Properties

Label 280.2.bv
Level $280$
Weight $2$
Character orbit 280.bv
Rep. character $\chi_{280}(117,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
Newform subspaces $5$
Sturm bound $96$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
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 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176 q - 2 q^{2} - 8 q^{7} + 4 q^{8} + O(q^{10}) \) \( 176 q - 2 q^{2} - 8 q^{7} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 16 q^{15} - 12 q^{16} - 12 q^{17} - 16 q^{18} - 16 q^{22} - 4 q^{23} - 4 q^{25} - 12 q^{26} - 50 q^{28} + 8 q^{30} - 24 q^{31} + 18 q^{32} - 12 q^{33} - 48 q^{36} - 24 q^{38} + 54 q^{40} - 10 q^{42} - 28 q^{46} - 84 q^{47} - 12 q^{50} + 72 q^{52} - 20 q^{56} - 40 q^{57} + 2 q^{58} + 46 q^{60} - 24 q^{63} - 4 q^{65} - 156 q^{66} + 60 q^{68} - 112 q^{70} + 32 q^{71} + 52 q^{72} - 12 q^{73} - 24 q^{78} + 48 q^{80} - 54 q^{82} - 72 q^{86} - 48 q^{87} + 60 q^{88} + 12 q^{92} - 20 q^{95} - 96 q^{96} - 130 q^{98} + O(q^{100}) \)

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.bv.a 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None \(-4\) \(-2\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.b 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(4\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.c 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None \(2\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)
280.2.bv.d 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None \(4\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.e 280.bv 280.av $160$ $2.236$ None \(-2\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{12}]$