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Properties

Label 1755.2.bu
Level $1755$
Weight $2$
Character orbit 1755.bu
Rep. character $\chi_{1755}(946,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $148$
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.bu (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 528 148 380
Cusp forms 480 148 332
Eisenstein series 48 0 48

Trace form

\( 148 q + 72 q^{4} - 6 q^{7} + O(q^{10}) \) \( 148 q + 72 q^{4} - 6 q^{7} + 18 q^{13} - 68 q^{16} - 18 q^{19} - 12 q^{22} - 148 q^{25} - 48 q^{28} + 30 q^{37} - 26 q^{43} - 12 q^{46} + 100 q^{49} - 8 q^{52} - 8 q^{55} + 48 q^{58} - 4 q^{61} - 72 q^{64} + 48 q^{67} - 60 q^{76} - 8 q^{79} + 28 q^{82} - 28 q^{88} - 12 q^{91} - 32 q^{94} + 36 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)