Properties

Label 9450.2.a.cs
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: no (minimal twist has level 1890)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} - q^{7} + q^{8} + 3q^{11} - q^{13} - q^{14} + q^{16} + q^{17} - 2q^{19} + 3q^{22} - 7q^{23} - q^{26} - q^{28} - 5q^{29} - 5q^{31} + q^{32} + q^{34} + 2q^{37} - 2q^{38} + 6q^{41} - 5q^{43} + 3q^{44} - 7q^{46} - q^{47} + q^{49} - q^{52} - 12q^{53} - q^{56} - 5q^{58} + 4q^{59} - 12q^{61} - 5q^{62} + q^{64} + 4q^{67} + q^{68} - 6q^{71} - 2q^{73} + 2q^{74} - 2q^{76} - 3q^{77} + 5q^{79} + 6q^{82} - 5q^{86} + 3q^{88} + 10q^{89} + q^{91} - 7q^{92} - q^{94} - 18q^{97} + q^{98} + O(q^{100}) \)

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.cs 1
3.b odd 2 1 9450.2.a.f 1
5.b even 2 1 9450.2.a.bv 1
5.c odd 4 2 1890.2.g.f 2
15.d odd 2 1 9450.2.a.dg 1
15.e even 4 2 1890.2.g.h yes 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1890.2.g.f 2 5.c odd 4 2
1890.2.g.h yes 2 15.e even 4 2
9450.2.a.f 1 3.b odd 2 1
9450.2.a.bv 1 5.b even 2 1
9450.2.a.cs 1 1.a even 1 1 trivial
9450.2.a.dg 1 15.d odd 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\):

\( T_{11} - 3 \)
\( T_{13} + 1 \)
\( T_{17} - 1 \)
\( T_{19} + 2 \)