Properties

Label 280.2.bj
Level $280$
Weight $2$
Character orbit 280.bj
Rep. character $\chi_{280}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $6$
Sturm bound $96$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(96\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(3\), \(13\)

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

\( 64q - 2q^{2} - 2q^{4} + 4q^{8} + 32q^{9} + O(q^{10}) \) \( 64q - 2q^{2} - 2q^{4} + 4q^{8} + 32q^{9} + 8q^{11} + 30q^{12} - 18q^{14} - 6q^{16} - 48q^{22} - 36q^{24} - 32q^{25} - 30q^{26} + 2q^{28} - 22q^{32} - 60q^{36} + 60q^{38} + 2q^{42} - 16q^{43} - 14q^{44} + 18q^{46} + 16q^{49} + 4q^{50} - 40q^{51} - 36q^{52} + 72q^{54} + 20q^{56} + 32q^{57} + 6q^{58} - 48q^{59} + 14q^{60} + 52q^{64} + 24q^{66} - 40q^{67} + 20q^{70} - 40q^{72} - 48q^{73} + 14q^{74} - 72q^{78} - 24q^{81} - 42q^{82} - 88q^{84} + 24q^{86} + 16q^{88} - 24q^{89} + 64q^{91} - 108q^{92} + 54q^{94} - 144q^{96} + 10q^{98} + 80q^{99} + O(q^{100}) \)

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.bj.a \(4\) \(2.236\) \(\Q(\zeta_{12})\) None \(-4\) \(-6\) \(-2\) \(0\) \(q+(-1+\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2})q^{3}+\cdots\)
280.2.bj.b \(4\) \(2.236\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-6\) \(-2\) \(-10\) \(q+\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)
280.2.bj.c \(4\) \(2.236\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-6\) \(2\) \(10\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
280.2.bj.d \(4\) \(2.236\) \(\Q(\zeta_{12})\) None \(2\) \(-6\) \(2\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
280.2.bj.e \(24\) \(2.236\) None \(-3\) \(12\) \(12\) \(-10\)
280.2.bj.f \(24\) \(2.236\) None \(3\) \(12\) \(-12\) \(10\)

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

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