Properties

Label 225.2.a.d
Level 225
Weight 2
Character orbit 225.a
Self dual Yes
Analytic conductor 1.797
Analytic rank 0
Dimension 1
CM disc. -3
Inner twists 2

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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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{4} + 5q^{7} + O(q^{10}) \) \( q - 2q^{4} + 5q^{7} + 5q^{13} + 4q^{16} - q^{19} - 10q^{28} - 7q^{31} - 10q^{37} + 5q^{43} + 18q^{49} - 10q^{52} - 13q^{61} - 8q^{64} + 5q^{67} - 10q^{73} + 2q^{76} - 4q^{79} + 25q^{91} + 5q^{97} + O(q^{100}) \)

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
0 0 −2.00000 0 0 5.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
3.b Odd 1 CM by \(\Q(\sqrt{-3}) \) yes

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(225))\):

\( T_{2} \)
\( T_{7} - 5 \)