Properties

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

Related objects

Downloads

Learn more

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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{4} - q^{5} + O(q^{10}) \) \( q - 2q^{4} - q^{5} + 3q^{11} - 5q^{13} + 4q^{16} + 3q^{17} - 2q^{19} + 2q^{20} + 6q^{23} + q^{25} - 3q^{29} + 4q^{31} + 2q^{37} - 12q^{41} - 10q^{43} - 6q^{44} + 9q^{47} + 10q^{52} - 12q^{53} - 3q^{55} - 8q^{61} - 8q^{64} + 5q^{65} - 4q^{67} - 6q^{68} - 2q^{73} + 4q^{76} - q^{79} - 4q^{80} + 12q^{83} - 3q^{85} - 12q^{89} - 12q^{92} + 2q^{95} + q^{97} + O(q^{100}) \)

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
0 0 −2.00000 −1.00000 0 0 0 0 0
\(n\): 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.e 1
3.b odd 2 1 245.2.a.c 1
7.b odd 2 1 315.2.a.b 1
12.b even 2 1 3920.2.a.ba 1
15.d odd 2 1 1225.2.a.e 1
15.e even 4 2 1225.2.b.d 2
21.c even 2 1 35.2.a.a 1
21.g even 6 2 245.2.e.a 2
21.h odd 6 2 245.2.e.b 2
28.d even 2 1 5040.2.a.v 1
35.c odd 2 1 1575.2.a.f 1
35.f even 4 2 1575.2.d.c 2
84.h odd 2 1 560.2.a.b 1
105.g even 2 1 175.2.a.b 1
105.k odd 4 2 175.2.b.a 2
168.e odd 2 1 2240.2.a.u 1
168.i even 2 1 2240.2.a.k 1
231.h odd 2 1 4235.2.a.c 1
273.g even 2 1 5915.2.a.f 1
420.o odd 2 1 2800.2.a.z 1
420.w even 4 2 2800.2.g.l 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.2.a.a 1 21.c even 2 1
175.2.a.b 1 105.g even 2 1
175.2.b.a 2 105.k odd 4 2
245.2.a.c 1 3.b odd 2 1
245.2.e.a 2 21.g even 6 2
245.2.e.b 2 21.h odd 6 2
315.2.a.b 1 7.b odd 2 1
560.2.a.b 1 84.h odd 2 1
1225.2.a.e 1 15.d odd 2 1
1225.2.b.d 2 15.e even 4 2
1575.2.a.f 1 35.c odd 2 1
1575.2.d.c 2 35.f even 4 2
2205.2.a.e 1 1.a even 1 1 trivial
2240.2.a.k 1 168.i even 2 1
2240.2.a.u 1 168.e odd 2 1
2800.2.a.z 1 420.o odd 2 1
2800.2.g.l 2 420.w even 4 2
3920.2.a.ba 1 12.b even 2 1
4235.2.a.c 1 231.h odd 2 1
5040.2.a.v 1 28.d even 2 1
5915.2.a.f 1 273.g even 2 1

Hecke kernels

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

\( T_{2} \)
\( T_{11} - 3 \)
\( T_{13} + 5 \)
\( T_{17} - 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( -3 + T \)
$13$ \( 5 + T \)
$17$ \( -3 + T \)
$19$ \( 2 + T \)
$23$ \( -6 + T \)
$29$ \( 3 + T \)
$31$ \( -4 + T \)
$37$ \( -2 + T \)
$41$ \( 12 + T \)
$43$ \( 10 + T \)
$47$ \( -9 + T \)
$53$ \( 12 + T \)
$59$ \( T \)
$61$ \( 8 + T \)
$67$ \( 4 + T \)
$71$ \( T \)
$73$ \( 2 + T \)
$79$ \( 1 + T \)
$83$ \( -12 + T \)
$89$ \( 12 + T \)
$97$ \( -1 + T \)
show more
show less