Properties

Label 1323.2.bi
Level $1323$
Weight $2$
Character orbit 1323.bi
Rep. character $\chi_{1323}(146,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
Sturm bound $336$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.bi (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1056 744 312
Cusp forms 960 696 264
Eisenstein series 96 48 48

Trace form

\( 696q + 12q^{2} + 12q^{4} - 36q^{8} + O(q^{10}) \) \( 696q + 12q^{2} + 12q^{4} - 36q^{8} + 24q^{11} + 24q^{16} + 12q^{18} - 24q^{22} + 12q^{25} + 12q^{29} - 96q^{30} - 24q^{32} + 6q^{37} - 6q^{39} - 24q^{43} + 18q^{44} + 6q^{46} - 66q^{50} + 30q^{51} - 48q^{57} + 12q^{58} + 36q^{60} + 252q^{64} - 126q^{65} + 12q^{67} - 108q^{71} - 228q^{72} + 84q^{74} - 108q^{78} - 60q^{79} + 72q^{81} - 126q^{85} - 36q^{86} + 36q^{88} + 12q^{92} + 36q^{93} - 240q^{95} + 144q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)