Properties

Label 4275.2.a.h
Level $4275$
Weight $2$
Character orbit 4275.a
Self dual yes
Analytic conductor $34.136$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4275.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(34.1360468641\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 285)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{4} + 2 q^{7} + 3 q^{8} + O(q^{10}) \) \( q - q^{2} - q^{4} + 2 q^{7} + 3 q^{8} + 6 q^{11} - 2 q^{14} - q^{16} - 6 q^{17} + q^{19} - 6 q^{22} - 8 q^{23} - 2 q^{28} - 4 q^{29} - 5 q^{32} + 6 q^{34} - 4 q^{37} - q^{38} + 2 q^{43} - 6 q^{44} + 8 q^{46} - 8 q^{47} - 3 q^{49} + 2 q^{53} + 6 q^{56} + 4 q^{58} - 12 q^{59} + 2 q^{61} + 7 q^{64} + 8 q^{67} + 6 q^{68} - 16 q^{71} - 14 q^{73} + 4 q^{74} - q^{76} + 12 q^{77} + 8 q^{79} - 2 q^{86} + 18 q^{88} + 8 q^{92} + 8 q^{94} + 12 q^{97} + 3 q^{98} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(5\) \(1\)
\(19\) \(-1\)

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 4275.2.a.h 1
3.b odd 2 1 1425.2.a.g 1
5.b even 2 1 855.2.a.c 1
15.d odd 2 1 285.2.a.a 1
15.e even 4 2 1425.2.c.c 2
60.h even 2 1 4560.2.a.h 1
285.b even 2 1 5415.2.a.h 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
285.2.a.a 1 15.d odd 2 1
855.2.a.c 1 5.b even 2 1
1425.2.a.g 1 3.b odd 2 1
1425.2.c.c 2 15.e even 4 2
4275.2.a.h 1 1.a even 1 1 trivial
4560.2.a.h 1 60.h even 2 1
5415.2.a.h 1 285.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4275))\):

\( T_{2} + 1 \)
\( T_{7} - 2 \)
\( T_{11} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -2 + T \)
$11$ \( -6 + T \)
$13$ \( T \)
$17$ \( 6 + T \)
$19$ \( -1 + T \)
$23$ \( 8 + T \)
$29$ \( 4 + T \)
$31$ \( T \)
$37$ \( 4 + T \)
$41$ \( T \)
$43$ \( -2 + T \)
$47$ \( 8 + T \)
$53$ \( -2 + T \)
$59$ \( 12 + T \)
$61$ \( -2 + T \)
$67$ \( -8 + T \)
$71$ \( 16 + T \)
$73$ \( 14 + T \)
$79$ \( -8 + T \)
$83$ \( T \)
$89$ \( T \)
$97$ \( -12 + T \)
show more
show less