Properties

Label 280.2.bl
Level $280$
Weight $2$
Character orbit 280.bl
Rep. character $\chi_{280}(221,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 104 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

Trace form

\( 64q + 2q^{2} - 2q^{4} - 4q^{8} + 32q^{9} + O(q^{10}) \) \( 64q + 2q^{2} - 2q^{4} - 4q^{8} + 32q^{9} - 10q^{12} + 18q^{14} - 14q^{16} - 8q^{20} - 40q^{22} - 8q^{23} - 32q^{24} + 32q^{25} - 2q^{26} - 22q^{28} + 2q^{32} - 40q^{34} + 20q^{36} - 40q^{38} - 62q^{42} + 26q^{44} + 22q^{46} - 40q^{47} + 124q^{48} + 16q^{49} + 4q^{50} + 12q^{52} - 40q^{54} - 32q^{55} + 24q^{56} - 32q^{57} + 6q^{58} + 14q^{60} - 16q^{62} - 80q^{63} + 4q^{64} + 60q^{66} + 28q^{68} + 20q^{70} - 48q^{71} - 60q^{72} + 16q^{73} - 42q^{74} - 20q^{76} - 40q^{78} + 40q^{79} - 40q^{81} - 34q^{82} - 8q^{84} - 56q^{86} + 48q^{87} - 4q^{88} + 8q^{89} - 36q^{90} + 84q^{92} - 66q^{94} - 16q^{96} - 64q^{97} - 58q^{98} + O(q^{100}) \)

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.bl.a \(4\) \(2.236\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-8\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
280.2.bl.b \(60\) \(2.236\) None \(4\) \(0\) \(0\) \(8\)

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

\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)