Properties

Label 255.2.g
Level $255$
Weight $2$
Character orbit 255.g
Rep. character $\chi_{255}(16,\cdot)$
Character field $\Q$
Dimension $12$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
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 40 12 28
Cusp forms 32 12 20
Eisenstein series 8 0 8

Trace form

\( 12 q + 16 q^{4} - 12 q^{9} + O(q^{10}) \) \( 12 q + 16 q^{4} - 12 q^{9} - 16 q^{13} + 4 q^{15} + 32 q^{16} - 8 q^{17} - 16 q^{19} - 12 q^{25} + 24 q^{26} - 4 q^{30} - 80 q^{32} + 12 q^{34} + 8 q^{35} - 16 q^{36} + 16 q^{38} - 32 q^{42} - 8 q^{43} + 32 q^{47} - 4 q^{49} + 12 q^{51} - 8 q^{52} + 48 q^{53} - 16 q^{55} + 8 q^{59} + 4 q^{60} + 20 q^{64} + 36 q^{66} - 32 q^{67} + 8 q^{68} + 8 q^{69} + 36 q^{70} - 116 q^{76} + 12 q^{81} + 16 q^{83} + 36 q^{84} + 4 q^{85} - 64 q^{86} + 32 q^{87} + 16 q^{89} + 8 q^{93} + 4 q^{94} + 16 q^{98} + O(q^{100}) \)

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.g.a 255.g 17.b $4$ $2.036$ \(\Q(i, \sqrt{13})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(2-\beta _{3})q^{4}+\cdots\)
255.2.g.b 255.g 17.b $8$ $2.036$ 8.0.\(\cdots\).1 None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{5}q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)

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

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