Properties

Label 9450.2.a.j
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: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)  \(=\)  \(q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 2q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut +\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut +\mathstrut q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut +\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut +\mathstrut 3q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 8q^{74} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 2q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 5q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut -\mathstrut 2q^{94} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.

Atkin-Lehner signs

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

Hecke kernels

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

\(T_{11} \) \(\mathstrut +\mathstrut 2 \)
\(T_{13} \) \(\mathstrut -\mathstrut 5 \)
\(T_{17} \) \(\mathstrut +\mathstrut 5 \)
\(T_{19} \) \(\mathstrut -\mathstrut 8 \)