Properties

Label 225.2.a.a
Level 225
Weight 2
Character orbit 225.a
Self dual Yes
Analytic conductor 1.797
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 225.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.79663404548\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - 2q^{2} + 2q^{4} - 3q^{7} + O(q^{10}) \) \( q - 2q^{2} + 2q^{4} - 3q^{7} - 2q^{11} + q^{13} + 6q^{14} - 4q^{16} - 2q^{17} - 5q^{19} + 4q^{22} - 6q^{23} - 2q^{26} - 6q^{28} - 10q^{29} - 3q^{31} + 8q^{32} + 4q^{34} + 2q^{37} + 10q^{38} + 8q^{41} + q^{43} - 4q^{44} + 12q^{46} - 2q^{47} + 2q^{49} + 2q^{52} + 4q^{53} + 20q^{58} + 10q^{59} + 7q^{61} + 6q^{62} - 8q^{64} - 3q^{67} - 4q^{68} + 8q^{71} - 14q^{73} - 4q^{74} - 10q^{76} + 6q^{77} - 16q^{82} - 6q^{83} - 2q^{86} - 3q^{91} - 12q^{92} + 4q^{94} + 17q^{97} - 4q^{98} + O(q^{100}) \)

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
−2.00000 0 2.00000 0 0 −3.00000 0 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
\(3\) \(-1\)
\(5\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(225))\):

\( T_{2} + 2 \)
\( T_{7} + 3 \)