Properties

Label 4275.2.a.o
Level $4275$
Weight $2$
Character orbit 4275.a
Self dual yes
Analytic conductor $34.136$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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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: \(0\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + 2 q^{7} - 3 q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} + 2 q^{7} - 3 q^{8} + 2 q^{11} + 4 q^{13} + 2 q^{14} - q^{16} + 2 q^{17} - q^{19} + 2 q^{22} - 4 q^{23} + 4 q^{26} - 2 q^{28} - 4 q^{29} + 5 q^{32} + 2 q^{34} - q^{38} + 10 q^{43} - 2 q^{44} - 4 q^{46} + 12 q^{47} - 3 q^{49} - 4 q^{52} - 2 q^{53} - 6 q^{56} - 4 q^{58} - 4 q^{59} + 2 q^{61} + 7 q^{64} + 16 q^{67} - 2 q^{68} + 2 q^{73} + q^{76} + 4 q^{77} - 8 q^{79} - 12 q^{83} + 10 q^{86} - 6 q^{88} + 8 q^{91} + 4 q^{92} + 12 q^{94} + 16 q^{97} - 3 q^{98} + O(q^{100}) \)

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.o 1
3.b odd 2 1 1425.2.a.d 1
5.b even 2 1 855.2.a.b 1
15.d odd 2 1 285.2.a.b 1
15.e even 4 2 1425.2.c.d 2
60.h even 2 1 4560.2.a.v 1
285.b even 2 1 5415.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
285.2.a.b 1 15.d odd 2 1
855.2.a.b 1 5.b even 2 1
1425.2.a.d 1 3.b odd 2 1
1425.2.c.d 2 15.e even 4 2
4275.2.a.o 1 1.a even 1 1 trivial
4560.2.a.v 1 60.h even 2 1
5415.2.a.c 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4275))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -2 + T \)
$11$ \( -2 + T \)
$13$ \( -4 + T \)
$17$ \( -2 + T \)
$19$ \( 1 + T \)
$23$ \( 4 + T \)
$29$ \( 4 + T \)
$31$ \( T \)
$37$ \( T \)
$41$ \( T \)
$43$ \( -10 + T \)
$47$ \( -12 + T \)
$53$ \( 2 + T \)
$59$ \( 4 + T \)
$61$ \( -2 + T \)
$67$ \( -16 + T \)
$71$ \( T \)
$73$ \( -2 + T \)
$79$ \( 8 + T \)
$83$ \( 12 + T \)
$89$ \( T \)
$97$ \( -16 + T \)
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