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Properties

Label 255.2.k
Level $255$
Weight $2$
Character orbit 255.k
Rep. character $\chi_{255}(98,\cdot)$
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.k (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

\( 64 q - 4 q^{6} - 8 q^{9} + O(q^{10}) \) \( 64 q - 4 q^{6} - 8 q^{9} + 12 q^{10} - 4 q^{13} - 12 q^{15} - 64 q^{16} + 4 q^{18} - 8 q^{21} - 40 q^{22} - 4 q^{24} + 4 q^{25} + 72 q^{28} + 16 q^{30} - 24 q^{31} - 4 q^{33} - 4 q^{34} - 72 q^{37} + 32 q^{39} + 8 q^{40} + 32 q^{42} - 36 q^{43} + 24 q^{45} + 8 q^{46} - 16 q^{49} - 8 q^{51} + 24 q^{52} - 32 q^{54} + 8 q^{55} - 8 q^{58} + 8 q^{60} - 32 q^{61} - 8 q^{67} + 24 q^{70} + 56 q^{72} + 44 q^{75} - 84 q^{78} - 48 q^{79} - 16 q^{81} + 72 q^{82} - 4 q^{85} - 40 q^{87} - 124 q^{90} + 24 q^{91} - 36 q^{93} + 128 q^{94} - 12 q^{96} + 48 q^{97} + 4 q^{99} + O(q^{100}) \)

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