Properties

Label 585.2.bs
Level $585$
Weight $2$
Character orbit 585.bs
Rep. character $\chi_{585}(289,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
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.bs (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 76 108
Cusp forms 152 68 84
Eisenstein series 32 8 24

Trace form

\( 68 q + 32 q^{4} + 2 q^{5} + O(q^{10}) \) \( 68 q + 32 q^{4} + 2 q^{5} - 3 q^{10} - 4 q^{11} + 20 q^{14} - 28 q^{16} - 12 q^{19} + 17 q^{20} + 10 q^{25} + 24 q^{26} - 6 q^{29} - 24 q^{34} - 20 q^{35} + 2 q^{40} + 26 q^{41} - 36 q^{44} - 22 q^{46} + 34 q^{49} + 11 q^{50} + 14 q^{55} + 40 q^{56} - 8 q^{59} - 30 q^{61} - 100 q^{64} - 37 q^{65} - 116 q^{70} + 8 q^{71} + 4 q^{74} + 86 q^{76} - 40 q^{79} - 29 q^{80} - 33 q^{85} - 44 q^{86} + 44 q^{89} - 12 q^{91} + 56 q^{94} + 8 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(585, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
585.2.bs.a $12$ $4.671$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{6}-\beta _{10})q^{4}+(1+\cdots)q^{5}+\cdots\)
585.2.bs.b $24$ $4.671$ None \(0\) \(0\) \(-4\) \(0\)
585.2.bs.c $32$ $4.671$ None \(0\) \(0\) \(0\) \(0\)

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

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