Properties

Label 575.2.a.c
Level $575$
Weight $2$
Character orbit 575.a
Self dual yes
Analytic conductor $4.591$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.59139811622\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{4} + q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{4} + q^{7} + 3 q^{8} - 3 q^{9} - q^{11} + q^{13} - q^{14} - q^{16} + 3 q^{18} - 5 q^{19} + q^{22} + q^{23} - q^{26} - q^{28} - 5 q^{29} - 2 q^{31} - 5 q^{32} + 3 q^{36} - 4 q^{37} + 5 q^{38} - 5 q^{41} - 9 q^{43} + q^{44} - q^{46} - 6 q^{47} - 6 q^{49} - q^{52} + 2 q^{53} + 3 q^{56} + 5 q^{58} + 8 q^{59} - 8 q^{61} + 2 q^{62} - 3 q^{63} + 7 q^{64} + 8 q^{67} - 10 q^{71} - 9 q^{72} - 3 q^{73} + 4 q^{74} + 5 q^{76} - q^{77} - 3 q^{79} + 9 q^{81} + 5 q^{82} + 3 q^{83} + 9 q^{86} - 3 q^{88} + 10 q^{89} + q^{91} - q^{92} + 6 q^{94} - 2 q^{97} + 6 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 0 0 1.00000 3.00000 −3.00000 0
\(n\): 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 575.2.a.c 1
3.b odd 2 1 5175.2.a.u 1
4.b odd 2 1 9200.2.a.r 1
5.b even 2 1 575.2.a.d yes 1
5.c odd 4 2 575.2.b.b 2
15.d odd 2 1 5175.2.a.e 1
20.d odd 2 1 9200.2.a.u 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
575.2.a.c 1 1.a even 1 1 trivial
575.2.a.d yes 1 5.b even 2 1
575.2.b.b 2 5.c odd 4 2
5175.2.a.e 1 15.d odd 2 1
5175.2.a.u 1 3.b odd 2 1
9200.2.a.r 1 4.b odd 2 1
9200.2.a.u 1 20.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(575))\):

\( T_{2} + 1 \) Copy content Toggle raw display
\( T_{3} \) Copy content Toggle raw display

Hecke characteristic polynomials

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