↑

Properties

Label 1053.2.bt
Level $1053$
Weight $2$
Character orbit 1053.bt
Rep. character $\chi_{1053}(206,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $480$
Sturm bound $252$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.bt (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 351 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(252\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1053, [\chi])\).

Total New Old
Modular forms 1584 528 1056
Cusp forms 1440 480 960
Eisenstein series 144 48 96

Trace form

\( 480 q + 12 q^{2} - 18 q^{4} + 12 q^{5} - 12 q^{7} + 18 q^{8} + O(q^{10}) \) \( 480 q + 12 q^{2} - 18 q^{4} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 12 q^{13} + 24 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 12 q^{20} - 6 q^{22} + 18 q^{23} + 54 q^{26} - 24 q^{28} + 6 q^{29} - 12 q^{31} - 12 q^{32} - 6 q^{37} - 108 q^{38} + 36 q^{41} - 18 q^{43} + 162 q^{44} - 6 q^{46} + 6 q^{47} - 18 q^{49} + 54 q^{50} - 66 q^{52} - 12 q^{55} + 18 q^{56} + 42 q^{58} - 24 q^{59} - 6 q^{61} + 18 q^{62} + 24 q^{65} - 12 q^{67} - 42 q^{68} + 96 q^{70} + 18 q^{71} - 24 q^{73} - 30 q^{74} + 36 q^{76} + 216 q^{77} + 48 q^{79} - 144 q^{80} - 36 q^{82} + 108 q^{83} + 90 q^{85} + 276 q^{86} - 18 q^{88} + 18 q^{89} - 6 q^{91} - 240 q^{92} - 6 q^{94} + 18 q^{95} - 12 q^{97} - 54 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1053, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1053, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1053, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)