Properties

Label 280.2.x
Level $280$
Weight $2$
Character orbit 280.x
Rep. character $\chi_{280}(97,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 112 24 88
Cusp forms 80 24 56
Eisenstein series 32 0 32

Trace form

\( 24q + 4q^{7} + O(q^{10}) \) \( 24q + 4q^{7} + 8q^{11} - 8q^{15} + 16q^{21} - 32q^{23} + 8q^{25} + 12q^{35} - 8q^{37} + 16q^{43} - 24q^{51} - 16q^{53} + 20q^{63} - 48q^{65} - 32q^{67} - 32q^{71} - 40q^{77} - 72q^{81} + 16q^{85} - 64q^{91} + 72q^{93} - 24q^{95} + O(q^{100}) \)

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.x.a \(24\) \(2.236\) None \(0\) \(0\) \(0\) \(4\)

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

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