Properties

Label 1323.2.p
Level $1323$
Weight $2$
Character orbit 1323.p
Rep. character $\chi_{1323}(80,\cdot)$
Character field $\Q(\zeta_{6})$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 106q + 52q^{4} + O(q^{10}) \) \( 106q + 52q^{4} - 6q^{10} - 82q^{16} + 3q^{19} + 72q^{22} - 49q^{25} + 39q^{31} - 14q^{37} + 12q^{40} + 46q^{43} + 42q^{46} - 36q^{52} + 20q^{58} - 15q^{61} - 280q^{64} - 72q^{67} - 51q^{73} + 92q^{79} - 18q^{82} + 4q^{85} + 38q^{88} + 138q^{94} + O(q^{100}) \)

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

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