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Properties

Label 3969.2.be
Level $3969$
Weight $2$
Character orbit 3969.be
Rep. character $\chi_{3969}(521,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3969.be (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

\( 696 q - 3 q^{2} + 3 q^{4} - 9 q^{5} + 36 q^{8} + O(q^{10}) \) \( 696 q - 3 q^{2} + 3 q^{4} - 9 q^{5} + 36 q^{8} - 15 q^{11} - 3 q^{16} - 18 q^{17} + 18 q^{20} - 24 q^{22} - 18 q^{23} + 3 q^{25} + 42 q^{29} + 9 q^{31} + 33 q^{32} + 18 q^{34} - 3 q^{37} - 99 q^{38} + 54 q^{40} - 24 q^{43} - 9 q^{44} - 3 q^{46} + 45 q^{47} + 39 q^{50} + 9 q^{52} - 45 q^{53} + 3 q^{58} + 36 q^{59} + 9 q^{61} - 99 q^{62} + 252 q^{64} + 99 q^{65} + 3 q^{67} + 36 q^{68} + 108 q^{71} + 9 q^{73} + 123 q^{74} - 36 q^{76} + 39 q^{79} + 72 q^{80} + 18 q^{82} - 90 q^{83} - 81 q^{85} - 99 q^{86} + 27 q^{88} - 18 q^{89} + 258 q^{92} + 9 q^{94} - 183 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)