↑

Properties

Label 280.3.bt
Level $280$
Weight $3$
Character orbit 280.bt
Rep. character $\chi_{280}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{12})\)
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 400 400 0
Cusp forms 368 368 0
Eisenstein series 32 32 0

Trace form

\( 368 q - 2 q^{2} - 16 q^{6} - 8 q^{7} - 20 q^{8} + O(q^{10}) \) \( 368 q - 2 q^{2} - 16 q^{6} - 8 q^{7} - 20 q^{8} - 2 q^{10} + 34 q^{12} - 16 q^{15} - 28 q^{16} - 4 q^{17} + 56 q^{20} - 24 q^{22} - 4 q^{23} - 4 q^{25} - 116 q^{26} - 122 q^{28} + 68 q^{30} - 8 q^{31} - 62 q^{32} - 76 q^{33} - 144 q^{36} - 52 q^{38} - 22 q^{40} - 32 q^{41} - 78 q^{42} + 68 q^{46} + 188 q^{47} + 244 q^{48} - 404 q^{50} + 192 q^{52} - 216 q^{55} - 132 q^{56} + 56 q^{57} + 190 q^{58} + 70 q^{60} + 512 q^{62} - 240 q^{63} - 4 q^{65} - 180 q^{66} - 88 q^{68} - 396 q^{70} - 544 q^{71} - 8 q^{72} - 4 q^{73} + 784 q^{76} - 280 q^{78} + 96 q^{80} + 1104 q^{81} + 150 q^{82} + 64 q^{86} - 40 q^{87} + 192 q^{88} - 80 q^{90} + 396 q^{92} - 188 q^{95} + 136 q^{96} - 80 q^{97} - 538 q^{98} + O(q^{100}) \)

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.bt.a 280.bt 280.at $368$ $7.629$ None \(-2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$