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Properties

Label 9.12.c
Level $9$
Weight $12$
Character orbit 9.c
Rep. character $\chi_{9}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 12 \)
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: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(9, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

Trace form

\( 20 q - 33 q^{2} - 12 q^{3} - 9217 q^{4} - 7230 q^{5} + 20583 q^{6} + 8512 q^{7} - 29118 q^{8} + 135504 q^{9} + O(q^{10}) \) \( 20 q - 33 q^{2} - 12 q^{3} - 9217 q^{4} - 7230 q^{5} + 20583 q^{6} + 8512 q^{7} - 29118 q^{8} + 135504 q^{9} + 4092 q^{10} - 112776 q^{11} + 1027860 q^{12} + 279706 q^{13} - 3901584 q^{14} - 6358608 q^{15} - 7342081 q^{16} + 27765792 q^{17} + 8682876 q^{18} + 7029400 q^{19} - 34163508 q^{20} + 55012206 q^{21} + 2274591 q^{22} - 69371616 q^{23} - 211100355 q^{24} - 45286204 q^{25} + 481929144 q^{26} - 83699352 q^{27} - 61345796 q^{28} - 25437246 q^{29} - 23582592 q^{30} + 114575368 q^{31} + 80396559 q^{32} + 31338342 q^{33} - 243855063 q^{34} - 178147464 q^{35} - 19984653 q^{36} - 134218328 q^{37} + 489799995 q^{38} - 1999064976 q^{39} + 107425416 q^{40} + 331873026 q^{41} + 4171968882 q^{42} - 1118847584 q^{43} + 278477274 q^{44} + 1749349170 q^{45} + 2882537592 q^{46} - 1469650704 q^{47} - 9335236125 q^{48} - 3553434720 q^{49} - 6643771701 q^{50} + 1736777052 q^{51} + 3632448874 q^{52} + 14914261944 q^{53} + 18127857753 q^{54} + 4981449984 q^{55} - 27669139026 q^{56} - 7855424196 q^{57} - 1387480560 q^{58} - 26505032592 q^{59} - 10283356116 q^{60} + 990409066 q^{61} + 91044996180 q^{62} + 51565206888 q^{63} - 7516709566 q^{64} - 39045315390 q^{65} - 93201828246 q^{66} + 6557215720 q^{67} - 77299152993 q^{68} + 6907292550 q^{69} - 785437278 q^{70} + 122053719744 q^{71} + 161899013547 q^{72} - 12612893936 q^{73} - 109519086216 q^{74} - 218383044348 q^{75} + 14574055597 q^{76} - 88616208018 q^{77} + 150319870614 q^{78} - 7621233248 q^{79} + 399166683072 q^{80} + 222307104312 q^{81} - 59168477334 q^{82} - 99007044180 q^{83} - 711968015814 q^{84} + 12911595156 q^{85} - 214357830519 q^{86} + 99715491216 q^{87} - 54423523605 q^{88} + 476597704824 q^{89} + 620021743884 q^{90} + 138211652216 q^{91} - 461776423998 q^{92} - 572981484354 q^{93} + 13393667064 q^{94} - 418952909328 q^{95} + 118587589272 q^{96} + 123483551938 q^{97} + 1310123604078 q^{98} + 621154334268 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.12.c.a 9.c 9.c $20$ $6.915$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-33\) \(-12\) \(-7230\) \(8512\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)