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Properties

Label 1890.2.bs
Level $1890$
Weight $2$
Character orbit 1890.bs
Rep. character $\chi_{1890}(211,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $432$
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.bs (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
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 432 2208
Cusp forms 2544 432 2112
Eisenstein series 96 0 96

Trace form

\( 432 q - 12 q^{8} - 12 q^{9} + O(q^{10}) \) \( 432 q - 12 q^{8} - 12 q^{9} - 24 q^{11} - 12 q^{12} + 24 q^{18} - 36 q^{22} + 132 q^{27} + 144 q^{29} - 12 q^{33} - 36 q^{34} - 12 q^{35} + 24 q^{38} - 12 q^{39} - 60 q^{41} - 36 q^{43} - 24 q^{51} + 144 q^{53} + 84 q^{57} + 24 q^{59} - 216 q^{64} + 24 q^{65} - 36 q^{67} + 24 q^{68} + 96 q^{69} + 48 q^{71} + 96 q^{74} + 72 q^{76} + 96 q^{78} + 72 q^{79} + 132 q^{81} + 120 q^{83} - 12 q^{84} + 72 q^{85} + 84 q^{86} + 72 q^{88} + 12 q^{89} + 96 q^{90} - 24 q^{93} + 96 q^{95} + 24 q^{96} - 36 q^{97} - 12 q^{98} - 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)