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Properties

Label 280.3.u
Level $280$
Weight $3$
Character orbit 280.u
Rep. character $\chi_{280}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(280, [\chi])\).

Total New Old
Modular forms 200 144 56
Cusp forms 184 144 40
Eisenstein series 16 0 16

Trace form

\( 144 q + 24 q^{6} + O(q^{10}) \) \( 144 q + 24 q^{6} - 16 q^{10} + 48 q^{12} + 56 q^{16} + 16 q^{17} + 28 q^{18} - 20 q^{20} - 172 q^{22} + 48 q^{25} - 96 q^{26} - 124 q^{30} + 256 q^{31} - 200 q^{32} - 320 q^{36} + 224 q^{38} - 356 q^{40} + 140 q^{42} + 400 q^{46} + 256 q^{48} + 400 q^{50} + 208 q^{52} + 168 q^{56} - 228 q^{58} + 160 q^{60} - 440 q^{62} + 112 q^{65} - 416 q^{66} - 776 q^{68} - 680 q^{72} + 240 q^{73} - 648 q^{76} + 788 q^{78} - 500 q^{80} - 1296 q^{81} + 392 q^{82} + 536 q^{86} + 896 q^{87} + 200 q^{88} + 584 q^{90} + 848 q^{92} + 808 q^{96} - 144 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
280.3.u.a 280.u 40.i $144$ $7.629$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)