Properties

Label 9450.2.a.df
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

Related objects

Downloads

Learn more about

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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{11} - q^{13} + q^{14} + q^{16} - 4q^{19} - 3q^{22} - 3q^{23} - q^{26} + q^{28} + 6q^{29} - 4q^{31} + q^{32} - q^{37} - 4q^{38} + 6q^{41} + 8q^{43} - 3q^{44} - 3q^{46} - 3q^{47} + q^{49} - q^{52} - 12q^{53} + q^{56} + 6q^{58} + 3q^{59} - 7q^{61} - 4q^{62} + q^{64} - 4q^{67} - 3q^{71} - 10q^{73} - q^{74} - 4q^{76} - 3q^{77} - 10q^{79} + 6q^{82} + 12q^{83} + 8q^{86} - 3q^{88} + 6q^{89} - q^{91} - 3q^{92} - 3q^{94} - 13q^{97} + q^{98} + O(q^{100}) \)

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.df yes 1
3.b odd 2 1 9450.2.a.bu yes 1
5.b even 2 1 9450.2.a.g 1
15.d odd 2 1 9450.2.a.ct yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
9450.2.a.g 1 5.b even 2 1
9450.2.a.bu yes 1 3.b odd 2 1
9450.2.a.ct yes 1 15.d odd 2 1
9450.2.a.df yes 1 1.a even 1 1 trivial

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\):

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

Hecke Characteristic Polynomials

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