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Properties

Label 268.2.e
Level $268$
Weight $2$
Character orbit 268.e
Rep. character $\chi_{268}(29,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $1$
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: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(268, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
268.2.e.a 268.e 67.c $12$ $2.140$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{3}-\beta _{8}q^{5}+(\beta _{6}-\beta _{7})q^{7}+\beta _{3}q^{9}+\cdots\)

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

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