Properties

Label 9450.2.a.k
Level 9450
Weight 2
Character orbit 9450.a
Self dual yes
Analytic conductor 75.459
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 9450.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(75.4586299101\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{7} - q^{8} - q^{11} + 3q^{13} + q^{14} + q^{16} + 4q^{17} - 6q^{19} + q^{22} - 3q^{23} - 3q^{26} - q^{28} + 6q^{29} + 2q^{31} - q^{32} - 4q^{34} - 7q^{37} + 6q^{38} - 2q^{41} - 2q^{43} - q^{44} + 3q^{46} + 7q^{47} + q^{49} + 3q^{52} + 2q^{53} + q^{56} - 6q^{58} - 13q^{59} - 11q^{61} - 2q^{62} + q^{64} + 4q^{68} + 13q^{71} + 2q^{73} + 7q^{74} - 6q^{76} + q^{77} - 8q^{79} + 2q^{82} + 4q^{83} + 2q^{86} + q^{88} - 4q^{89} - 3q^{91} - 3q^{92} - 7q^{94} + 17q^{97} - q^{98} + O(q^{100}) \)

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

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 9450.2.a.k 1
3.b odd 2 1 9450.2.a.cp yes 1
5.b even 2 1 9450.2.a.di yes 1
15.d odd 2 1 9450.2.a.bq yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
9450.2.a.k 1 1.a even 1 1 trivial
9450.2.a.bq yes 1 15.d odd 2 1
9450.2.a.cp yes 1 3.b odd 2 1
9450.2.a.di yes 1 5.b even 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(7\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\):

\( T_{11} + 1 \)
\( T_{13} - 3 \)
\( T_{17} - 4 \)
\( T_{19} + 6 \)