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Properties

Label 255.2.r
Level $255$
Weight $2$
Character orbit 255.r
Rep. character $\chi_{255}(38,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 255 \)
Character field: \(\Q(i)\)
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 80 80 0
Cusp forms 64 64 0
Eisenstein series 16 16 0

Trace form

\( 64 q - 4 q^{3} - 4 q^{6} - 8 q^{7} + 8 q^{9} + O(q^{10}) \) \( 64 q - 4 q^{3} - 4 q^{6} - 8 q^{7} + 8 q^{9} - 20 q^{10} - 4 q^{13} + 12 q^{15} - 64 q^{16} + 4 q^{18} - 8 q^{21} + 4 q^{24} - 4 q^{25} - 40 q^{27} + 16 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{34} - 32 q^{39} + 64 q^{40} - 32 q^{42} + 36 q^{43} + 24 q^{45} + 8 q^{46} + 36 q^{48} + 16 q^{49} - 8 q^{51} + 24 q^{52} + 32 q^{54} + 8 q^{55} + 16 q^{57} - 8 q^{60} - 32 q^{61} - 108 q^{63} - 8 q^{67} - 24 q^{70} + 56 q^{72} - 40 q^{73} - 44 q^{75} + 48 q^{79} - 16 q^{81} - 28 q^{85} + 40 q^{87} + 24 q^{88} + 4 q^{90} + 24 q^{91} + 36 q^{93} - 128 q^{94} - 12 q^{96} - 4 q^{99} + O(q^{100}) \)

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.r.a 255.r 255.r $8$ $2.036$ 8.0.1871773696.1 None \(0\) \(-8\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{7})q^{3}+(2\beta _{3}+\cdots)q^{4}+\cdots\)
255.2.r.b 255.r 255.r $56$ $2.036$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$