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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

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

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

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