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Properties

Label 1755.2.fe
Level $1755$
Weight $2$
Character orbit 1755.fe
Rep. character $\chi_{1755}(41,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2016$
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.fe (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 351 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 3072 2016 1056
Cusp forms 2976 2016 960
Eisenstein series 96 0 96

Trace form

\( 2016 q + O(q^{10}) \) \( 2016 q - 12 q^{11} + 48 q^{21} - 72 q^{24} + 108 q^{26} + 72 q^{27} + 144 q^{30} - 144 q^{32} - 96 q^{39} + 24 q^{41} + 144 q^{44} - 72 q^{47} + 72 q^{51} + 108 q^{52} + 72 q^{54} + 72 q^{57} - 108 q^{58} - 72 q^{59} + 72 q^{63} - 96 q^{66} + 336 q^{72} + 36 q^{73} - 120 q^{74} + 432 q^{77} - 72 q^{79} + 84 q^{81} + 72 q^{83} + 48 q^{84} - 72 q^{85} + 312 q^{86} + 144 q^{87} - 240 q^{92} + 120 q^{93} + 168 q^{96} - 144 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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