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Properties

Label 1764.4.by
Level $1764$
Weight $4$
Character orbit 1764.by
Rep. character $\chi_{1764}(85,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2016$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.by (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).

Total New Old
Modular forms 12168 2016 10152
Cusp forms 12024 2016 10008
Eisenstein series 144 0 144

Trace form

\( 2016 q - 20 q^{5} + 6 q^{7} - 70 q^{9} + O(q^{10}) \) \( 2016 q - 20 q^{5} + 6 q^{7} - 70 q^{9} - 24 q^{13} + 84 q^{15} + 368 q^{17} + 120 q^{19} + 176 q^{21} + 210 q^{23} + 4200 q^{25} - 438 q^{27} + 70 q^{29} - 60 q^{31} + 760 q^{33} + 824 q^{35} - 840 q^{37} - 700 q^{39} - 1548 q^{41} + 84 q^{43} + 364 q^{45} - 330 q^{47} + 78 q^{49} + 1428 q^{51} - 1344 q^{53} - 3060 q^{55} - 2688 q^{57} - 1208 q^{59} - 2136 q^{61} - 2484 q^{63} - 784 q^{65} + 588 q^{67} - 3372 q^{69} + 3500 q^{71} - 672 q^{73} + 11018 q^{75} - 512 q^{77} - 168 q^{79} - 1834 q^{81} - 1136 q^{83} - 1812 q^{87} + 10648 q^{89} - 240 q^{91} - 9380 q^{93} - 140 q^{95} - 528 q^{97} + 18956 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

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