Properties

Label 2.24.a
Level $2$
Weight $24$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(2))\).

Total New Old
Modular forms 7 1 6
Cusp forms 5 1 4
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(+\)\(1\)

Trace form

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

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
2.24.a.a 2.a 1.a $1$ $6.704$ \(\Q\) None \(-2048\) \(-505908\) \(-90135570\) \(6872255096\) $+$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}-505908q^{3}+2^{22}q^{4}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)