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Properties

Label 1764.3.ch
Level $1764$
Weight $3$
Character orbit 1764.ch
Rep. character $\chi_{1764}(29,\cdot)$
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.ch (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

\( 1344 q + q^{7} - 40 q^{9} + O(q^{10}) \) \( 1344 q + q^{7} - 40 q^{9} - 10 q^{13} - 6 q^{15} - 28 q^{19} - 85 q^{21} + 135 q^{23} - 560 q^{25} - 141 q^{27} - 180 q^{29} - 16 q^{31} + 10 q^{33} - 110 q^{37} - 124 q^{39} + 144 q^{41} + 32 q^{43} + q^{45} - 540 q^{47} + 37 q^{49} - 12 q^{51} + 120 q^{55} - 528 q^{57} - 90 q^{59} - 131 q^{61} - 57 q^{63} + 126 q^{65} - 70 q^{67} - 54 q^{69} - 196 q^{73} - 454 q^{75} + 279 q^{77} - 154 q^{79} - 220 q^{81} - 414 q^{87} + 218 q^{91} + 277 q^{93} + 432 q^{95} + 38 q^{97} - 130 q^{99} + O(q^{100}) \)

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

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