Properties

Label 2.24.a.a
Level 2
Weight 24
Character orbit 2.a
Self dual Yes
Analytic conductor 6.704
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 24 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(6.7040807469\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 2048q^{2} \) \(\mathstrut -\mathstrut 505908q^{3} \) \(\mathstrut +\mathstrut 4194304q^{4} \) \(\mathstrut -\mathstrut 90135570q^{5} \) \(\mathstrut +\mathstrut 1036099584q^{6} \) \(\mathstrut +\mathstrut 6872255096q^{7} \) \(\mathstrut -\mathstrut 8589934592q^{8} \) \(\mathstrut +\mathstrut 161799725637q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2048q^{2} \) \(\mathstrut -\mathstrut 505908q^{3} \) \(\mathstrut +\mathstrut 4194304q^{4} \) \(\mathstrut -\mathstrut 90135570q^{5} \) \(\mathstrut +\mathstrut 1036099584q^{6} \) \(\mathstrut +\mathstrut 6872255096q^{7} \) \(\mathstrut -\mathstrut 8589934592q^{8} \) \(\mathstrut +\mathstrut 161799725637q^{9} \) \(\mathstrut +\mathstrut 184597647360q^{10} \) \(\mathstrut -\mathstrut 965328798588q^{11} \) \(\mathstrut -\mathstrut 2121931948032q^{12} \) \(\mathstrut +\mathstrut 542359999142q^{13} \) \(\mathstrut -\mathstrut 14074378436608q^{14} \) \(\mathstrut +\mathstrut 45600305947560q^{15} \) \(\mathstrut +\mathstrut 17592186044416q^{16} \) \(\mathstrut +\mathstrut 82083537265266q^{17} \) \(\mathstrut -\mathstrut 331365838104576q^{18} \) \(\mathstrut +\mathstrut 555748551616700q^{19} \) \(\mathstrut -\mathstrut 378055981793280q^{20} \) \(\mathstrut -\mathstrut 3476728831107168q^{21} \) \(\mathstrut +\mathstrut 1976993379508224q^{22} \) \(\mathstrut +\mathstrut 6508638190765032q^{23} \) \(\mathstrut +\mathstrut 4345716629569536q^{24} \) \(\mathstrut -\mathstrut 3796507975853225q^{25} \) \(\mathstrut -\mathstrut 1110753278242816q^{26} \) \(\mathstrut -\mathstrut 34227988283553480q^{27} \) \(\mathstrut +\mathstrut 28824327038173184q^{28} \) \(\mathstrut -\mathstrut 12202037915600490q^{29} \) \(\mathstrut -\mathstrut 93389426580602880q^{30} \) \(\mathstrut +\mathstrut 119978011042749152q^{31} \) \(\mathstrut -\mathstrut 36028797018963968q^{32} \) \(\mathstrut +\mathstrut 488367561836057904q^{33} \) \(\mathstrut -\mathstrut 168107084319264768q^{34} \) \(\mathstrut -\mathstrut 619434630263364720q^{35} \) \(\mathstrut +\mathstrut 678637236438171648q^{36} \) \(\mathstrut -\mathstrut 619510980267421234q^{37} \) \(\mathstrut -\mathstrut 1138173033711001600q^{38} \) \(\mathstrut -\mathstrut 274384262445930936q^{39} \) \(\mathstrut +\mathstrut 774258650712637440q^{40} \) \(\mathstrut -\mathstrut 1587735553771936038q^{41} \) \(\mathstrut +\mathstrut 7120340646107480064q^{42} \) \(\mathstrut +\mathstrut 8377717142038508132q^{43} \) \(\mathstrut -\mathstrut 4048882441232842752q^{44} \) \(\mathstrut -\mathstrut 14583910496134608090q^{45} \) \(\mathstrut -\mathstrut 13329691014686785536q^{46} \) \(\mathstrut +\mathstrut 13100457020745462096q^{47} \) \(\mathstrut -\mathstrut 8900027657358409728q^{48} \) \(\mathstrut +\mathstrut 19859142764417052873q^{49} \) \(\mathstrut +\mathstrut 