Properties

Label 9450.2.a.r
Level 9450
Weight 2
Character orbit 9450.a
Self dual yes
Analytic conductor 75.459
Analytic rank 0
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{7} - q^{8} + q^{11} + 5q^{13} + q^{14} + q^{16} + 4q^{17} + 2q^{19} - q^{22} + 5q^{23} - 5q^{26} - q^{28} - 6q^{29} + 10q^{31} - q^{32} - 4q^{34} - q^{37} - 2q^{38} + 2q^{41} - 6q^{43} + q^{44} - 5q^{46} - q^{47} + q^{49} + 5q^{52} - 6q^{53} + q^{56} + 6q^{58} + 13q^{59} + 13q^{61} - 10q^{62} + q^{64} + 4q^{68} + 11q^{71} + 14q^{73} + q^{74} + 2q^{76} - q^{77} - 2q^{82} - 12q^{83} + 6q^{86} - q^{88} - 4q^{89} - 5q^{91} + 5q^{92} + q^{94} - q^{97} - q^{98} + O(q^{100}) \)

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.r 1
3.b odd 2 1 9450.2.a.cj yes 1
5.b even 2 1 9450.2.a.dp yes 1
15.d odd 2 1 9450.2.a.bj yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
9450.2.a.r 1 1.a even 1 1 trivial
9450.2.a.bj yes 1 15.d odd 2 1
9450.2.a.cj yes 1 3.b odd 2 1
9450.2.a.dp 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\):

\( T_{11} - 1 \)
\( T_{13} - 5 \)
\( T_{17} - 4 \)
\( T_{19} - 2 \)