Properties

Label 1800.2.a.b
Level 1800
Weight 2
Character orbit 1800.a
Self dual Yes
Analytic conductor 14.373
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1800.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(14.3730723638\)
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

\(f(q)\) \(=\) \( q - 4q^{7} + O(q^{10}) \) \( q - 4q^{7} - 4q^{11} + 4q^{13} + 6q^{17} - 4q^{19} + 4q^{23} - 4q^{29} + 4q^{37} + 8q^{41} + 12q^{47} + 9q^{49} + 2q^{53} + 12q^{59} + 2q^{61} + 8q^{67} + 8q^{71} - 16q^{73} + 16q^{77} - 8q^{79} + 8q^{83} - 16q^{91} - 8q^{97} + O(q^{100}) \)

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 0 0 0 −4.00000 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
\(2\) \(1\)
\(3\) \(1\)
\(5\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\):

\( T_{7} + 4 \)
\( T_{11} + 4 \)
\( T_{13} - 4 \)