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Properties

Label 1755.2.df
Level $1755$
Weight $2$
Character orbit 1755.df
Rep. character $\chi_{1755}(44,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.df (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1755, [\chi])\).

Total New Old
Modular forms 1056 352 704
Cusp forms 960 320 640
Eisenstein series 96 32 64

Trace form

\( 320 q + 6 q^{5} + O(q^{10}) \) \( 320 q + 6 q^{5} + 24 q^{11} + 24 q^{14} + 128 q^{16} - 16 q^{19} + 18 q^{20} + 24 q^{29} - 4 q^{31} + 4 q^{34} + 12 q^{40} - 12 q^{41} - 32 q^{46} + 108 q^{50} - 16 q^{55} + 12 q^{59} - 8 q^{61} - 40 q^{70} + 72 q^{74} - 4 q^{76} + 16 q^{79} - 16 q^{85} + 120 q^{86} - 16 q^{91} + 40 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1755, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1755, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)