Properties

Label 4.10.a.a
Level 4
Weight 10
Character orbit 4.a
Self dual Yes
Analytic conductor 2.060
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 4.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.06014334466\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 228q^{3} \) \(\mathstrut -\mathstrut 666q^{5} \) \(\mathstrut -\mathstrut 6328q^{7} \) \(\mathstrut +\mathstrut 32301q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 228q^{3} \) \(\mathstrut -\mathstrut 666q^{5} \) \(\mathstrut -\mathstrut 6328q^{7} \) \(\mathstrut +\mathstrut 32301q^{9} \) \(\mathstrut -\mathstrut 30420q^{11} \) \(\mathstrut -\mathstrut 32338q^{13} \) \(\mathstrut -\mathstrut 151848q^{15} \) \(\mathstrut +\mathstrut 590994q^{17} \) \(\mathstrut +\mathstrut 34676q^{19} \) \(\mathstrut -\mathstrut 1442784q^{21} \) \(\mathstrut +\mathstrut 1048536q^{23} \) \(\mathstrut -\mathstrut 1509569q^{25} \) \(\mathstrut +\mathstrut 2876904q^{27} \) \(\mathstrut +\mathstrut 4409406q^{29} \) \(\mathstrut -\mathstrut 7401184q^{31} \) \(\mathstrut -\mathstrut 6935760q^{33} \) \(\mathstrut +\mathstrut 4214448q^{35} \) \(\mathstrut +\mathstrut 10234502q^{37} \) \(\mathstrut -\mathstrut 7373064q^{39} \) \(\mathstrut +\mathstrut 18352746q^{41} \) \(\mathstrut -\mathstrut 252340q^{43} \) \(\mathstrut -\mathstrut 21512466q^{45} \) \(\mathstrut -\mathstrut 49517136q^{47} \) \(\mathstrut -\mathstrut 310023q^{49} \) \(\mathstrut +\mathstrut 134746632q^{51} \) \(\mathstrut -\mathstrut 66396906q^{53} \) \(\mathstrut +\mathstrut 20259720q^{55} \) \(\mathstrut +\mathstrut 7906128q^{57} \) \(\mathstrut -\mathstrut 61523748q^{59} \) \(\mathstrut +\mathstrut 35638622q^{61} \) \(\mathstrut -\mathstrut 204400728q^{63} \) \(\mathstrut +\mathstrut 21537108q^{65} \) \(\mathstrut +\mathstrut 181742372q^{67} \) \(\mathstrut +\mathstrut 239066208q^{69} \) \(\mathstrut +\mathstrut 90904968q^{71} \) \(\mathstrut -\mathstrut 262978678q^{73} \) \(\mathstrut -\mathstrut 344181732q^{75} \) \(\mathstrut +\mathstrut 192497760q^{77} \) \(\mathstrut -\mathstrut 116502832q^{79} \) \(\mathstrut +\mathstrut 20153529q^{81} \) \(\mathstrut -\mathstrut 9563724q^{83} \) \(\mathstrut -\mathstrut 393602004q^{85} \) \(\mathstrut +\mathstrut 1005344568q^{87} \) \(\mathstrut +\mathstrut 611826714q^{89} \) \(\mathstrut +\mathstrut 204634864q^{91} \) \(\mathstrut -\mathstrut 1687469952q^{93} \) \(\mathstrut -\mathstrut 23094216q^{95} \) \(\mathstrut -\mathstrut 259312798q^{97} \) \(\mathstrut -\mathstrut 982596420q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
0 228.000 0 −666.000 0 −6328.00 0 32301.0 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
\(2\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{10}^{\mathrm{new}}(\Gamma_0(4))\).