Properties

Label 128.4.a.c
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

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

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 \(S_{4}^{\mathrm{new}}(\Gamma_0(128))\):

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