q^{43} + 6q^{44} + 3q^{46} + q^{50} + 4q^{52} + 6q^{53} - 6q^{55} + 3q^{58} - 6q^{59} - 5q^{61} - 8q^{62} + q^{64} - 4q^{65} + 5q^{67} + 6q^{71} + 16q^{73} - 4q^{74} - 2q^{76} + 2q^{79} - q^{80} + 9q^{82} + 3q^{83} - 7q^{86} + 6q^{88} - 15q^{89} + 3q^{92} + 2q^{95} - 14q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(-1\)

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 4410.2.a.bd 1
3.b odd 2 1 490.2.a.b 1
7.b odd 2 1 4410.2.a.bm 1
7.d odd 6 2 630.2.k.b 2
12.b even 2 1 3920.2.a.bc 1
15.d odd 2 1 2450.2.a.bc 1
15.e even 4 2 2450.2.c.l 2
21.c even 2 1 490.2.a.c 1
21.g even 6 2 70.2.e.c 2
21.h odd 6 2 490.2.e.h 2
84.h odd 2 1 3920.2.a.p 1
84.j odd 6 2 560.2.q.g 2
105.g even 2 1 2450.2.a.w 1
105.k odd 4 2 2450.2.c.g 2
105.p even 6 2 350.2.e.e 2
105.w odd 12 4 350.2.j.b 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.2.e.c 2 21.g even 6 2
350.2.e.e 2 105.p even 6 2
350.2.j.b 4 105.w odd 12 4
490.2.a.b 1 3.b odd 2 1
490.2.a.c 1 21.c even 2 1
490.2.e.h 2 21.h odd 6 2
560.2.q.g 2 84.j odd 6 2
630.2.k.b 2 7.d odd 6 2
2450.2.a.w 1 105.g even 2 1
2450.2.a.bc 1 15.d odd 2 1
2450.2.c.g 2 105.k odd 4 2
2450.2.c.l 2 15.e even 4 2
3920.2.a.p 1 84.h odd 2 1
3920.2.a.bc 1 12.b even 2 1
4410.2.a.bd 1 1.a even 1 1 trivial
4410.2.a.bm 1 7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\):

\( T_{11} - 6 \)
\( T_{13} - 4 \)
\( T_{17} \)
\( T_{19} + 2 \)
\( T_{29} - 3 \)
\( T_{31} + 8 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( -6 + T \)
$13$ \( -4 + T \)
$17$ \( T \)
$19$ \( 2 + T \)
$23$ \( -3 + T \)
$29$ \( -3 + T \)
$31$ \( 8 + T \)
$37$ \( 4 + T \)
$41$ \( -9 + T \)
$43$ \( 7 + T \)
$47$ \( T \)
$53$ \( -6 + T \)
$59$ \( 6 + T \)
$61$ \( 5 + T \)
$67$ \( -5 + T \)
$71$ \( -6 + T \)
$73$ \( -16 + T \)
$79$ \( -2 + T \)
$83$ \( -3 + T \)
$89$ \( 15 + T \)
$97$ \( 14 + T \)
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