Properties

Label 1425.2.a.c
Level $1425$
Weight $2$
Character orbit 1425.a
Self dual yes
Analytic conductor $11.379$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1425.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.3786822880\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} - q^{6} - 4q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} - q^{4} - q^{6} - 4q^{7} + 3q^{8} + q^{9} + 4q^{11} - q^{12} - 2q^{13} + 4q^{14} - q^{16} - 2q^{17} - q^{18} - q^{19} - 4q^{21} - 4q^{22} + 4q^{23} + 3q^{24} + 2q^{26} + q^{27} + 4q^{28} - 2q^{29} - 5q^{32} + 4q^{33} + 2q^{34} - q^{36} + 6q^{37} + q^{38} - 2q^{39} - 6q^{41} + 4q^{42} - 8q^{43} - 4q^{44} - 4q^{46} + 12q^{47} - q^{48} + 9q^{49} - 2q^{51} + 2q^{52} + 14q^{53} - q^{54} - 12q^{56} - q^{57} + 2q^{58} + 4q^{59} + 14q^{61} - 4q^{63} + 7q^{64} - 4q^{66} + 4q^{67} + 2q^{68} + 4q^{69} + 3q^{72} + 14q^{73} - 6q^{74} + q^{76} - 16q^{77} + 2q^{78} + 16q^{79} + q^{81} + 6q^{82} + 4q^{84} + 8q^{86} - 2q^{87} + 12q^{88} - 6q^{89} + 8q^{91} - 4q^{92} - 12q^{94} - 5q^{96} + 10q^{97} - 9q^{98} + 4q^{99} + O(q^{100}) \)

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
−1.00000 1.00000 −1.00000 0 −1.00000 −4.00000 3.00000 1.00000 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 1425.2.a.c 1
3.b odd 2 1 4275.2.a.j 1
5.b even 2 1 285.2.a.c 1
5.c odd 4 2 1425.2.c.f 2
15.d odd 2 1 855.2.a.a 1
20.d odd 2 1 4560.2.a.w 1
95.d odd 2 1 5415.2.a.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
285.2.a.c 1 5.b even 2 1
855.2.a.a 1 15.d odd 2 1
1425.2.a.c 1 1.a even 1 1 trivial
1425.2.c.f 2 5.c odd 4 2
4275.2.a.j 1 3.b odd 2 1
4560.2.a.w 1 20.d odd 2 1
5415.2.a.e 1 95.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1425))\):

\( T_{2} + 1 \)
\( T_{7} + 4 \)
\( T_{11} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( 4 + T \)
$11$ \( -4 + T \)
$13$ \( 2 + T \)
$17$ \( 2 + T \)
$19$ \( 1 + T \)
$23$ \( -4 + T \)
$29$ \( 2 + T \)
$31$ \( T \)
$37$ \( -6 + T \)
$41$ \( 6 + T \)
$43$ \( 8 + T \)
$47$ \( -12 + T \)
$53$ \( -14 + T \)
$59$ \( -4 + T \)
$61$ \( -14 + T \)
$67$ \( -4 + T \)
$71$ \( T \)
$73$ \( -14 + T \)
$79$ \( -16 + T \)
$83$ \( T \)
$89$ \( 6 + T \)
$97$ \( -10 + T \)
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