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Properties

Label 3969.2.bm
Level $3969$
Weight $2$
Character orbit 3969.bm
Rep. character $\chi_{3969}(190,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2664$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3969.bm (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 6192 2712 3480
Cusp forms 5904 2664 3240
Eisenstein series 288 48 240

Trace form

\( 2664 q + 230 q^{4} + 17 q^{7} + O(q^{10}) \) \( 2664 q + 230 q^{4} + 17 q^{7} - 4 q^{10} + 20 q^{13} + 218 q^{16} - 68 q^{19} + 2 q^{22} + 224 q^{25} - 40 q^{28} + 64 q^{31} + 2 q^{34} + 30 q^{37} - 34 q^{40} + 50 q^{43} - 124 q^{46} + 5 q^{49} - 114 q^{52} + 320 q^{55} - 148 q^{58} - 9 q^{61} - 388 q^{64} + 22 q^{67} + 2 q^{70} - 16 q^{73} + 82 q^{76} + 94 q^{79} - 4 q^{82} - 10 q^{85} - 46 q^{88} - 34 q^{91} - 22 q^{94} + 34 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)