Properties

Label 255.2.d
Level 255
Weight 2
Character orbit d
Rep. character \(\chi_{255}(169,\cdot)\)
Character field \(\Q\)
Dimension 16
Newform subspaces 2
Sturm bound 72
Trace bound 3

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Defining parameters

Level: \( N \) = \( 255 = 3 \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 255.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 85 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 40 16 24
Cusp forms 32 16 16
Eisenstein series 8 0 8

Trace form

\( 16q - 8q^{4} + 16q^{9} + O(q^{10}) \) \( 16q - 8q^{4} + 16q^{9} + 2q^{15} - 16q^{16} - 28q^{19} - 8q^{21} + 10q^{25} + 32q^{26} - 24q^{30} - 20q^{34} + 12q^{35} - 8q^{36} + 8q^{49} - 20q^{50} - 8q^{51} - 14q^{55} + 8q^{59} - 8q^{60} + 44q^{64} + 12q^{66} + 12q^{69} - 12q^{70} + 52q^{76} + 16q^{81} - 20q^{84} - 14q^{85} + 88q^{86} - 8q^{89} + 124q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(255, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
255.2.d.a \(8\) \(2.036\) 8.0.\(\cdots\).1 None \(0\) \(-8\) \(-1\) \(4\) \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
255.2.d.b \(8\) \(2.036\) 8.0.\(\cdots\).1 None \(0\) \(8\) \(1\) \(-4\) \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

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

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