Properties

Label 1323.2.bz
Level $1323$
Weight $2$
Character orbit 1323.bz
Rep. character $\chi_{1323}(143,\cdot)$
Character field $\Q(\zeta_{42})$
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.bz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 648q + 21q^{2} + 99q^{4} + 18q^{5} - 5q^{7} + O(q^{10}) \) \( 648q + 21q^{2} + 99q^{4} + 18q^{5} - 5q^{7} - 22q^{10} + 18q^{11} - 4q^{13} - 66q^{14} - 105q^{16} + 9q^{17} - 36q^{19} + 27q^{20} - 9q^{22} + 27q^{23} + 38q^{25} - 6q^{26} - 26q^{28} - 3q^{29} + 21q^{32} - 13q^{34} - 13q^{37} + 90q^{38} - 31q^{40} + 27q^{41} - 9q^{43} - 51q^{44} - 108q^{46} - 75q^{47} - 13q^{49} + 45q^{50} + 64q^{52} + 12q^{53} + 14q^{55} - 3q^{56} - 90q^{58} - 15q^{59} - 56q^{61} - 66q^{62} + 64q^{64} + 21q^{65} - 26q^{67} - 3q^{68} - 22q^{70} + 63q^{71} - 22q^{73} + 12q^{74} - 63q^{76} + 69q^{77} - 2q^{79} + 45q^{80} - 28q^{82} + 51q^{83} - 10q^{85} + 72q^{86} + 4q^{88} - 132q^{89} - 13q^{91} + 15q^{92} - 7q^{94} + 21q^{95} + 3q^{97} - 21q^{98} + O(q^{100}) \)

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

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