Properties

Label 115.2.a.a
Level $115$
Weight $2$
Character orbit 115.a
Self dual yes
Analytic conductor $0.918$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 115.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.918279623245\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{4} - q^{5} + q^{7} - 3q^{9} + O(q^{10}) \) \( q + 2q^{2} + 2q^{4} - q^{5} + q^{7} - 3q^{9} - 2q^{10} + 2q^{11} - 2q^{13} + 2q^{14} - 4q^{16} + 3q^{17} - 6q^{18} - 2q^{19} - 2q^{20} + 4q^{22} + q^{23} + q^{25} - 4q^{26} + 2q^{28} + 7q^{29} - 5q^{31} - 8q^{32} + 6q^{34} - q^{35} - 6q^{36} + 11q^{37} - 4q^{38} + q^{41} + 4q^{44} + 3q^{45} + 2q^{46} - 6q^{49} + 2q^{50} - 4q^{52} + 11q^{53} - 2q^{55} + 14q^{58} - 13q^{59} - 8q^{61} - 10q^{62} - 3q^{63} - 8q^{64} + 2q^{65} + 5q^{67} + 6q^{68} - 2q^{70} + 5q^{71} + 6q^{73} + 22q^{74} - 4q^{76} + 2q^{77} - 12q^{79} + 4q^{80} + 9q^{81} + 2q^{82} + 9q^{83} - 3q^{85} + 4q^{89} + 6q^{90} - 2q^{91} + 2q^{92} + 2q^{95} - 14q^{97} - 12q^{98} - 6q^{99} + O(q^{100}) \)

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 1.00000 0 −3.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(23\) \(-1\)

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 115.2.a.a 1
3.b odd 2 1 1035.2.a.b 1
4.b odd 2 1 1840.2.a.d 1
5.b even 2 1 575.2.a.b 1
5.c odd 4 2 575.2.b.a 2
7.b odd 2 1 5635.2.a.j 1
8.b even 2 1 7360.2.a.q 1
8.d odd 2 1 7360.2.a.n 1
15.d odd 2 1 5175.2.a.y 1
20.d odd 2 1 9200.2.a.t 1
23.b odd 2 1 2645.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.2.a.a 1 1.a even 1 1 trivial
575.2.a.b 1 5.b even 2 1
575.2.b.a 2 5.c odd 4 2
1035.2.a.b 1 3.b odd 2 1
1840.2.a.d 1 4.b odd 2 1
2645.2.a.c 1 23.b odd 2 1
5175.2.a.y 1 15.d odd 2 1
5635.2.a.j 1 7.b odd 2 1
7360.2.a.n 1 8.d odd 2 1
7360.2.a.q 1 8.b even 2 1
9200.2.a.t 1 20.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(115))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( T \)
$5$ \( 1 + T \)
$7$ \( -1 + T \)
$11$ \( -2 + T \)
$13$ \( 2 + T \)
$17$ \( -3 + T \)
$19$ \( 2 + T \)
$23$ \( -1 + T \)
$29$ \( -7 + T \)
$31$ \( 5 + T \)
$37$ \( -11 + T \)
$41$ \( -1 + T \)
$43$ \( T \)
$47$ \( T \)
$53$ \( -11 + T \)
$59$ \( 13 + T \)
$61$ \( 8 + T \)
$67$ \( -5 + T \)
$71$ \( -5 + T \)
$73$ \( -6 + T \)
$79$ \( 12 + T \)
$83$ \( -9 + T \)
$89$ \( -4 + T \)
$97$ \( 14 + T \)
show more
show less