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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

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

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

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