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Properties

Label 1323.2.bp
Level $1323$
Weight $2$
Character orbit 1323.bp
Rep. character $\chi_{1323}(17,\cdot)$
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.bp (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

\( 648 q + 18 q^{2} - 60 q^{4} + 15 q^{5} - 5 q^{7} + O(q^{10}) \) \( 648 q + 18 q^{2} - 60 q^{4} + 15 q^{5} - 5 q^{7} - 22 q^{10} + 21 q^{11} - 10 q^{13} + 24 q^{14} + 42 q^{16} - 9 q^{17} - 36 q^{19} + 15 q^{20} - 9 q^{22} + 84 q^{23} - 97 q^{25} + 6 q^{26} - 26 q^{28} + 123 q^{29} - 6 q^{31} + 30 q^{32} - q^{34} - 13 q^{37} + 75 q^{38} - 7 q^{40} + 15 q^{41} - 9 q^{43} + 51 q^{44} - 108 q^{46} + 36 q^{47} + 5 q^{49} + 45 q^{50} - 35 q^{52} - 12 q^{53} + 14 q^{55} - 33 q^{56} + 33 q^{58} + 3 q^{59} + 55 q^{61} + 66 q^{62} + 64 q^{64} - 3 q^{65} + 13 q^{67} - 6 q^{68} + 11 q^{70} - 63 q^{71} - 22 q^{73} + 21 q^{74} + 21 q^{76} + 69 q^{77} + q^{79} - 45 q^{80} - 28 q^{82} - 9 q^{83} - 10 q^{85} + 21 q^{86} - 29 q^{88} + 132 q^{89} - 13 q^{91} - 195 q^{92} - 4 q^{94} + 129 q^{95} - 3 q^{97} + 21 q^{98} + O(q^{100}) \)

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

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