Properties

Label 280.2.l
Level $280$
Weight $2$
Character orbit 280.l
Rep. character $\chi_{280}(29,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(280, [\chi])\).

Total New Old
Modular forms 52 36 16
Cusp forms 44 36 8
Eisenstein series 8 0 8

Trace form

\( 36q + 4q^{4} - 4q^{6} + 36q^{9} + O(q^{10}) \) \( 36q + 4q^{4} - 4q^{6} + 36q^{9} - 8q^{10} + 20q^{16} - 24q^{20} - 48q^{24} + 4q^{25} - 4q^{26} + 4q^{30} - 16q^{31} + 12q^{34} - 20q^{36} - 32q^{39} + 16q^{40} - 8q^{41} + 56q^{44} - 36q^{49} - 12q^{50} - 52q^{54} - 32q^{55} + 12q^{56} - 20q^{60} - 20q^{64} - 24q^{65} - 28q^{66} - 12q^{70} + 56q^{71} - 24q^{74} + 48q^{76} + 24q^{79} + 64q^{80} + 36q^{81} + 24q^{86} - 40q^{89} - 52q^{90} - 92q^{94} + 40q^{95} + 48q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
280.2.l.a \(36\) \(2.236\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)