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Properties

Label 255.2.w
Level $255$
Weight $2$
Character orbit 255.w
Rep. character $\chi_{255}(76,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $48$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 160 48 112
Cusp forms 128 48 80
Eisenstein series 32 0 32

Trace form

\( 48 q + 8 q^{6} + O(q^{10}) \) \( 48 q + 8 q^{6} - 48 q^{16} + 16 q^{17} + 16 q^{22} - 16 q^{23} - 8 q^{24} - 32 q^{26} - 48 q^{28} + 16 q^{29} - 32 q^{33} + 8 q^{34} - 8 q^{36} - 16 q^{37} - 16 q^{39} - 16 q^{40} + 16 q^{41} - 16 q^{42} + 16 q^{43} + 32 q^{44} - 32 q^{46} + 16 q^{49} + 96 q^{52} + 16 q^{53} + 8 q^{54} + 32 q^{56} + 64 q^{58} - 48 q^{59} + 8 q^{60} - 80 q^{61} - 32 q^{62} + 16 q^{66} - 32 q^{67} + 80 q^{68} - 16 q^{71} - 96 q^{74} - 16 q^{76} - 96 q^{77} + 48 q^{78} - 16 q^{79} + 64 q^{80} + 16 q^{82} + 48 q^{83} + 48 q^{84} + 32 q^{86} - 64 q^{88} + 64 q^{91} + 64 q^{92} - 56 q^{94} + 64 q^{96} - 32 q^{97} + O(q^{100}) \)

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.w.a 255.w 17.d $16$ $2.036$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\beta _{2}-\beta _{5}-\beta _{7}-\beta _{8}-\beta _{10}+\beta _{13}+\cdots)q^{2}+\cdots\)
255.2.w.b 255.w 17.d $32$ $2.036$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(255, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)