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Properties

Label 1323.2.bk
Level $1323$
Weight $2$
Character orbit 1323.bk
Rep. character $\chi_{1323}(37,\cdot)$
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.bk (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

\( 648 q + 5 q^{2} - 109 q^{4} + 12 q^{5} - 7 q^{7} + 16 q^{8} + O(q^{10}) \) \( 648 q + 5 q^{2} - 109 q^{4} + 12 q^{5} - 7 q^{7} + 16 q^{8} - 22 q^{10} + 8 q^{11} - 4 q^{13} + 26 q^{14} - 97 q^{16} + 37 q^{17} - 14 q^{19} + 11 q^{20} - q^{22} - 31 q^{23} + 38 q^{25} + 44 q^{26} - 22 q^{28} - 73 q^{29} - 20 q^{31} + q^{32} - 7 q^{34} + 32 q^{35} - 39 q^{37} + 40 q^{38} - q^{40} + 17 q^{41} - q^{43} + 31 q^{44} + 56 q^{46} - 5 q^{47} - q^{49} + 21 q^{50} - 48 q^{52} - 50 q^{53} + 20 q^{55} - 127 q^{56} - 82 q^{58} - 53 q^{59} + 42 q^{61} + 30 q^{62} - 88 q^{64} + 11 q^{65} - 26 q^{67} - 145 q^{68} - 46 q^{70} + 19 q^{71} - 40 q^{73} - 18 q^{74} + 43 q^{76} - 7 q^{77} - 26 q^{79} - 163 q^{80} - 28 q^{82} + 221 q^{83} - 10 q^{85} + 18 q^{86} - 4 q^{88} + 104 q^{89} - 49 q^{91} - 119 q^{92} - 13 q^{94} - 37 q^{95} - 11 q^{97} + 33 q^{98} + O(q^{100}) \)

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

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