Properties

Label 1053.2.bq
Level $1053$
Weight $2$
Character orbit 1053.bq
Rep. character $\chi_{1053}(40,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $1944$
Sturm bound $252$

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Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.bq (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(252\)

Dimensions

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

Total New Old
Modular forms 2304 1944 360
Cusp forms 2232 1944 288
Eisenstein series 72 0 72

Trace form

\( 1944 q + O(q^{10}) \) \( 1944 q - 18 q^{18} - 72 q^{20} - 54 q^{21} - 54 q^{23} - 54 q^{26} - 54 q^{30} - 54 q^{33} - 54 q^{35} - 72 q^{36} - 18 q^{38} - 36 q^{41} - 90 q^{42} - 198 q^{48} - 126 q^{51} - 252 q^{54} - 252 q^{56} - 126 q^{59} - 198 q^{62} - 54 q^{67} + 162 q^{68} - 36 q^{69} - 108 q^{70} + 144 q^{71} + 144 q^{74} + 180 q^{75} - 162 q^{76} + 144 q^{77} + 504 q^{80} + 144 q^{81} + 144 q^{83} + 504 q^{84} + 144 q^{87} - 162 q^{88} + 126 q^{89} + 18 q^{90} - 90 q^{92} - 36 q^{93} - 108 q^{94} - 216 q^{95} + 252 q^{96} - 54 q^{97} - 216 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1053, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)