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Properties

Label 255.2.m
Level $255$
Weight $2$
Character orbit 255.m
Rep. character $\chi_{255}(137,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
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 80 64 16
Cusp forms 64 64 0
Eisenstein series 16 0 16

Trace form

\( 64 q - 4 q^{3} - 8 q^{6} - 8 q^{7} + O(q^{10}) \) \( 64 q - 4 q^{3} - 8 q^{6} - 8 q^{7} - 8 q^{10} + 16 q^{12} + 4 q^{13} - 16 q^{15} - 64 q^{16} - 12 q^{18} - 16 q^{21} + 24 q^{22} - 24 q^{25} - 16 q^{27} - 24 q^{28} + 20 q^{30} - 16 q^{31} + 8 q^{33} + 56 q^{36} + 24 q^{37} - 24 q^{40} + 12 q^{42} - 36 q^{43} - 32 q^{45} + 48 q^{46} + 68 q^{48} + 8 q^{52} + 32 q^{55} + 16 q^{57} - 8 q^{58} - 52 q^{60} - 32 q^{61} + 4 q^{63} - 8 q^{66} - 8 q^{67} - 64 q^{70} + 28 q^{72} + 24 q^{73} - 8 q^{75} + 40 q^{76} - 76 q^{78} + 16 q^{81} + 40 q^{82} - 88 q^{87} + 120 q^{88} + 32 q^{90} + 16 q^{91} - 92 q^{93} - 24 q^{96} - 80 q^{97} + O(q^{100}) \)

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.m.a 255.m 15.e $64$ $2.036$ None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$