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Properties

Label 1053.2.bc
Level $1053$
Weight $2$
Character orbit 1053.bc
Rep. character $\chi_{1053}(512,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $216$
Sturm bound $252$

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Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
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 552 232 320
Cusp forms 456 216 240
Eisenstein series 96 16 80

Trace form

\( 216 q + 14 q^{7} + O(q^{10}) \) \( 216 q + 14 q^{7} + 4 q^{13} + 104 q^{16} - 28 q^{19} + 8 q^{22} + 120 q^{28} - 36 q^{31} + 12 q^{34} + 12 q^{37} - 24 q^{40} - 24 q^{46} - 88 q^{52} - 16 q^{55} + 32 q^{58} + 8 q^{61} + 2 q^{67} - 52 q^{70} - 4 q^{73} + 36 q^{76} + 56 q^{79} + 12 q^{85} - 88 q^{91} - 112 q^{94} + 6 q^{97} + O(q^{100}) \)

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

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