Properties

Label 280.2.bo
Level $280$
Weight $2$
Character orbit 280.bo
Rep. character $\chi_{280}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $48$
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.bo (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
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 224 48 176
Cusp forms 160 48 112
Eisenstein series 64 0 64

Trace form

\( 48q - 4q^{7} + O(q^{10}) \) \( 48q - 4q^{7} + 4q^{11} + 8q^{15} - 4q^{21} - 4q^{23} - 8q^{25} - 36q^{33} + 24q^{35} + 8q^{37} - 16q^{43} + 48q^{45} + 24q^{51} + 16q^{53} - 96q^{57} - 36q^{61} - 68q^{63} + 12q^{65} - 16q^{67} - 64q^{71} - 48q^{73} - 48q^{75} + 4q^{77} - 40q^{85} - 12q^{87} - 80q^{91} + 24q^{95} + O(q^{100}) \)

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.bo.a \(48\) \(2.236\) None \(0\) \(0\) \(0\) \(-4\)

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

\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)