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Properties

Label 280.2.s
Level $280$
Weight $2$
Character orbit 280.s
Rep. character $\chi_{280}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $3$
Sturm bound $96$
Trace bound $2$

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Defining parameters

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

\( 88 q - 4 q^{2} - 4 q^{7} - 16 q^{8} + O(q^{10}) \) \( 88 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} - 24 q^{16} - 8 q^{18} + 4 q^{22} - 8 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} + 24 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 16 q^{57} - 68 q^{58} + 32 q^{60} + 12 q^{63} - 8 q^{65} + 16 q^{70} - 80 q^{71} + 80 q^{72} - 132 q^{78} - 72 q^{81} - 72 q^{86} + 48 q^{88} - 24 q^{92} + 80 q^{95} + 40 q^{98} + O(q^{100}) \)

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.s.a 280.s 280.s $8$ $2.236$ 8.0.\(\cdots\).8 \(\Q(\sqrt{-14}) \) \(-8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-\beta _{3})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+2\beta _{3}q^{4}+\cdots\)
280.2.s.b 280.s 280.s $8$ $2.236$ 8.0.\(\cdots\).8 \(\Q(\sqrt{-14}) \) \(8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{4})q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}-\beta _{5}q^{5}+\cdots\)
280.2.s.c 280.s 280.s $72$ $2.236$ None \(-4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$