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Properties

Label 9.24.c
Level $9$
Weight $24$
Character orbit 9.c
Rep. character $\chi_{9}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 24 \)
Character orbit: \([\chi]\) \(=\) 9.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(9, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 44 44 0
Eisenstein series 4 4 0

Trace form

\( 44 q - 2049 q^{2} - 162336 q^{3} - 88080385 q^{4} - 121251630 q^{5} - 922041945 q^{6} + 670564216 q^{7} - 6691053918 q^{8} - 15707798892 q^{9} + O(q^{10}) \) \( 44 q - 2049 q^{2} - 162336 q^{3} - 88080385 q^{4} - 121251630 q^{5} - 922041945 q^{6} + 670564216 q^{7} - 6691053918 q^{8} - 15707798892 q^{9} + 16777212 q^{10} - 834713462220 q^{11} + 7026776146932 q^{12} - 836409074438 q^{13} - 49481283295200 q^{14} + 102746096401032 q^{15} - 334251543232513 q^{16} + 120083682347784 q^{17} - 1015637709578004 q^{18} - 745603994398880 q^{19} - 1503637276800468 q^{20} - 1271308283377674 q^{21} - 1473502675712001 q^{22} - 3679461828533208 q^{23} + 33161190854087277 q^{24} - 47725536118995304 q^{25} + 94954460053109496 q^{26} + 31441379169979512 q^{27} - 22359663915827204 q^{28} + 74193246572635578 q^{29} + 330990272769168 q^{30} + 37179877563593008 q^{31} + 762398671820981103 q^{32} - 929357005571791038 q^{33} + 197454196983031785 q^{34} + 294749392153846296 q^{35} - 1123405663575587085 q^{36} + 505487426555396104 q^{37} - 2428499521734691845 q^{38} + 2712286427477886624 q^{39} + 2719367624094865176 q^{40} - 7700023562640527586 q^{41} + 11934917111168297586 q^{42} + 5794805018803476772 q^{43} - 3238176441154481574 q^{44} + 15901630393312558890 q^{45} + 50081208177256522872 q^{46} + 1628941612006937136 q^{47} - 40480058382647533725 q^{48} - 33218403710486360796 q^{49} + 60292693474323111579 q^{50} - 178319943871935954552 q^{51} - 15744443200659821126 q^{52} + 204793840184028628968 q^{53} - 113698830373567787655 q^{54} - 284939964206251375296 q^{55} - 300114618501826843026 q^{56} + 226240579268459200920 q^{57} - 114877202134075988784 q^{58} - 463245442071979972044 q^{59} - 953628633609756094116 q^{60} + 268265631289703179114 q^{61} + 2628541357679956163892 q^{62} - 68499165113084132064 q^{63} + 3213688127963905689794 q^{64} - 1997037743269587539550 q^{65} + 3571588029002089420170 q^{66} - 945076028367099827684 q^{67} - 5047263655313480939601 q^{68} - 6641159390196078076074 q^{69} - 1467653347829277326238 q^{70} + 6494044679499737775456 q^{71} + 9630260525966953701195 q^{72} + 512564707186334144008 q^{73} - 14747903598820025990136 q^{74} + 16394554011602186361312 q^{75} + 1536640628754754106029 q^{76} - 15032143710582413809746 q^{77} - 62516515852228971184362 q^{78} + 448733959768191455344 q^{79} + 124840513667892435119232 q^{80} - 4457129282696628137772 q^{81} - 16984693030482179939478 q^{82} - 59073684846962336818188 q^{83} + 157363438547234314093098 q^{84} + 4013564834180787284196 q^{85} - 144057590205300200616951 q^{86} - 108494475880475744101872 q^{87} - 29072574321615539860629 q^{88} + 84554286588958415194008 q^{89} + 108434693280500456315724 q^{90} - 200404829743635601720 q^{91} - 106234755999779561354526 q^{92} + 172144963592860836762462 q^{93} - 41065115870555109581784 q^{94} - 128702104748021338202328 q^{95} - 624214773059653515520152 q^{96} + 175277958184753771027366 q^{97} + 256940436403922054740686 q^{98} + 23801989380986068508916 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.24.c.a 9.c 9.c $44$ $30.168$ None \(-2049\) \(-162336\) \(-121251630\) \(670564216\) $\mathrm{SU}(2)[C_{3}]$