7775248334547404800q^{50} \) \(\mathstrut -\mathstrut 41526718170796191528q^{51} \) \(\mathstrut +\mathstrut 2274822713841287168q^{52} \) \(\mathstrut +\mathstrut 41795979279875033022q^{53} \) \(\mathstrut +\mathstrut 70098920004717527040q^{54} \) \(\mathstrut +\mathstrut 87010461498144575160q^{55} \) \(\mathstrut -\mathstrut 59032221774178680832q^{56} \) \(\mathstrut -\mathstrut 281157638251301463600q^{57} \) \(\mathstrut +\mathstrut 24989773651149803520q^{58} \) \(\mathstrut -\mathstrut 74383865281405054380q^{59} \) \(\mathstrut +\mathstrut 191261545637074698240q^{60} \) \(\mathstrut -\mathstrut 271922036586947177098q^{61} \) \(\mathstrut -\mathstrut 245714966615550263296q^{62} \) \(\mathstrut +\mathstrut 1111928989040275096152q^{63} \) \(\mathstrut +\mathstrut 73786976294838206464q^{64} \) \(\mathstrut -\mathstrut 48885927667863680940q^{65} \) \(\mathstrut -\mathstrut 1000176766640246587392q^{66} \) \(\mathstrut +\mathstrut 1748137016509219336076q^{67} \) \(\mathstrut +\mathstrut 344283308685854244864q^{68} \) \(\mathstrut -\mathstrut 3292772129813555809056q^{69} \) \(\mathstrut +\mathstrut 1268602122779370946560q^{70} \) \(\mathstrut -\mathstrut 2717986658231940967368q^{71} \) \(\mathstrut -\mathstrut 1389849060225375535104q^{72} \) \(\mathstrut +\mathstrut 4312780994675837739962q^{73} \) \(\mathstrut +\mathstrut 1268758487587678687232q^{74} \) \(\mathstrut +\mathstrut 1920683757047953353300q^{75} \) \(\mathstrut +\mathstrut 2330978373040131276800q^{76} \) \(\mathstrut -\mathstrut 6633985755411940604448q^{77} \) \(\mathstrut +\mathstrut 561938969489266556928q^{78} \) \(\mathstrut +\mathstrut 3598562784411776110640q^{79} \) \(\mathstrut -\mathstrut 1585681716659481477120q^{80} \) \(\mathstrut +\mathstrut 2083872591752346472041q^{81} \) \(\mathstrut +\mathstrut 3251682414124925005824q^{82} \) \(\mathstrut -\mathstrut 225004177003815933828q^{83} \) \(\mathstrut -\mathstrut 14582457643228119171072q^{84} \) \(\mathstrut -\mathstrut 7398646419020992111620q^{85} \) \(\mathstrut -\mathstrut 17157564706894864654336q^{86} \) \(\mathstrut +\mathstrut 6173108597805612694920q^{87} \) \(\mathstrut +\mathstrut 8292111239644861956096q^{88} \) \(\mathstrut +\mathstrut 33892422870920675328810q^{89} \) \(\mathstrut +\mathstrut 29867848696083677368320q^{90} \) \(\mathstrut +\mathstrut 3727236267970165127632q^{91} \) \(\mathstrut +\mathstrut 27299207198078536777728q^{92} \) \(\mathstrut -\mathstrut 60697835610615137990016q^{93} \) \(\mathstrut -\mathstrut 26829735978486706372608q^{94} \) \(\mathstrut -\mathstrut 50092712476645676019000q^{95} \) \(\mathstrut +\mathstrut 18227256642270023122944q^{96} \) \(\mathstrut +\mathstrut 92121571514147280134306q^{97} \) \(\mathstrut -\mathstrut 40671524381526124283904q^{98} \) \(\mathstrut -\mathstrut 156189934761033233000556q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
−2048.00 −505908. 4.19430e6 −9.01356e7 1.03610e9 6.87226e9 −8.58993e9 1.61800e11 1.84598e11
\(n\): 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 \(S_{24}^{\mathrm{new}}(\Gamma_0(2))\).