Properties

Label 90.2.a.c
Level 90
Weight 2
Character orbit 90.a
Self dual Yes
Analytic conductor 0.719
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 90.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.718653618192\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{5} - 4q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{5} - 4q^{7} + q^{8} + q^{10} + 2q^{13} - 4q^{14} + q^{16} - 6q^{17} - 4q^{19} + q^{20} + q^{25} + 2q^{26} - 4q^{28} + 6q^{29} + 8q^{31} + q^{32} - 6q^{34} - 4q^{35} + 2q^{37} - 4q^{38} + q^{40} + 6q^{41} - 4q^{43} + 9q^{49} + q^{50} + 2q^{52} + 6q^{53} - 4q^{56} + 6q^{58} - 10q^{61} + 8q^{62} + q^{64} + 2q^{65} - 4q^{67} - 6q^{68} - 4q^{70} + 2q^{73} + 2q^{74} - 4q^{76} + 8q^{79} + q^{80} + 6q^{82} - 12q^{83} - 6q^{85} - 4q^{86} - 18q^{89} - 8q^{91} - 4q^{95} + 2q^{97} + 9q^{98} + O(q^{100}) \)

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 1.00000 0 −4.00000 1.00000 0 1.00000
\(n\): 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
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(90))\):

\( T_{7} + 4 \)
\( T_{11} \)