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Properties

Label 1764.3.bd
Level $1764$
Weight $3$
Character orbit 1764.bd
Rep. character $\chi_{1764}(1489,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1764, [\chi])\).

Total New Old
Modular forms 1392 160 1232
Cusp forms 1296 160 1136
Eisenstein series 96 0 96

Trace form

\( 160 q - 20 q^{9} + O(q^{10}) \) \( 160 q - 20 q^{9} - 12 q^{11} + 15 q^{13} - 15 q^{15} + 27 q^{17} + 39 q^{23} + 400 q^{25} - 9 q^{27} - 60 q^{29} - 11 q^{37} + 185 q^{39} - 90 q^{41} + 16 q^{43} + 156 q^{45} + 27 q^{51} - 66 q^{53} - 83 q^{57} - 174 q^{65} - 70 q^{67} + 105 q^{69} - 90 q^{71} + 75 q^{75} + 62 q^{79} + 132 q^{81} + 378 q^{83} - 60 q^{85} + 78 q^{87} + 261 q^{89} + 429 q^{93} - 336 q^{95} - 57 q^{97} - 7 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)