Properties

Label 280.2.h
Level $280$
Weight $2$
Character orbit 280.h
Rep. character $\chi_{280}(251,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(13\)

Dimensions

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

Total New Old
Modular forms 52 32 20
Cusp forms 44 32 12
Eisenstein series 8 0 8

Trace form

\( 32q + 2q^{2} + 2q^{4} + 2q^{8} - 32q^{9} + O(q^{10}) \) \( 32q + 2q^{2} + 2q^{4} + 2q^{8} - 32q^{9} - 8q^{11} + 6q^{14} + 18q^{16} - 30q^{18} + 12q^{22} + 32q^{25} - 2q^{28} - 38q^{32} + 30q^{36} + 64q^{42} - 8q^{43} - 40q^{44} + 12q^{46} - 16q^{49} + 2q^{50} - 80q^{51} + 34q^{56} - 32q^{57} + 36q^{58} + 28q^{60} - 46q^{64} + 40q^{67} - 8q^{70} - 26q^{72} - 56q^{74} - 12q^{78} + 48q^{81} - 32q^{84} - 48q^{86} - 88q^{88} - 64q^{91} - 60q^{92} - 34q^{98} + 40q^{99} + O(q^{100}) \)

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.h.a \(16\) \(2.236\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1\) \(0\) \(-16\) \(0\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{9}q^{4}-q^{5}+\beta _{6}q^{6}+\cdots\)
280.2.h.b \(16\) \(2.236\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1\) \(0\) \(16\) \(0\) \(q+\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{9}q^{4}+q^{5}-\beta _{6}q^{6}+\cdots\)

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

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