Properties

Label 90.6.i
Level $90$
Weight $6$
Character orbit 90.i
Rep. character $\chi_{90}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $60$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 90.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(90, [\chi])\).

Total New Old
Modular forms 188 60 128
Cusp forms 172 60 112
Eisenstein series 16 0 16

Trace form

\( 60q + 480q^{4} + 58q^{5} - 80q^{6} - 754q^{9} + O(q^{10}) \) \( 60q + 480q^{4} + 58q^{5} - 80q^{6} - 754q^{9} + 104q^{11} - 1528q^{14} - 2780q^{15} - 7680q^{16} - 928q^{20} + 11776q^{21} - 640q^{24} + 3306q^{25} - 16224q^{26} - 5262q^{29} - 3128q^{30} + 8868q^{31} + 5072q^{35} - 13568q^{36} - 9708q^{39} + 41546q^{41} + 3328q^{44} + 61748q^{45} - 18960q^{46} + 70200q^{49} - 19376q^{50} - 45008q^{51} - 52696q^{54} - 984q^{55} + 24448q^{56} - 34228q^{59} - 59776q^{60} - 23370q^{61} - 245760q^{64} + 77184q^{65} - 65104q^{66} + 148898q^{69} - 26664q^{70} + 96744q^{71} - 99760q^{74} + 57716q^{75} + 17448q^{79} - 29696q^{80} + 335146q^{81} + 132128q^{84} - 40812q^{85} - 75440q^{86} + 1011388q^{89} + 169888q^{90} + 64680q^{91} + 48120q^{94} + 376884q^{95} + 10240q^{96} - 1412012q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(90, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
90.6.i.a \(60\) \(14.435\) None \(0\) \(0\) \(58\) \(0\)

Decomposition of \(S_{6}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(90, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)