↑

Properties

Label 3969.2.bi
Level $3969$
Weight $2$
Character orbit 3969.bi
Rep. character $\chi_{3969}(440,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
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.bi (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 3168 744 2424
Cusp forms 2880 696 2184
Eisenstein series 288 48 240

Trace form

\( 696 q - 12 q^{2} + 12 q^{4} + 36 q^{8} + O(q^{10}) \) \( 696 q - 12 q^{2} + 12 q^{4} + 36 q^{8} - 24 q^{11} + 24 q^{16} - 24 q^{22} + 12 q^{25} - 12 q^{29} + 24 q^{32} + 6 q^{37} - 24 q^{43} - 18 q^{44} + 6 q^{46} + 66 q^{50} + 12 q^{58} + 252 q^{64} + 126 q^{65} + 12 q^{67} + 108 q^{71} - 84 q^{74} - 60 q^{79} - 126 q^{85} + 36 q^{86} + 36 q^{88} - 12 q^{92} + 240 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)