↑

Properties

Label 3969.2.bo
Level $3969$
Weight $2$
Character orbit 3969.bo
Rep. character $\chi_{3969}(67,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $6408$
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.bo (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 567 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 9216 6552 2664
Cusp forms 8928 6408 2520
Eisenstein series 288 144 144

Trace form

\( 6408 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 9 q^{5} + 36 q^{6} - 72 q^{8} + 9 q^{9} + O(q^{10}) \) \( 6408 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 9 q^{5} + 36 q^{6} - 72 q^{8} + 9 q^{9} + 9 q^{10} + 9 q^{11} + 9 q^{12} + 36 q^{13} - 72 q^{15} + 9 q^{16} + 9 q^{17} + 9 q^{18} + 9 q^{19} + 36 q^{20} - 72 q^{22} + 36 q^{23} + 9 q^{24} + 9 q^{25} - 117 q^{26} + 36 q^{27} - 72 q^{29} - 99 q^{30} + 9 q^{31} + 9 q^{32} + 117 q^{33} + 36 q^{34} - 72 q^{36} + 9 q^{37} + 9 q^{38} + 9 q^{39} + 9 q^{40} + 54 q^{41} - 72 q^{43} + 9 q^{44} + 9 q^{45} + 9 q^{46} - 99 q^{47} + 135 q^{48} - 72 q^{50} + 9 q^{51} - 27 q^{52} - 9 q^{53} + 135 q^{54} + 18 q^{55} - 72 q^{57} + 9 q^{58} + 9 q^{59} + 9 q^{60} + 9 q^{61} + 135 q^{62} - 72 q^{64} - 27 q^{65} - 63 q^{66} + 9 q^{67} - 81 q^{68} + 54 q^{69} + 72 q^{71} - 207 q^{72} + 9 q^{73} + 9 q^{74} + 9 q^{75} + 36 q^{76} + 243 q^{78} + 225 q^{79} - 234 q^{80} + 9 q^{81} + 18 q^{82} + 36 q^{83} - 180 q^{85} - 135 q^{86} - 135 q^{87} + 9 q^{88} + 9 q^{89} + 36 q^{90} + 450 q^{92} - 63 q^{93} + 225 q^{94} - 207 q^{95} + 9 q^{96} + 36 q^{97} + 108 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)