Properties

Label 1323.2.bl
Level $1323$
Weight $2$
Character orbit 1323.bl
Rep. character $\chi_{1323}(100,\cdot)$
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.bl (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

\( 648q + 8q^{2} + 44q^{4} - 3q^{5} - 7q^{7} + 16q^{8} + O(q^{10}) \) \( 648q + 8q^{2} + 44q^{4} - 3q^{5} - 7q^{7} + 16q^{8} - 22q^{10} + 5q^{11} - 4q^{13} - 52q^{14} + 38q^{16} + 37q^{17} - 14q^{19} + 11q^{20} - q^{22} + 20q^{23} - 97q^{25} + 44q^{26} - 22q^{28} + 53q^{29} + 10q^{31} + 10q^{32} - 7q^{34} + 32q^{35} - 39q^{37} - 59q^{38} - 19q^{40} + 17q^{41} - q^{43} + 31q^{44} + 56q^{46} - 50q^{47} - 19q^{49} + 21q^{50} - 9q^{52} - 50q^{53} + 20q^{55} + 239q^{56} + 17q^{58} + 37q^{59} - 105q^{61} + 30q^{62} - 88q^{64} + 5q^{65} + 13q^{67} + 290q^{68} + 17q^{70} + 19q^{71} - 40q^{73} + 57q^{74} - 41q^{76} - 19q^{77} + 13q^{79} - 163q^{80} - 28q^{82} - 73q^{83} - 10q^{85} - 15q^{86} - 13q^{88} + 104q^{89} - 49q^{91} + 91q^{92} - 4q^{94} + 29q^{95} - 11q^{97} + 33q^{98} + O(q^{100}) \)

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

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