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Properties

Label 1755.2.dm
Level $1755$
Weight $2$
Character orbit 1755.dm
Rep. character $\chi_{1755}(287,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.dm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 288 768
Cusp forms 960 288 672
Eisenstein series 96 0 96

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 144 q^{16} + 48 q^{20} - 12 q^{25} + 120 q^{32} - 24 q^{37} + 24 q^{41} - 96 q^{46} + 48 q^{47} - 96 q^{50} - 24 q^{55} + 96 q^{56} + 24 q^{58} - 24 q^{61} - 12 q^{67} + 144 q^{68} - 24 q^{76} - 48 q^{77} + 144 q^{86} - 24 q^{88} - 228 q^{92} - 120 q^{95} - 12 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)