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Properties

Label 1053.2.bo
Level $1053$
Weight $2$
Character orbit 1053.bo
Rep. character $\chi_{1053}(10,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $240$
Sturm bound $252$

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Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.bo (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 351 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(252\)

Dimensions

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

Total New Old
Modular forms 792 264 528
Cusp forms 720 240 480
Eisenstein series 72 24 48

Trace form

\( 240 q + 9 q^{2} - 3 q^{4} - 9 q^{7} + O(q^{10}) \) \( 240 q + 9 q^{2} - 3 q^{4} - 9 q^{7} - 6 q^{10} + 9 q^{11} - 6 q^{13} + 12 q^{14} - 15 q^{16} - 27 q^{17} + 9 q^{20} - 3 q^{22} + 27 q^{23} - 12 q^{25} + 21 q^{26} - 18 q^{28} - 6 q^{29} + 99 q^{32} + 18 q^{34} - 90 q^{35} + 54 q^{38} - 54 q^{40} + 9 q^{41} - 3 q^{43} + 72 q^{44} - 45 q^{47} - 3 q^{49} + 18 q^{50} + 15 q^{52} - 78 q^{53} - 6 q^{55} - 6 q^{56} - 9 q^{58} + 9 q^{59} - 3 q^{61} - 51 q^{62} + 72 q^{64} + 18 q^{65} - 9 q^{67} + 57 q^{68} - 81 q^{70} + 9 q^{71} + 27 q^{73} + 33 q^{74} - 9 q^{76} + 24 q^{79} + 90 q^{80} - 6 q^{82} + 27 q^{83} - 63 q^{85} + 162 q^{86} - 45 q^{88} + 9 q^{89} - 12 q^{91} - 6 q^{92} - 57 q^{94} - 24 q^{95} - 9 q^{97} - 126 q^{98} + O(q^{100}) \)

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

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