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Properties

Label 1764.3.cy
Level $1764$
Weight $3$
Character orbit 1764.cy
Rep. character $\chi_{1764}(61,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1344$
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.cy (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 8136 1344 6792
Cusp forms 7992 1344 6648
Eisenstein series 144 0 144

Trace form

\( 1344 q - q^{7} - 104 q^{9} + O(q^{10}) \) \( 1344 q - q^{7} - 104 q^{9} - 15 q^{13} - 3 q^{15} + 27 q^{17} + 36 q^{21} - 45 q^{23} + 1120 q^{25} - 96 q^{27} + 96 q^{29} + 24 q^{31} - 81 q^{33} - 141 q^{35} + 143 q^{37} + q^{39} + 90 q^{41} + 16 q^{43} + 430 q^{45} + 396 q^{47} + 61 q^{49} - 93 q^{51} - 672 q^{53} - 84 q^{55} + 254 q^{57} - 45 q^{59} + 67 q^{61} + 93 q^{63} - 21 q^{65} + 35 q^{67} - 49 q^{69} + 129 q^{71} - 729 q^{75} + 123 q^{77} - 43 q^{79} + 380 q^{81} + 504 q^{83} + 797 q^{87} - 264 q^{89} - 45 q^{91} + 355 q^{93} - 72 q^{95} + 57 q^{97} - 127 q^{99} + O(q^{100}) \)

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

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