Properties

Label 4410.2.a.n
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 1470)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{5} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2q^{11} - 2q^{13} + q^{16} - 4q^{17} + q^{20} + 2q^{22} - 8q^{23} + q^{25} + 2q^{26} + 2q^{31} - q^{32} + 4q^{34} + 8q^{37} - q^{40} - 2q^{41} - 2q^{43} - 2q^{44} + 8q^{46} + 10q^{47} - q^{50} - 2q^{52} + 2q^{53} - 2q^{55} + 4q^{59} + 10q^{61} - 2q^{62} + q^{64} - 2q^{65} + 2q^{67} - 4q^{68} + 12q^{71} - 10q^{73} - 8q^{74} + 16q^{79} + q^{80} + 2q^{82} + 16q^{83} - 4q^{85} + 2q^{86} + 2q^{88} + 14q^{89} - 8q^{92} - 10q^{94} - 6q^{97} + O(q^{100}) \)

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:

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.n 1
3.b odd 2 1 1470.2.a.p yes 1
7.b odd 2 1 4410.2.a.e 1
15.d odd 2 1 7350.2.a.o 1
21.c even 2 1 1470.2.a.n 1
21.g even 6 2 1470.2.i.g 2
21.h odd 6 2 1470.2.i.c 2
105.g even 2 1 7350.2.a.bh 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1470.2.a.n 1 21.c even 2 1
1470.2.a.p yes 1 3.b odd 2 1
1470.2.i.c 2 21.h odd 6 2
1470.2.i.g 2 21.g even 6 2
4410.2.a.e 1 7.b odd 2 1
4410.2.a.n 1 1.a even 1 1 trivial
7350.2.a.o 1 15.d odd 2 1
7350.2.a.bh 1 105.g even 2 1

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ 1
$5$ \( 1 - T \)
$7$ 1
$11$ \( 1 + 2 T + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 + 4 T + 17 T^{2} \)
$19$ \( 1 + 19 T^{2} \)
$23$ \( 1 + 8 T + 23 T^{2} \)
$29$ \( 1 + 29 T^{2} \)
$31$ \( 1 - 2 T + 31 T^{2} \)
$37$ \( 1 - 8 T + 37 T^{2} \)
$41$ \( 1 + 2 T + 41 T^{2} \)
$43$ \( 1 + 2 T + 43 T^{2} \)
$47$ \( 1 - 10 T + 47 T^{2} \)
$53$ \( 1 - 2 T + 53 T^{2} \)
$59$ \( 1 - 4 T + 59 T^{2} \)
$61$ \( 1 - 10 T + 61 T^{2} \)
$67$ \( 1 - 2 T + 67 T^{2} \)
$71$ \( 1 - 12 T + 71 T^{2} \)
$73$ \( 1 + 10 T + 73 T^{2} \)
$79$ \( 1 - 16 T + 79 T^{2} \)
$83$ \( 1 - 16 T + 83 T^{2} \)
$89$ \( 1 - 14 T + 89 T^{2} \)
$97$ \( 1 + 6 T + 97 T^{2} \)
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