Properties

Label 4410.2.a.bl
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

Related objects

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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 630)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{5} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} - 6q^{13} + q^{16} + 4q^{17} - 6q^{19} + q^{20} + 4q^{22} + q^{25} - 6q^{26} + 6q^{29} + 4q^{31} + q^{32} + 4q^{34} + 8q^{37} - 6q^{38} + q^{40} + 10q^{41} - 2q^{43} + 4q^{44} + 10q^{47} + q^{50} - 6q^{52} - 14q^{53} + 4q^{55} + 6q^{58} - 4q^{59} + 8q^{61} + 4q^{62} + q^{64} - 6q^{65} + 6q^{67} + 4q^{68} + 2q^{71} + 10q^{73} + 8q^{74} - 6q^{76} + 16q^{79} + q^{80} + 10q^{82} - 8q^{83} + 4q^{85} - 2q^{86} + 4q^{88} + 2q^{89} + 10q^{94} - 6q^{95} - 2q^{97} + O(q^{100}) \)

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.bl 1
3.b odd 2 1 4410.2.a.a 1
7.b odd 2 1 630.2.a.g yes 1
21.c even 2 1 630.2.a.e 1
28.d even 2 1 5040.2.a.n 1
35.c odd 2 1 3150.2.a.s 1
35.f even 4 2 3150.2.g.s 2
84.h odd 2 1 5040.2.a.bp 1
105.g even 2 1 3150.2.a.bh 1
105.k odd 4 2 3150.2.g.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.a.e 1 21.c even 2 1
630.2.a.g yes 1 7.b odd 2 1
3150.2.a.s 1 35.c odd 2 1
3150.2.a.bh 1 105.g even 2 1
3150.2.g.b 2 105.k odd 4 2
3150.2.g.s 2 35.f even 4 2
4410.2.a.a 1 3.b odd 2 1
4410.2.a.bl 1 1.a even 1 1 trivial
5040.2.a.n 1 28.d even 2 1
5040.2.a.bp 1 84.h odd 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\):

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

Hecke Characteristic Polynomials

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