Properties

Label 1890.2.dd
Level $1890$
Weight $2$
Character orbit 1890.dd
Rep. character $\chi_{1890}(101,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $576$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.dd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 576 q - 18 q^{6} + 12 q^{9} + O(q^{10}) \) \( 576 q - 18 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 48 q^{21} + 36 q^{23} + 6 q^{29} - 6 q^{36} - 24 q^{39} + 108 q^{47} - 18 q^{49} - 36 q^{51} + 108 q^{54} + 12 q^{56} + 48 q^{57} + 180 q^{59} - 36 q^{63} + 288 q^{64} - 12 q^{65} + 72 q^{69} + 18 q^{70} + 144 q^{71} - 36 q^{74} + 12 q^{77} + 96 q^{78} - 36 q^{79} + 12 q^{81} + 6 q^{84} + 72 q^{85} - 48 q^{86} - 180 q^{87} + 36 q^{91} + 36 q^{92} - 48 q^{93} + 72 q^{98} + 144 q^{99} + O(q^{100}) \)

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

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