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Properties

Label 1890.2.bt
Level $1890$
Weight $2$
Character orbit 1890.bt
Rep. character $\chi_{1890}(331,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $576$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.bt (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).

Total New Old
Modular forms 2640 576 2064
Cusp forms 2544 576 1968
Eisenstein series 96 0 96

Trace form

\( 576 q - 6 q^{6} - 24 q^{9} + O(q^{10}) \) \( 576 q - 6 q^{6} - 24 q^{9} - 24 q^{11} + 6 q^{14} + 48 q^{17} + 24 q^{21} - 36 q^{23} - 6 q^{29} + 72 q^{33} - 6 q^{36} + 12 q^{39} + 12 q^{41} - 6 q^{45} - 36 q^{47} - 36 q^{49} + 72 q^{51} + 72 q^{54} + 6 q^{56} + 48 q^{57} + 120 q^{59} - 18 q^{61} + 96 q^{62} + 36 q^{63} - 288 q^{64} + 12 q^{65} + 108 q^{69} + 18 q^{70} - 48 q^{71} - 144 q^{73} + 72 q^{74} + 60 q^{77} - 96 q^{78} + 36 q^{79} + 12 q^{80} - 24 q^{81} + 6 q^{84} - 72 q^{85} + 48 q^{86} + 120 q^{87} - 72 q^{91} - 36 q^{92} + 48 q^{93} + 36 q^{94} + 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)