↑

Properties

Label 3211.2.cd
Level $3211$
Weight $2$
Character orbit 3211.cd
Rep. character $\chi_{3211}(87,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $7248$
Sturm bound $606$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3211 = 13^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3211.cd (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3211 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(606\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3211, [\chi])\).

Total New Old
Modular forms 7344 7344 0
Cusp forms 7248 7248 0
Eisenstein series 96 96 0

Trace form

\( 7248 q - 14 q^{2} - 16 q^{3} + 288 q^{4} - 11 q^{5} - 22 q^{6} - 49 q^{7} - 40 q^{8} + 286 q^{9} + O(q^{10}) \) \( 7248 q - 14 q^{2} - 16 q^{3} + 288 q^{4} - 11 q^{5} - 22 q^{6} - 49 q^{7} - 40 q^{8} + 286 q^{9} - 11 q^{10} - 52 q^{11} - 26 q^{12} - 64 q^{13} - 23 q^{14} + 69 q^{15} + 286 q^{16} - 11 q^{17} - 50 q^{18} - 19 q^{19} - 70 q^{20} - 19 q^{21} - 148 q^{22} - 24 q^{23} - 27 q^{24} + 285 q^{25} - 64 q^{26} - 16 q^{27} - 67 q^{28} + 19 q^{29} + 57 q^{30} - 26 q^{31} - 76 q^{32} - q^{33} + 118 q^{34} + 3 q^{35} + 275 q^{36} - 47 q^{37} - 10 q^{38} - 78 q^{39} - 12 q^{40} + 6 q^{41} - 67 q^{42} + 7 q^{43} - 103 q^{44} - 135 q^{45} - 42 q^{46} + 100 q^{47} - 60 q^{48} + 153 q^{49} - 66 q^{50} + 100 q^{51} - 46 q^{52} - 26 q^{53} + 31 q^{54} + 222 q^{55} - 71 q^{56} - 38 q^{57} - 32 q^{58} + q^{59} - 50 q^{60} - 17 q^{61} + 113 q^{62} - 47 q^{63} - 612 q^{64} - 85 q^{65} - 187 q^{66} + 15 q^{67} - 99 q^{68} - 123 q^{69} - 31 q^{70} - 23 q^{71} - 48 q^{73} + 57 q^{74} - 77 q^{75} - 86 q^{76} - 64 q^{77} + 166 q^{78} - 37 q^{79} + 76 q^{80} + 309 q^{81} - 527 q^{82} - 30 q^{83} - 82 q^{84} - 18 q^{85} - 11 q^{86} + 196 q^{87} - 651 q^{88} - 4 q^{89} - 14 q^{90} - 31 q^{91} - 232 q^{92} + 13 q^{93} - 64 q^{94} - 220 q^{95} - 50 q^{96} + q^{97} + 21 q^{98} - 81 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3211, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.