Properties

Label 3969.2.e
Level $3969$
Weight $2$
Character orbit 3969.e
Rep. character $\chi_{3969}(2431,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $304$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3969.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 336 768
Cusp forms 912 304 608
Eisenstein series 192 32 160

Trace form

\( 304 q - 146 q^{4} + O(q^{10}) \) \( 304 q - 146 q^{4} + 12 q^{10} - 4 q^{13} - 158 q^{16} + 8 q^{19} + 48 q^{22} - 122 q^{25} - 10 q^{31} + 2 q^{37} + 12 q^{40} + 8 q^{43} - 48 q^{46} + 14 q^{52} + 108 q^{55} - 30 q^{58} - 4 q^{61} + 280 q^{64} - 40 q^{67} - 4 q^{73} - 112 q^{76} - 40 q^{79} - 72 q^{82} - 36 q^{85} - 90 q^{88} + 30 q^{94} - 4 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)