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Properties

Label 1053.2.bd
Level $1053$
Weight $2$
Character orbit 1053.bd
Rep. character $\chi_{1053}(80,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $208$
Sturm bound $252$

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Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(252\)

Dimensions

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

Total New Old
Modular forms 552 240 312
Cusp forms 456 208 248
Eisenstein series 96 32 64

Trace form

\( 208 q + 12 q^{4} + 12 q^{7} + O(q^{10}) \) \( 208 q + 12 q^{4} + 12 q^{7} + 12 q^{10} + 20 q^{13} + 84 q^{16} - 24 q^{19} + 4 q^{22} - 32 q^{28} - 8 q^{31} - 12 q^{34} - 56 q^{37} + 48 q^{40} - 36 q^{43} - 24 q^{46} + 12 q^{49} - 112 q^{52} - 8 q^{55} - 32 q^{58} + 40 q^{61} - 12 q^{67} + 124 q^{70} - 24 q^{73} - 40 q^{76} - 32 q^{79} - 24 q^{82} - 48 q^{85} + 12 q^{88} + 4 q^{94} - 32 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1053, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)