Properties

Label 128.4.a.b
Level 128
Weight 4
Character orbit 128.a
Self dual Yes
Analytic conductor 7.552
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 128.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.55224448073\)
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

\(f(q)\) \(=\) \( q - 2q^{3} + 6q^{5} - 20q^{7} - 23q^{9} + O(q^{10}) \) \( q - 2q^{3} + 6q^{5} - 20q^{7} - 23q^{9} - 14q^{11} + 54q^{13} - 12q^{15} - 66q^{17} - 162q^{19} + 40q^{21} - 172q^{23} - 89q^{25} + 100q^{27} - 2q^{29} + 128q^{31} + 28q^{33} - 120q^{35} + 158q^{37} - 108q^{39} + 202q^{41} + 298q^{43} - 138q^{45} + 408q^{47} + 57q^{49} + 132q^{51} - 690q^{53} - 84q^{55} + 324q^{57} + 322q^{59} - 298q^{61} + 460q^{63} + 324q^{65} - 202q^{67} + 344q^{69} + 700q^{71} - 418q^{73} + 178q^{75} + 280q^{77} - 744q^{79} + 421q^{81} + 678q^{83} - 396q^{85} + 4q^{87} - 82q^{89} - 1080q^{91} - 256q^{93} - 972q^{95} - 1122q^{97} + 322q^{99} + O(q^{100}) \)

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 −2.00000 0 6.00000 0 −20.0000 0 −23.0000 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
\(2\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(128))\):

\( T_{3} + 2 \)
\( T_{5} - 6 \)