Properties

Label 285.2.b
Level $285$
Weight $2$
Character orbit 285.b
Rep. character $\chi_{285}(284,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $3$
Sturm bound $80$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36q - 44q^{4} + 4q^{6} - 4q^{9} + O(q^{10}) \) \( 36q - 44q^{4} + 4q^{6} - 4q^{9} + 36q^{16} - 16q^{19} + 20q^{24} - 16q^{25} - 12q^{30} - 4q^{36} - 8q^{39} - 36q^{45} + 4q^{49} + 12q^{54} + 28q^{55} - 44q^{64} + 72q^{76} + 36q^{81} - 84q^{85} - 76q^{96} + 88q^{99} + O(q^{100}) \)

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.b.a \(4\) \(2.276\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-3q^{6}+\cdots\)
285.2.b.b \(16\) \(2.276\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2+\beta _{7})q^{4}-\beta _{2}q^{5}+\cdots\)
285.2.b.c \(16\) \(2.276\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)