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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

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

Display 100 coefficients 10 coefficients

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

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