Properties

Label 268.2.e
Level 268
Weight 2
Character orbit e
Rep. character \(\chi_{268}(29,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 12
Newforms 1
Sturm bound 68
Trace bound 0

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Defining parameters

Level: \( N \) = \( 268 = 2^{2} \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 268.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
Sturm bound: \(68\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(268, [\chi])\).

Total New Old
Modular forms 74 12 62
Cusp forms 62 12 50
Eisenstein series 12 0 12

Trace form

\( 12q - 4q^{3} + 6q^{5} - 3q^{7} + 4q^{9} + O(q^{10}) \) \( 12q - 4q^{3} + 6q^{5} - 3q^{7} + 4q^{9} - 5q^{11} + q^{13} + 2q^{15} + 3q^{17} + 3q^{19} - 6q^{21} + 5q^{23} + 26q^{25} + 2q^{27} + 9q^{29} - q^{31} + 2q^{33} - q^{35} - 10q^{37} - 17q^{39} - 11q^{41} - 28q^{43} + 6q^{45} - 4q^{47} - q^{49} - 26q^{51} - 12q^{53} - 4q^{55} - 14q^{57} - 6q^{59} - 21q^{61} + 5q^{63} - 18q^{67} - 13q^{69} + 16q^{71} + 11q^{73} + 26q^{75} + 34q^{77} - q^{79} - 12q^{81} + q^{83} - 2q^{85} - 21q^{87} + 56q^{89} - 58q^{91} + 5q^{93} + 39q^{95} - 31q^{97} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(268, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
268.2.e.a \(12\) \(2.140\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(6\) \(-3\) \(q+\beta _{2}q^{3}-\beta _{8}q^{5}+(\beta _{6}-\beta _{7})q^{7}+\beta _{3}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(268, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 2}\)