↑

Properties

Label 280.3.bp
Level $280$
Weight $3$
Character orbit 280.bp
Rep. character $\chi_{280}(3,\cdot)$
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.bp (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

\( 368 q - 2 q^{2} - 12 q^{3} + 4 q^{8} + O(q^{10}) \) \( 368 q - 2 q^{2} - 12 q^{3} + 4 q^{8} - 6 q^{10} - 8 q^{11} - 6 q^{12} + 20 q^{16} - 12 q^{17} + 8 q^{22} - 4 q^{25} - 12 q^{26} - 58 q^{28} - 72 q^{30} - 62 q^{32} - 12 q^{33} - 104 q^{35} - 144 q^{36} - 204 q^{38} + 54 q^{40} - 198 q^{42} - 16 q^{43} - 76 q^{46} + 316 q^{50} - 8 q^{51} - 72 q^{52} + 284 q^{56} + 56 q^{57} - 210 q^{58} - 74 q^{60} - 4 q^{65} + 204 q^{66} - 292 q^{67} + 60 q^{68} - 52 q^{70} + 332 q^{72} - 12 q^{73} - 12 q^{75} + 40 q^{78} - 600 q^{80} + 1040 q^{81} + 798 q^{82} + 336 q^{86} - 196 q^{88} - 400 q^{91} + 524 q^{92} - 1104 q^{96} + 30 q^{98} + O(q^{100}) \)

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