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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 $336$

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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

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

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

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