Properties

Label 285.2.bf
Level $285$
Weight $2$
Character orbit 285.bf
Rep. character $\chi_{285}(14,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $216$
Newform subspaces $3$
Sturm bound $80$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 264 264 0
Cusp forms 216 216 0
Eisenstein series 48 48 0

Trace form

\( 216 q - 18 q^{4} - 12 q^{6} - 12 q^{9} + O(q^{10}) \) \( 216 q - 18 q^{4} - 12 q^{6} - 12 q^{9} - 12 q^{10} + 15 q^{15} - 18 q^{16} - 48 q^{19} - 30 q^{21} - 84 q^{24} - 12 q^{25} - 24 q^{30} - 36 q^{31} + 18 q^{34} + 12 q^{36} - 66 q^{40} - 30 q^{45} + 36 q^{46} - 24 q^{49} + 96 q^{51} - 60 q^{54} - 90 q^{55} - 90 q^{60} + 12 q^{61} - 30 q^{64} + 108 q^{66} - 18 q^{69} - 18 q^{70} - 84 q^{76} - 120 q^{79} + 36 q^{81} + 198 q^{84} + 54 q^{85} + 66 q^{90} - 72 q^{91} - 72 q^{96} + 78 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
285.2.bf.a 285.bf 285.af $12$ $2.276$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) \(-9\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(-1+\beta _{4}-\beta _{5}-\beta _{6}+\beta _{11})q^{2}+\cdots\)
285.2.bf.b 285.bf 285.af $12$ $2.276$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) \(9\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(1-\beta _{4}-\beta _{5}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{11})q^{2}+\cdots\)
285.2.bf.c 285.bf 285.af $192$ $2.276$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$