Properties

Label 585.2.b
Level $585$
Weight $2$
Character orbit 585.b
Rep. character $\chi_{585}(181,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $7$
Sturm bound $168$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(168\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 92 22 70
Cusp forms 76 22 54
Eisenstein series 16 0 16

Trace form

\( 22 q - 18 q^{4} + O(q^{10}) \) \( 22 q - 18 q^{4} + 2 q^{10} + 8 q^{13} + 8 q^{14} + 2 q^{16} - 8 q^{17} + 24 q^{22} - 8 q^{23} - 22 q^{25} + 2 q^{26} + 12 q^{29} + 12 q^{35} - 4 q^{38} - 6 q^{40} + 24 q^{43} - 54 q^{49} + 36 q^{52} + 4 q^{53} - 4 q^{55} - 8 q^{56} + 12 q^{61} + 22 q^{64} + 6 q^{65} + 64 q^{68} - 60 q^{74} - 92 q^{77} + 16 q^{79} - 92 q^{82} - 20 q^{88} - 40 q^{91} + 100 q^{92} - 72 q^{94} + O(q^{100}) \)

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.b.a 585.b 13.b $2$ $4.671$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+iq^{5}+2iq^{7}+3iq^{8}+\cdots\)
585.2.b.b 585.b 13.b $2$ $4.671$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+iq^{5}+4iq^{7}+3iq^{8}+\cdots\)
585.2.b.c 585.b 13.b $2$ $4.671$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+iq^{5}-4iq^{7}+3iq^{8}+\cdots\)
585.2.b.d 585.b 13.b $2$ $4.671$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+iq^{5}-3iq^{7}-3iq^{11}+(2+\cdots)q^{13}+\cdots\)
585.2.b.e 585.b 13.b $4$ $4.671$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
585.2.b.f 585.b 13.b $4$ $4.671$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-2q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
585.2.b.g 585.b 13.b $6$ $4.671$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)