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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

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

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

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