Properties

Label 2205.2.a.m
Level $2205$
Weight $2$
Character orbit 2205.a
Self dual yes
Analytic conductor $17.607$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.6070136457\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{4} + q^{5} + O(q^{10}) \) \( q + 2q^{2} + 2q^{4} + q^{5} + 2q^{10} + 6q^{11} + 3q^{13} - 4q^{16} - 4q^{17} - q^{19} + 2q^{20} + 12q^{22} + 4q^{23} + q^{25} + 6q^{26} + 8q^{29} - q^{31} - 8q^{32} - 8q^{34} + 7q^{37} - 2q^{38} - 6q^{41} + q^{43} + 12q^{44} + 8q^{46} + 2q^{47} + 2q^{50} + 6q^{52} - 4q^{53} + 6q^{55} + 16q^{58} - 8q^{59} + 14q^{61} - 2q^{62} - 8q^{64} + 3q^{65} + 7q^{67} - 8q^{68} - 6q^{71} - q^{73} + 14q^{74} - 2q^{76} - q^{79} - 4q^{80} - 12q^{82} + 2q^{83} - 4q^{85} + 2q^{86} - 12q^{89} + 8q^{92} + 4q^{94} - q^{95} + 6q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

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

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 2205.2.a.m 1
3.b odd 2 1 735.2.a.a 1
7.b odd 2 1 2205.2.a.k 1
7.d odd 6 2 315.2.j.a 2
15.d odd 2 1 3675.2.a.p 1
21.c even 2 1 735.2.a.b 1
21.g even 6 2 105.2.i.b 2
21.h odd 6 2 735.2.i.f 2
84.j odd 6 2 1680.2.bg.l 2
105.g even 2 1 3675.2.a.o 1
105.p even 6 2 525.2.i.a 2
105.w odd 12 4 525.2.r.d 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.2.i.b 2 21.g even 6 2
315.2.j.a 2 7.d odd 6 2
525.2.i.a 2 105.p even 6 2
525.2.r.d 4 105.w odd 12 4
735.2.a.a 1 3.b odd 2 1
735.2.a.b 1 21.c even 2 1
735.2.i.f 2 21.h odd 6 2
1680.2.bg.l 2 84.j odd 6 2
2205.2.a.k 1 7.b odd 2 1
2205.2.a.m 1 1.a even 1 1 trivial
3675.2.a.o 1 105.g even 2 1
3675.2.a.p 1 15.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\):

\( T_{2} - 2 \)
\( T_{11} - 6 \)
\( T_{13} - 3 \)
\( T_{17} + 4 \)

Hecke characteristic polynomials

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