Properties

Label 28.2.e
Level 28
Weight 2
Character orbit e
Rep. character \(\chi_{28}(9,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(28, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
28.2.e.a \(2\) \(0.224\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-4\) \(q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)