Properties

Label 285.2.r
Level $285$
Weight $2$
Character orbit 285.r
Rep. character $\chi_{285}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(285, [\chi])\).

Total New Old
Modular forms 88 40 48
Cusp forms 72 40 32
Eisenstein series 16 0 16

Trace form

\( 40 q + 18 q^{4} - 2 q^{5} + 2 q^{6} + 20 q^{9} - 6 q^{10} - 16 q^{11} + 8 q^{14} - 2 q^{15} - 14 q^{16} - 4 q^{19} + 36 q^{20} + 12 q^{21} - 4 q^{25} + 56 q^{26} + 8 q^{29} - 8 q^{30} - 64 q^{31} - 14 q^{34}+ \cdots - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(285, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
285.2.r.a 285.r 95.i $40$ $2.276$ None 285.2.r.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(285, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(285, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)