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Properties

Label 28.2.e
Level $28$
Weight $2$
Character orbit 28.e
Rep. character $\chi_{28}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(28, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

Trace form

\( 2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9} + O(q^{10}) \) \( 2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} + 4 q^{13} + 6 q^{15} - 3 q^{17} + q^{19} - q^{21} - 3 q^{23} - 4 q^{25} - 10 q^{27} - 12 q^{29} + 7 q^{31} + 3 q^{33} + 15 q^{35} + q^{37} - 2 q^{39} + 12 q^{41} - 8 q^{43} + 6 q^{45} + 9 q^{47} + 2 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} - 2 q^{57} - 9 q^{59} + q^{61} - 10 q^{63} - 6 q^{65} + 7 q^{67} + 6 q^{69} + q^{73} - 4 q^{75} + 3 q^{77} + 13 q^{79} - q^{81} + 24 q^{83} + 18 q^{85} + 6 q^{87} - 15 q^{89} - 8 q^{91} + 7 q^{93} + 3 q^{95} - 20 q^{97} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.2.e.a 28.e 7.c $2$ $0.224$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)