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Properties

Label 3969.2.cc
Level $3969$
Weight $2$
Character orbit 3969.cc
Rep. character $\chi_{3969}(269,\cdot)$
Character field $\Q(\zeta_{42})$
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.cc (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 2664 q + 450 q^{4} + 7 q^{7} + O(q^{10}) \) \( 2664 q + 450 q^{4} + 7 q^{7} - 22 q^{10} - q^{13} - 414 q^{16} - 36 q^{19} + 6 q^{22} + 230 q^{25} - 8 q^{28} + 26 q^{34} - 91 q^{37} + 26 q^{40} + 30 q^{43} + 138 q^{46} + 29 q^{49} - 188 q^{52} - 238 q^{55} + 402 q^{58} + 7 q^{61} + 388 q^{64} + 22 q^{67} + 32 q^{70} - 22 q^{73} + 90 q^{76} - 26 q^{79} - 10 q^{82} + 20 q^{85} + 16 q^{88} - 73 q^{91} + 14 q^{94} - 15 q^{97} + O(q^{100}) \)

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

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