Properties

Label 1755.2.cc
Level $1755$
Weight $2$
Character orbit 1755.cc
Rep. character $\chi_{1755}(16,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $1008$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.cc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 351 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1755, [\chi])\).

Total New Old
Modular forms 1536 1008 528
Cusp forms 1488 1008 480
Eisenstein series 48 0 48

Trace form

\( 1008 q - 12 q^{9} + O(q^{10}) \) \( 1008 q - 12 q^{9} + 24 q^{11} + 18 q^{12} + 96 q^{17} - 48 q^{21} + 36 q^{24} + 18 q^{26} - 36 q^{27} + 18 q^{29} - 48 q^{30} + 36 q^{32} - 48 q^{35} - 60 q^{36} - 60 q^{38} - 24 q^{39} + 12 q^{41} - 24 q^{44} - 72 q^{47} + 72 q^{48} + 12 q^{51} - 54 q^{52} + 144 q^{53} + 36 q^{54} - 72 q^{57} + 216 q^{58} + 144 q^{59} + 192 q^{62} - 72 q^{63} - 504 q^{64} - 6 q^{65} + 96 q^{66} + 78 q^{68} + 84 q^{69} - 168 q^{72} + 18 q^{73} - 156 q^{74} + 72 q^{77} + 108 q^{78} - 36 q^{79} - 36 q^{81} + 18 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 36 q^{87} + 48 q^{90} + 36 q^{91} + 120 q^{92} - 60 q^{93} + 216 q^{94} + 12 q^{95} - 216 q^{96} + 48 q^{98} - 48 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1755, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1755, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)