Properties

Label 285.2.c
Level $285$
Weight $2$
Character orbit 285.c
Rep. character $\chi_{285}(229,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
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 20 24
Cusp forms 36 20 16
Eisenstein series 8 0 8

Trace form

\( 20q - 24q^{4} + 2q^{5} + 4q^{6} - 20q^{9} + O(q^{10}) \) \( 20q - 24q^{4} + 2q^{5} + 4q^{6} - 20q^{9} - 12q^{10} + 4q^{11} + 16q^{14} - 4q^{15} + 32q^{16} - 8q^{19} - 12q^{24} - 2q^{25} - 32q^{26} + 16q^{29} + 8q^{30} - 8q^{31} + 8q^{34} - 6q^{35} + 24q^{36} - 8q^{39} + 16q^{40} + 24q^{41} + 48q^{44} - 2q^{45} - 16q^{46} - 48q^{49} - 20q^{50} - 8q^{51} - 4q^{54} + 14q^{55} - 24q^{56} + 48q^{59} - 8q^{60} + 4q^{61} - 4q^{65} + 24q^{66} + 8q^{69} - 36q^{70} - 48q^{71} - 56q^{74} + 8q^{75} + 20q^{76} + 4q^{80} + 20q^{81} - 32q^{84} - 6q^{85} - 32q^{86} - 16q^{89} + 12q^{90} + 40q^{91} + 8q^{94} - 2q^{95} + 68q^{96} - 4q^{99} + O(q^{100}) \)

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.c.a \(6\) \(2.276\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
285.2.c.b \(14\) \(2.276\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)

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

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