Properties

Label 1323.2.bm
Level $1323$
Weight $2$
Character orbit 1323.bm
Rep. character $\chi_{1323}(64,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $648$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.bm (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 2088 696 1392
Cusp forms 1944 648 1296
Eisenstein series 144 48 96

Trace form

\( 648q + 5q^{2} + 47q^{4} + 9q^{5} - 7q^{7} + 28q^{8} + O(q^{10}) \) \( 648q + 5q^{2} + 47q^{4} + 9q^{5} - 7q^{7} + 28q^{8} - 28q^{10} + 5q^{11} - 7q^{13} + 38q^{14} + 47q^{16} + 16q^{17} - 44q^{19} + 29q^{20} - 13q^{22} + 20q^{23} + 41q^{25} + 20q^{26} - 28q^{28} + 35q^{29} - 20q^{31} + 25q^{32} - q^{34} + 44q^{35} - 30q^{37} + 7q^{38} + 5q^{40} + 29q^{41} - 13q^{43} + 88q^{44} + 32q^{46} + 55q^{47} - q^{49} - 6q^{50} + 3q^{52} + 136q^{53} - 100q^{55} - 145q^{56} + 17q^{58} + 19q^{59} + 42q^{61} - 96q^{62} - 124q^{64} + 11q^{65} - 26q^{67} - 166q^{68} - 7q^{70} + 22q^{71} + 8q^{73} + 45q^{74} - 41q^{76} - q^{77} - 26q^{79} + 440q^{80} - 28q^{82} - 61q^{83} + 5q^{85} - 15q^{86} - q^{88} - 22q^{89} - 16q^{91} + 43q^{92} - q^{94} + 38q^{95} - 14q^{97} + 144q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)