↑

Properties

Label 3969.2.bp
Level $3969$
Weight $2$
Character orbit 3969.bp
Rep. character $\chi_{3969}(148,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $6552$
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.bp (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
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 6732 2484
Cusp forms 8928 6552 2376
Eisenstein series 288 180 108

Trace form

\( 6552 q + 18 q^{2} + 18 q^{3} + 18 q^{4} + 18 q^{5} + 18 q^{6} - 90 q^{8} + 18 q^{9} + O(q^{10}) \) \( 6552 q + 18 q^{2} + 18 q^{3} + 18 q^{4} + 18 q^{5} + 18 q^{6} - 90 q^{8} + 18 q^{9} + 18 q^{10} + 18 q^{11} + 18 q^{12} + 18 q^{13} - 90 q^{15} + 18 q^{16} + 18 q^{17} + 27 q^{18} + 18 q^{19} + 54 q^{20} - 90 q^{22} - 9 q^{23} + 72 q^{24} + 18 q^{25} - 45 q^{26} + 45 q^{27} - 63 q^{29} - 36 q^{30} + 18 q^{31} + 72 q^{32} - 9 q^{33} + 18 q^{34} - 54 q^{36} + 18 q^{37} + 27 q^{38} + 18 q^{39} + 18 q^{40} - 90 q^{43} + 90 q^{44} + 72 q^{45} + 18 q^{46} - 36 q^{47} - 81 q^{48} + 27 q^{50} + 81 q^{51} + 63 q^{53} - 108 q^{54} + 9 q^{55} - 36 q^{57} + 18 q^{58} + 81 q^{59} + 135 q^{60} + 18 q^{61} - 81 q^{62} - 90 q^{64} + 108 q^{65} + 162 q^{66} + 45 q^{67} - 153 q^{68} - 72 q^{69} - 18 q^{71} + 234 q^{72} + 18 q^{73} - 126 q^{74} - 72 q^{75} + 99 q^{76} + 27 q^{78} - 36 q^{79} + 288 q^{80} - 54 q^{81} + 36 q^{82} - 54 q^{83} - 144 q^{85} + 162 q^{86} + 162 q^{87} + 99 q^{88} - 45 q^{89} - 63 q^{90} + 36 q^{92} + 180 q^{93} - 36 q^{94} - 162 q^{95} + 9 q^{96} + 45 q^{97} - 162 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)