Properties

Label 585.2.bf
Level $585$
Weight $2$
Character orbit 585.bf
Rep. character $\chi_{585}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $3$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 184 72 112
Cusp forms 152 64 88
Eisenstein series 32 8 24

Trace form

\( 64 q - 30 q^{4} + O(q^{10}) \) \( 64 q - 30 q^{4} + 2 q^{10} + 12 q^{11} - 20 q^{14} - 14 q^{16} + 12 q^{19} + 6 q^{20} + 4 q^{25} - 34 q^{26} + 24 q^{29} - 4 q^{35} - 56 q^{40} + 36 q^{41} - 54 q^{46} - 28 q^{49} - 42 q^{50} + 10 q^{55} + 68 q^{56} - 24 q^{59} + 20 q^{61} + 24 q^{64} + 4 q^{65} - 24 q^{71} + 2 q^{74} - 90 q^{76} - 16 q^{79} - 84 q^{80} + 4 q^{91} - 8 q^{94} - 6 q^{95} + O(q^{100}) \)

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.bf.a 585.bf 65.l $8$ $4.671$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
585.2.bf.b 585.bf 65.l $24$ $4.671$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
585.2.bf.c 585.bf 65.l $32$ $4.671$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)