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Properties

Label 585.2.cr
Level $585$
Weight $2$
Character orbit 585.cr
Rep. character $\chi_{585}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.cr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(585, [\chi])\).

Total New Old
Modular forms 352 352 0
Cusp forms 320 320 0
Eisenstein series 32 32 0

Trace form

\( 320 q - 6 q^{2} - 2 q^{3} - 12 q^{6} - 24 q^{8} + O(q^{10}) \) \( 320 q - 6 q^{2} - 2 q^{3} - 12 q^{6} - 24 q^{8} - 4 q^{10} - 12 q^{11} - 6 q^{12} - 2 q^{13} - 6 q^{15} + 140 q^{16} - 36 q^{18} - 12 q^{20} + 12 q^{21} + 18 q^{22} - 4 q^{25} - 48 q^{26} + 4 q^{27} + 30 q^{30} + 18 q^{32} - 42 q^{33} - 36 q^{35} - 100 q^{36} - 12 q^{37} + 36 q^{38} - 12 q^{40} - 72 q^{41} + 36 q^{42} - 4 q^{43} + 24 q^{45} - 24 q^{46} - 30 q^{47} - 52 q^{48} - 12 q^{50} + 8 q^{51} - 10 q^{52} + 6 q^{55} + 72 q^{57} - 6 q^{58} - 24 q^{60} - 8 q^{61} - 24 q^{62} + 12 q^{63} + 66 q^{65} - 120 q^{66} - 48 q^{71} + 114 q^{72} + 28 q^{75} - 60 q^{77} - 150 q^{78} + 30 q^{80} + 32 q^{81} - 36 q^{82} - 78 q^{85} + 108 q^{86} - 26 q^{87} - 42 q^{88} - 56 q^{90} - 28 q^{91} - 96 q^{92} - 60 q^{93} - 36 q^{95} + 72 q^{96} - 42 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(585, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
585.2.cr.a 585.cr 585.br $320$ $4.671$ None \(-6\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$