Properties

Label 605.2.a.c
Level $605$
Weight $2$
Character orbit 605.a
Self dual yes
Analytic conductor $4.831$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.83094932229\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - 3q^{3} - q^{4} + q^{5} - 3q^{6} + 3q^{7} - 3q^{8} + 6q^{9} + O(q^{10}) \) \( q + q^{2} - 3q^{3} - q^{4} + q^{5} - 3q^{6} + 3q^{7} - 3q^{8} + 6q^{9} + q^{10} + 3q^{12} - 4q^{13} + 3q^{14} - 3q^{15} - q^{16} + 6q^{18} - 4q^{19} - q^{20} - 9q^{21} - 8q^{23} + 9q^{24} + q^{25} - 4q^{26} - 9q^{27} - 3q^{28} - 6q^{29} - 3q^{30} - 2q^{31} + 5q^{32} + 3q^{35} - 6q^{36} - 8q^{37} - 4q^{38} + 12q^{39} - 3q^{40} + 5q^{41} - 9q^{42} - 5q^{43} + 6q^{45} - 8q^{46} - 3q^{47} + 3q^{48} + 2q^{49} + q^{50} + 4q^{52} + 4q^{53} - 9q^{54} - 9q^{56} + 12q^{57} - 6q^{58} - 2q^{59} + 3q^{60} + 11q^{61} - 2q^{62} + 18q^{63} + 7q^{64} - 4q^{65} - 13q^{67} + 24q^{69} + 3q^{70} + 2q^{71} - 18q^{72} + 8q^{73} - 8q^{74} - 3q^{75} + 4q^{76} + 12q^{78} - 10q^{79} - q^{80} + 9q^{81} + 5q^{82} - 4q^{83} + 9q^{84} - 5q^{86} + 18q^{87} + q^{89} + 6q^{90} - 12q^{91} + 8q^{92} + 6q^{93} - 3q^{94} - 4q^{95} - 15q^{96} - 8q^{97} + 2q^{98} + O(q^{100}) \)

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 −3.00000 −1.00000 1.00000 −3.00000 3.00000 −3.00000 6.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(11\) \(-1\)

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 605.2.a.c yes 1
3.b odd 2 1 5445.2.a.d 1
4.b odd 2 1 9680.2.a.be 1
5.b even 2 1 3025.2.a.c 1
11.b odd 2 1 605.2.a.a 1
11.c even 5 4 605.2.g.b 4
11.d odd 10 4 605.2.g.d 4
33.d even 2 1 5445.2.a.h 1
44.c even 2 1 9680.2.a.bf 1
55.d odd 2 1 3025.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
605.2.a.a 1 11.b odd 2 1
605.2.a.c yes 1 1.a even 1 1 trivial
605.2.g.b 4 11.c even 5 4
605.2.g.d 4 11.d odd 10 4
3025.2.a.c 1 5.b even 2 1
3025.2.a.g 1 55.d odd 2 1
5445.2.a.d 1 3.b odd 2 1
5445.2.a.h 1 33.d even 2 1
9680.2.a.be 1 4.b odd 2 1
9680.2.a.bf 1 44.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(605))\):

\( T_{2} - 1 \)
\( T_{3} + 3 \)

Hecke characteristic polynomials

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