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Properties

Label 1053.2.r
Level $1053$
Weight $2$
Character orbit 1053.r
Rep. character $\chi_{1053}(595,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
Sturm bound $252$

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Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(252\)

Dimensions

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

Total New Old
Modular forms 276 116 160
Cusp forms 228 108 120
Eisenstein series 48 8 40

Trace form

\( 108 q + 50 q^{4} + O(q^{10}) \) \( 108 q + 50 q^{4} + 2 q^{10} + 7 q^{13} - 46 q^{16} + 9 q^{19} - 10 q^{22} + 50 q^{25} - 18 q^{28} - 60 q^{31} + 12 q^{34} - 21 q^{37} - 20 q^{40} - 36 q^{43} - 6 q^{46} - 60 q^{49} + 76 q^{52} + 8 q^{55} + 6 q^{58} + 2 q^{61} - 44 q^{64} - 30 q^{70} - 13 q^{79} + 2 q^{82} + 30 q^{85} + 94 q^{88} - 51 q^{91} + 188 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1053, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)