↑

Properties

Label 255.2.z
Level $255$
Weight $2$
Character orbit 255.z
Rep. character $\chi_{255}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $80$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 255 = 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 255.z (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(255, [\chi])\).

Total New Old
Modular forms 160 80 80
Cusp forms 128 80 48
Eisenstein series 32 0 32

Trace form

\( 80 q - 8 q^{5} - 8 q^{6} + O(q^{10}) \) \( 80 q - 8 q^{5} - 8 q^{6} + 8 q^{10} - 16 q^{11} + 32 q^{14} - 128 q^{16} + 16 q^{19} + 40 q^{20} - 8 q^{24} - 24 q^{25} - 16 q^{26} - 64 q^{29} + 16 q^{31} + 8 q^{34} - 32 q^{35} + 8 q^{36} - 16 q^{39} + 24 q^{40} + 80 q^{41} - 32 q^{44} - 16 q^{45} + 32 q^{46} - 32 q^{49} + 32 q^{50} + 8 q^{54} + 16 q^{59} - 16 q^{61} - 96 q^{65} - 16 q^{66} - 48 q^{69} - 72 q^{70} - 48 q^{71} + 112 q^{74} + 16 q^{75} + 32 q^{76} + 80 q^{79} + 112 q^{80} + 144 q^{84} + 32 q^{85} - 32 q^{86} + 8 q^{90} - 96 q^{91} - 40 q^{94} + 88 q^{95} + 32 q^{96} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(255, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
255.2.z.a 255.z 85.m $80$ $2.036$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(255, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(255, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)