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Properties

Label 3969.2.w
Level $3969$
Weight $2$
Character orbit 3969.w
Rep. character $\chi_{3969}(442,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $708$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3969.w (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 3168 768 2400
Cusp forms 2880 708 2172
Eisenstein series 288 60 228

Trace form

\( 708 q - 6 q^{2} + 6 q^{4} - 9 q^{5} + 6 q^{8} + O(q^{10}) \) \( 708 q - 6 q^{2} + 6 q^{4} - 9 q^{5} + 6 q^{8} + 3 q^{10} - 3 q^{11} + 6 q^{13} + 9 q^{17} + 3 q^{19} + 3 q^{20} - 21 q^{22} - 12 q^{23} + 15 q^{25} - 66 q^{26} + 66 q^{29} + 15 q^{31} + 72 q^{32} + 9 q^{34} + 3 q^{37} + 18 q^{38} - 21 q^{40} - 51 q^{41} - 21 q^{43} - 9 q^{44} + 3 q^{46} - 69 q^{47} + 159 q^{50} + 45 q^{52} + 54 q^{53} + 12 q^{55} + 33 q^{58} + 30 q^{59} - 12 q^{61} - 12 q^{62} - 264 q^{64} + 75 q^{65} - 3 q^{67} + 15 q^{68} - 39 q^{71} - 6 q^{73} + 51 q^{74} - 60 q^{76} + 42 q^{79} - 138 q^{80} + 12 q^{82} + 9 q^{83} - 9 q^{85} + 9 q^{86} - 42 q^{88} + 57 q^{89} - 117 q^{92} + 69 q^{94} - 135 q^{95} + 15 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)