Properties

Label 255.2.bg
Level $255$
Weight $2$
Character orbit 255.bg
Rep. character $\chi_{255}(11,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $192$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 255 = 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 255.bg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 51 \)
Character field: \(\Q(\zeta_{16})\)
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 320 192 128
Cusp forms 256 192 64
Eisenstein series 64 0 64

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 48 q^{12} - 64 q^{18} - 48 q^{24} - 96 q^{28} - 32 q^{31} - 112 q^{34} - 64 q^{37} + 16 q^{39} + 32 q^{40} - 64 q^{43} + 32 q^{45} + 48 q^{46} + 160 q^{48} + 32 q^{49} + 64 q^{51} - 64 q^{54} + 32 q^{55} - 112 q^{57} + 64 q^{58} + 64 q^{60} + 32 q^{61} + 48 q^{63} + 32 q^{64} - 192 q^{66} - 192 q^{69} - 208 q^{72} - 64 q^{76} - 112 q^{81} + 96 q^{87} + 128 q^{88} - 96 q^{91} + 128 q^{93} + 192 q^{94} + 64 q^{97} + 128 q^{99} + O(q^{100}) \)

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.bg.a 255.bg 51.i $192$ $2.036$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

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

\( S_{2}^{\mathrm{old}}(255, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)