Properties

Label 28.2.f
Level 28
Weight 2
Character orbit f
Rep. character \(\chi_{28}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
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.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q(\zeta_{6})\)
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 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 20q^{28} \) \(\mathstrut +\mathstrut 16q^{29} \) \(\mathstrut -\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 8q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut +\mathstrut 16q^{56} \) \(\mathstrut -\mathstrut 36q^{57} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut +\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 24q^{78} \) \(\mathstrut -\mathstrut 24q^{80} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut +\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 54q^{89} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 30q^{94} \) \(\mathstrut -\mathstrut 24q^{96} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.f.a \(4\) \(0.224\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-6\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)