↑

Properties

Label 3969.2.dg
Level $3969$
Weight $2$
Character orbit 3969.dg
Rep. character $\chi_{3969}(47,\cdot)$
Character field $\Q(\zeta_{378})$
Dimension $54216$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3969.dg (of order \(378\) and degree \(108\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3969 \)
Character field: \(\Q(\zeta_{378})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3969, [\chi])\).

Total New Old
Modular forms 54648 54648 0
Cusp forms 54216 54216 0
Eisenstein series 432 432 0

Trace form

\( 54216 q - 117 q^{2} - 99 q^{3} - 117 q^{4} - 99 q^{5} - 126 q^{6} - 108 q^{7} - 90 q^{8} - 117 q^{9} + O(q^{10}) \) \( 54216 q - 117 q^{2} - 99 q^{3} - 117 q^{4} - 99 q^{5} - 126 q^{6} - 108 q^{7} - 90 q^{8} - 117 q^{9} - 99 q^{10} - 117 q^{11} - 99 q^{12} - 126 q^{13} - 108 q^{14} - 90 q^{15} - 117 q^{16} - 99 q^{17} - 54 q^{18} - 162 q^{19} - 126 q^{20} - 135 q^{21} - 90 q^{22} + 234 q^{23} - 99 q^{24} - 117 q^{25} - 162 q^{26} - 126 q^{27} - 54 q^{28} - 90 q^{29} + 54 q^{30} - 162 q^{31} - 117 q^{32} - 99 q^{33} - 126 q^{34} - 54 q^{35} - 90 q^{36} - 117 q^{37} - 99 q^{38} - 117 q^{39} - 99 q^{40} - 72 q^{41} - 63 q^{42} - 90 q^{43} - 117 q^{44} - 99 q^{45} - 117 q^{46} + 279 q^{47} - 297 q^{48} - 108 q^{49} - 216 q^{50} - 117 q^{51} - 99 q^{52} - 162 q^{53} + 279 q^{54} - 63 q^{55} - 324 q^{56} - 90 q^{57} - 117 q^{58} - 99 q^{59} - 117 q^{60} - 99 q^{61} + 171 q^{62} - 54 q^{63} - 90 q^{64} - 117 q^{65} - 99 q^{66} - 54 q^{67} - 162 q^{68} - 180 q^{69} - 90 q^{71} - 117 q^{72} - 99 q^{73} - 117 q^{74} - 99 q^{75} - 126 q^{76} - 180 q^{77} - 63 q^{78} - 54 q^{79} - 117 q^{81} - 198 q^{82} - 126 q^{83} - 207 q^{84} - 90 q^{85} - 117 q^{86} - 99 q^{87} - 117 q^{88} - 99 q^{89} - 126 q^{90} - 108 q^{91} + 630 q^{92} - 117 q^{93} - 99 q^{94} + 99 q^{95} - 99 q^{96} - 234 q^{98} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces

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