Properties

Label 585.2.c
Level $585$
Weight $2$
Character orbit 585.c
Rep. character $\chi_{585}(469,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $4$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
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 92 30 62
Cusp forms 76 30 46
Eisenstein series 16 0 16

Trace form

\( 30 q - 26 q^{4} + 4 q^{5} + O(q^{10}) \) \( 30 q - 26 q^{4} + 4 q^{5} - 14 q^{10} + 4 q^{11} + 16 q^{14} + 26 q^{16} + 16 q^{19} - 8 q^{20} + 10 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} - 28 q^{34} - 16 q^{35} + 30 q^{40} + 16 q^{41} + 48 q^{46} - 62 q^{49} - 56 q^{50} - 8 q^{55} - 40 q^{56} + 8 q^{59} + 4 q^{61} - 18 q^{64} - 2 q^{65} - 28 q^{70} + 16 q^{71} + 20 q^{74} - 68 q^{76} + 8 q^{79} - 28 q^{80} + 28 q^{85} + 32 q^{86} + 28 q^{89} - 12 q^{91} + 96 q^{94} + 40 q^{95} + O(q^{100}) \)

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.c.a 585.c 5.b $2$ $4.671$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+(1+2i)q^{5}-iq^{7}+q^{11}+\cdots\)
585.2.c.b 585.c 5.b $6$ $4.671$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots\)
585.2.c.c 585.c 5.b $10$ $4.671$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
585.2.c.d 585.c 5.b $12$ $4.671$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}+(-1-\beta _{9})q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)