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Properties

Label 1755.2.ca
Level $1755$
Weight $2$
Character orbit 1755.ca
Rep. character $\chi_{1755}(196,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $864$
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.ca (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
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 864 672
Cusp forms 1488 864 624
Eisenstein series 48 0 48

Trace form

\( 864 q + 12 q^{6} + 36 q^{8} + O(q^{10}) \) \( 864 q + 12 q^{6} + 36 q^{8} + 12 q^{11} + 36 q^{12} + 72 q^{14} - 24 q^{18} + 36 q^{22} - 72 q^{23} + 60 q^{24} + 12 q^{27} + 36 q^{29} + 12 q^{33} + 36 q^{34} + 96 q^{36} + 36 q^{38} + 60 q^{41} - 120 q^{42} + 36 q^{43} + 36 q^{45} - 264 q^{48} + 36 q^{49} + 12 q^{51} - 168 q^{54} - 12 q^{56} + 84 q^{57} + 36 q^{59} + 36 q^{61} - 132 q^{62} + 120 q^{63} - 432 q^{64} + 36 q^{67} - 288 q^{68} + 36 q^{69} - 72 q^{70} - 48 q^{71} + 120 q^{72} - 48 q^{74} - 216 q^{76} + 36 q^{77} - 168 q^{80} - 72 q^{81} + 24 q^{83} - 36 q^{84} + 12 q^{86} + 60 q^{87} - 216 q^{88} - 36 q^{89} - 48 q^{90} + 24 q^{92} - 96 q^{93} - 72 q^{94} - 168 q^{96} + 108 q^{97} + 108 q^{98} - 240 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)