Properties

Label 1575.2.a.h
Level 1575
Weight 2
Character orbit 1575.a
Self dual Yes
Analytic conductor 12.576
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(12.5764383184\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - q^{7} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} - q^{7} - 3q^{8} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - 8q^{19} + 8q^{23} + 6q^{26} + q^{28} + 2q^{29} + 4q^{31} + 5q^{32} + 2q^{34} + 2q^{37} - 8q^{38} + 6q^{41} - 4q^{43} + 8q^{46} + 8q^{47} + q^{49} - 6q^{52} + 10q^{53} + 3q^{56} + 2q^{58} - 4q^{59} - 2q^{61} + 4q^{62} + 7q^{64} - 4q^{67} - 2q^{68} + 12q^{71} + 2q^{73} + 2q^{74} + 8q^{76} + 8q^{79} + 6q^{82} - 4q^{83} - 4q^{86} + 6q^{89} - 6q^{91} - 8q^{92} + 8q^{94} + 18q^{97} + q^{98} + O(q^{100}) \)

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 0 0 −1.00000 −3.00000 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
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\):

\( T_{2} - 1 \)
\( T_{11} \)
\( T_{13} - 6 \)