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 $5$

Related objects

Downloads

Learn more

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

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

Decomposition of \(S_{2}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
280.2.h.a 280.h 56.e $16$ $2.236$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{9}q^{4}-q^{5}+\beta _{6}q^{6}+\cdots\)
280.2.h.b 280.h 56.e $16$ $2.236$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{9}q^{4}+q^{5}-\beta _{6}q^{6}+\cdots\)

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

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