Properties

Label 3969.2.f
Level $3969$
Weight $2$
Character orbit 3969.f
Rep. character $\chi_{3969}(1324,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $318$
Sturm bound $1008$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 1104 338 766
Cusp forms 912 318 594
Eisenstein series 192 20 172

Trace form

\( 318 q - 156 q^{4} + 12 q^{10} + 3 q^{13} - 150 q^{16} - 18 q^{19} + 12 q^{22} - 135 q^{25} + 24 q^{31} - 30 q^{34} - 18 q^{37} - 54 q^{40} + 36 q^{43} + 48 q^{46} + 24 q^{52} - 48 q^{55} + 42 q^{58} - 15 q^{61}+ \cdots + 21 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)