Properties

Label 585.2.i
Level $585$
Weight $2$
Character orbit 585.i
Rep. character $\chi_{585}(196,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $8$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

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

Total New Old
Modular forms 176 96 80
Cusp forms 160 96 64
Eisenstein series 16 0 16

Trace form

\( 96 q + 4 q^{2} + 4 q^{3} - 48 q^{4} + 4 q^{5} - 4 q^{6} - 24 q^{8} + 16 q^{9} + O(q^{10}) \) \( 96 q + 4 q^{2} + 4 q^{3} - 48 q^{4} + 4 q^{5} - 4 q^{6} - 24 q^{8} + 16 q^{9} - 4 q^{11} - 4 q^{12} - 24 q^{14} - 48 q^{16} + 24 q^{17} + 12 q^{18} + 24 q^{19} + 12 q^{20} + 28 q^{21} - 12 q^{22} - 12 q^{23} - 16 q^{24} - 48 q^{25} + 4 q^{27} - 12 q^{29} + 4 q^{30} + 68 q^{32} - 68 q^{33} - 36 q^{36} - 24 q^{38} + 12 q^{40} - 8 q^{41} + 24 q^{42} - 12 q^{43} + 112 q^{44} - 24 q^{45} + 40 q^{47} - 60 q^{49} + 4 q^{50} + 28 q^{51} + 32 q^{53} + 16 q^{54} - 40 q^{56} - 8 q^{57} - 24 q^{59} + 28 q^{60} - 12 q^{61} - 176 q^{62} - 32 q^{63} + 72 q^{64} + 8 q^{65} + 64 q^{66} - 12 q^{67} - 48 q^{68} - 28 q^{69} - 12 q^{70} - 64 q^{71} - 24 q^{72} + 72 q^{73} + 48 q^{74} + 4 q^{75} - 24 q^{76} + 28 q^{77} + 20 q^{78} - 56 q^{80} + 24 q^{81} + 24 q^{82} - 36 q^{84} + 4 q^{86} + 24 q^{87} - 36 q^{88} + 8 q^{89} - 16 q^{90} - 68 q^{92} - 4 q^{93} - 12 q^{94} + 108 q^{96} - 36 q^{97} + 152 q^{98} - 68 q^{99} + O(q^{100}) \)

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.i.a 585.i 9.c $2$ $4.671$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
585.2.i.b 585.i 9.c $2$ $4.671$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
585.2.i.c 585.i 9.c $2$ $4.671$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
585.2.i.d 585.i 9.c $2$ $4.671$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
585.2.i.e 585.i 9.c $16$ $4.671$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(1\) \(8\) \(11\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{2}+(-\beta _{7}+\beta _{14})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
585.2.i.f 585.i 9.c $16$ $4.671$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1\) \(-2\) \(-8\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
585.2.i.g 585.i 9.c $26$ $4.671$ None \(1\) \(1\) \(-13\) \(-10\) $\mathrm{SU}(2)[C_{3}]$
585.2.i.h 585.i 9.c $30$ $4.671$ None \(1\) \(1\) \(15\) \(-10\) $\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)