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Properties

Label 1323.2.bt
Level $1323$
Weight $2$
Character orbit 1323.bt
Rep. character $\chi_{1323}(62,\cdot)$
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.bt (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

\( 648 q + 15 q^{2} - 57 q^{4} + 21 q^{5} - 5 q^{7} + O(q^{10}) \) \( 648 q + 15 q^{2} - 57 q^{4} + 21 q^{5} - 5 q^{7} - 28 q^{10} + 15 q^{11} - 7 q^{13} + 114 q^{14} + 39 q^{16} + 21 q^{20} + 3 q^{22} - 30 q^{23} + 41 q^{25} - 20 q^{28} - 75 q^{29} + 39 q^{32} - 7 q^{34} - 10 q^{37} - 21 q^{38} - 7 q^{40} + 21 q^{41} + 3 q^{43} - 72 q^{46} + 147 q^{47} - 13 q^{49} + 18 q^{50} - 35 q^{52} - 112 q^{55} + 63 q^{56} + 33 q^{58} + 21 q^{59} - 56 q^{61} + 52 q^{64} - 27 q^{65} - 26 q^{67} - 25 q^{70} - 28 q^{73} - 33 q^{74} + 21 q^{76} - 3 q^{77} - 2 q^{79} - 28 q^{82} + 21 q^{83} + 5 q^{85} + 123 q^{86} - 41 q^{88} - 4 q^{91} + 225 q^{92} - 7 q^{94} + 12 q^{95} + O(q^{100}) \)

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

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