Properties

Label 1323.2.e
Level $1323$
Weight $2$
Character orbit 1323.e
Rep. character $\chi_{1323}(1108,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $106$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

Total New Old
Modular forms 384 106 278
Cusp forms 288 106 182
Eisenstein series 96 0 96

Trace form

\( 106q - 52q^{4} + O(q^{10}) \) \( 106q - 52q^{4} + 2q^{10} - 18q^{16} + 9q^{19} - 64q^{22} - 53q^{25} - 13q^{31} + 6q^{37} + 50q^{43} + 26q^{46} - 20q^{52} - 32q^{55} - 4q^{58} - 15q^{61} - 24q^{64} + 72q^{67} - 7q^{73} + 76q^{76} + 68q^{79} + 118q^{82} + 68q^{85} + 78q^{88} - 30q^{94} + 14q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

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