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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
285.2.bf.a \(12\) \(2.276\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) \(-9\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{4}-\beta _{5}-\beta _{6}+\beta _{11})q^{2}+\cdots\)
285.2.bf.b \(12\) \(2.276\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) \(9\) \(0\) \(0\) \(0\) \(q+(1-\beta _{4}-\beta _{5}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{11})q^{2}+\cdots\)
285.2.bf.c \(192\) \(2.276\) None \(0\) \(0\) \(0\) \(0\)