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Properties

Label 1764.3.cg
Level $1764$
Weight $3$
Character orbit 1764.cg
Rep. character $\chi_{1764}(137,\cdot)$
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.cg (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

\( 1344 q + q^{7} - 40 q^{9} + O(q^{10}) \) \( 1344 q + q^{7} - 40 q^{9} + 5 q^{13} + 3 q^{15} - 27 q^{17} + 14 q^{19} + 8 q^{21} - 27 q^{23} - 560 q^{25} + 165 q^{27} - 36 q^{29} - 16 q^{31} - 116 q^{33} - 45 q^{35} - 143 q^{37} - 13 q^{39} - 72 q^{41} - 16 q^{43} + 112 q^{45} + 756 q^{47} + 37 q^{49} + 87 q^{51} + 144 q^{53} - 60 q^{55} + 264 q^{57} - 131 q^{61} + 99 q^{63} - 70 q^{67} + 153 q^{69} + 945 q^{71} + 98 q^{73} + 65 q^{75} + 135 q^{77} - 154 q^{79} - 340 q^{81} - 474 q^{87} + 1386 q^{89} - 109 q^{91} + 148 q^{93} - 19 q^{97} + 65 q^{99} + O(q^{100}) \)

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

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