Properties

Label 280.2.w
Level $280$
Weight $2$
Character orbit 280.w
Rep. character $\chi_{280}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 104 72 32
Cusp forms 88 72 16
Eisenstein series 16 0 16

Trace form

\( 72q + 8q^{6} + O(q^{10}) \) \( 72q + 8q^{6} + 16q^{10} - 16q^{12} - 8q^{16} + 8q^{17} - 28q^{18} - 20q^{20} - 36q^{22} - 8q^{25} - 32q^{26} - 4q^{30} + 40q^{32} + 64q^{36} - 4q^{40} + 20q^{42} - 64q^{43} + 48q^{46} - 80q^{48} - 32q^{51} + 16q^{52} - 24q^{56} + 4q^{58} - 80q^{60} - 40q^{62} - 8q^{65} + 32q^{66} - 24q^{68} + 40q^{72} - 40q^{73} + 112q^{75} - 8q^{76} + 28q^{78} - 20q^{80} - 72q^{81} + 24q^{82} + 80q^{83} + 8q^{86} - 88q^{88} + 136q^{90} - 96q^{92} - 56q^{96} - 8q^{97} + O(q^{100}) \)

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.w.a \(72\) \(2.236\) None \(0\) \(0\) \(0\) \(0\)

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

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