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Properties

Label 280.2.ba
Level $280$
Weight $2$
Character orbit 280.ba
Rep. character $\chi_{280}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
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 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88 q - 2 q^{4} - 40 q^{9} + O(q^{10}) \) \( 88 q - 2 q^{4} - 40 q^{9} - 12 q^{10} - 4 q^{11} - 14 q^{14} - 6 q^{16} - 12 q^{19} + 12 q^{24} - 2 q^{25} + 6 q^{26} - 20 q^{30} - 2 q^{35} - 20 q^{36} + 12 q^{40} + 30 q^{44} + 38 q^{46} - 8 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 72 q^{56} - 60 q^{59} - 42 q^{60} + 4 q^{64} + 8 q^{65} + 84 q^{66} - 22 q^{70} + 2 q^{74} - 6 q^{75} - 96 q^{80} - 36 q^{81} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 32 q^{91} - 42 q^{94} + 96 q^{96} + 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.ba.a 280.ba 280.aa $8$ $2.236$ 8.0.3317760000.3 \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{4}q^{2}-2\beta _{3}q^{4}+\beta _{6}q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
280.2.ba.b 280.ba 280.aa $80$ $2.236$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$