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Properties

Label 1764.3.bh
Level $1764$
Weight $3$
Character orbit 1764.bh
Rep. character $\chi_{1764}(1145,\cdot)$
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.bh (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

\( 160 q + 12 q^{9} + O(q^{10}) \) \( 160 q + 12 q^{9} - 36 q^{11} + 5 q^{13} + 55 q^{15} - 27 q^{17} + 14 q^{19} + 117 q^{23} + 400 q^{25} - 45 q^{27} - 36 q^{29} - 16 q^{31} - 116 q^{33} + 11 q^{37} - 97 q^{39} - 72 q^{41} - 16 q^{43} + 154 q^{45} + 179 q^{51} + 216 q^{53} + 24 q^{55} - 105 q^{57} - 82 q^{61} - 70 q^{67} + 97 q^{69} + 98 q^{73} + 149 q^{75} - 130 q^{79} + 116 q^{81} + 60 q^{85} + 86 q^{87} - 189 q^{89} - 233 q^{93} - 19 q^{97} + 361 q^{99} + O(q^{100}) \)

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

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