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Properties

Label 1323.4.bi
Level $1323$
Weight $4$
Character orbit 1323.bi
Rep. character $\chi_{1323}(146,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2136$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.bi (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).

Total New Old
Modular forms 3072 2184 888
Cusp forms 2976 2136 840
Eisenstein series 96 48 48

Trace form

\( 2136 q + 12 q^{2} + 12 q^{4} - 36 q^{8} + 108 q^{9} + O(q^{10}) \) \( 2136 q + 12 q^{2} + 12 q^{4} - 36 q^{8} + 108 q^{9} - 12 q^{11} - 288 q^{15} + 60 q^{16} + 12 q^{18} - 24 q^{22} + 828 q^{23} + 12 q^{25} + 228 q^{29} + 696 q^{30} + 1776 q^{32} - 3132 q^{36} + 6 q^{37} + 696 q^{39} - 24 q^{43} + 18 q^{44} + 6 q^{46} - 858 q^{50} - 924 q^{51} - 1110 q^{57} + 12 q^{58} + 9000 q^{60} + 62964 q^{64} + 612 q^{65} + 12 q^{67} - 756 q^{71} + 8520 q^{72} - 7872 q^{74} + 3132 q^{78} + 5628 q^{79} - 1116 q^{81} + 3546 q^{85} - 11844 q^{86} + 2988 q^{88} + 4368 q^{92} - 9180 q^{93} - 4416 q^{95} - 16056 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)