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Properties

Label 3969.2.bv
Level $3969$
Weight $2$
Character orbit 3969.bv
Rep. character $\chi_{3969}(404,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2640$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3969.bv (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
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 2736 3456
Cusp forms 5904 2640 3264
Eisenstein series 288 96 192

Trace form

\( 2640 q - 190 q^{4} + 28 q^{7} + O(q^{10}) \) \( 2640 q - 190 q^{4} + 28 q^{7} - 44 q^{10} + 28 q^{13} + 238 q^{16} - 72 q^{19} + 36 q^{22} + 230 q^{25} - 36 q^{28} + 60 q^{31} + 28 q^{34} - 78 q^{37} + 76 q^{40} - 20 q^{43} - 216 q^{46} + 20 q^{49} + 6 q^{52} + 28 q^{55} - 78 q^{58} + 18 q^{61} + 352 q^{64} + 22 q^{67} - 98 q^{70} - 8 q^{73} - 168 q^{76} + 22 q^{79} - 56 q^{82} + 64 q^{85} + 50 q^{88} + 106 q^{91} + 118 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)