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Properties

Label 585.2.dj
Level $585$
Weight $2$
Character orbit 585.dj
Rep. character $\chi_{585}(92,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.dj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 352 288 64
Cusp forms 320 288 32
Eisenstein series 32 0 32

Trace form

\( 288 q + 4 q^{3} - 16 q^{6} + O(q^{10}) \) \( 288 q + 4 q^{3} - 16 q^{6} - 16 q^{12} + 4 q^{15} + 144 q^{16} - 56 q^{18} - 48 q^{20} + 16 q^{21} - 12 q^{25} - 32 q^{27} - 64 q^{30} - 120 q^{32} + 8 q^{33} + 48 q^{36} - 24 q^{37} - 24 q^{41} - 4 q^{42} + 44 q^{45} - 96 q^{46} - 48 q^{47} + 52 q^{48} + 96 q^{50} - 96 q^{51} - 24 q^{55} - 96 q^{56} + 56 q^{57} + 24 q^{58} - 156 q^{60} - 24 q^{61} - 48 q^{63} - 88 q^{66} - 12 q^{67} - 144 q^{68} - 36 q^{72} - 120 q^{75} - 24 q^{76} + 48 q^{77} + 48 q^{81} - 144 q^{86} + 92 q^{87} - 24 q^{88} + 208 q^{90} + 228 q^{92} + 44 q^{93} + 120 q^{95} - 12 q^{97} + O(q^{100}) \)

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.dj.a 585.dj 45.l $288$ $4.671$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(585, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)