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Properties

Label 1764.3.cl
Level $1764$
Weight $3$
Character orbit 1764.cl
Rep. character $\chi_{1764}(13,\cdot)$
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.cl (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

\( 1344 q - q^{7} + 40 q^{9} + O(q^{10}) \) \( 1344 q - q^{7} + 40 q^{9} + 6 q^{15} - 45 q^{21} - 45 q^{23} - 560 q^{25} - 105 q^{27} + 60 q^{29} + 66 q^{35} + 110 q^{37} + 76 q^{39} - 32 q^{43} + 469 q^{45} - 252 q^{47} - 11 q^{49} - 12 q^{51} + 1092 q^{53} + 168 q^{55} - 508 q^{57} + 49 q^{61} + 183 q^{63} + 42 q^{65} - 70 q^{67} - 112 q^{69} - 258 q^{71} + 840 q^{75} + 51 q^{77} + 86 q^{79} + 260 q^{81} + 882 q^{83} + 560 q^{87} + 1050 q^{89} + 90 q^{91} - 887 q^{93} + 144 q^{95} + 254 q^{99} + O(q^{100}) \)

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

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