Properties

Label 28.3.g
Level 28
Weight 3
Character orbit g
Rep. character \(\chi_{28}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 12
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 28.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(28, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 24q^{12} \) \(\mathstrut -\mathstrut 24q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 56q^{18} \) \(\mathstrut +\mathstrut 152q^{20} \) \(\mathstrut -\mathstrut 78q^{21} \) \(\mathstrut +\mathstrut 44q^{22} \) \(\mathstrut -\mathstrut 44q^{24} \) \(\mathstrut +\mathstrut 56q^{26} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 72q^{29} \) \(\mathstrut -\mathstrut 74q^{30} \) \(\mathstrut -\mathstrut 112q^{32} \) \(\mathstrut -\mathstrut 14q^{33} \) \(\mathstrut -\mathstrut 316q^{34} \) \(\mathstrut -\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 86q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 148q^{40} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 68q^{42} \) \(\mathstrut +\mathstrut 64q^{44} \) \(\mathstrut +\mathstrut 156q^{45} \) \(\mathstrut +\mathstrut 162q^{46} \) \(\mathstrut +\mathstrut 512q^{48} \) \(\mathstrut +\mathstrut 108q^{49} \) \(\mathstrut +\mathstrut 208q^{50} \) \(\mathstrut -\mathstrut 64q^{52} \) \(\mathstrut -\mathstrut 74q^{53} \) \(\mathstrut +\mathstrut 182q^{54} \) \(\mathstrut +\mathstrut 16q^{56} \) \(\mathstrut -\mathstrut 220q^{57} \) \(\mathstrut -\mathstrut 176q^{58} \) \(\mathstrut -\mathstrut 232q^{60} \) \(\mathstrut +\mathstrut 86q^{61} \) \(\mathstrut -\mathstrut 532q^{62} \) \(\mathstrut -\mathstrut 160q^{64} \) \(\mathstrut -\mathstrut 140q^{65} \) \(\mathstrut +\mathstrut 102q^{66} \) \(\mathstrut -\mathstrut 68q^{68} \) \(\mathstrut -\mathstrut 300q^{69} \) \(\mathstrut +\mathstrut 90q^{70} \) \(\mathstrut +\mathstrut 152q^{72} \) \(\mathstrut -\mathstrut 234q^{73} \) \(\mathstrut +\mathstrut 290q^{74} \) \(\mathstrut +\mathstrut 576q^{76} \) \(\mathstrut -\mathstrut 262q^{77} \) \(\mathstrut +\mathstrut 64q^{78} \) \(\mathstrut +\mathstrut 146q^{81} \) \(\mathstrut +\mathstrut 272q^{82} \) \(\mathstrut -\mathstrut 28q^{84} \) \(\mathstrut +\mathstrut 268q^{85} \) \(\mathstrut -\mathstrut 16q^{86} \) \(\mathstrut -\mathstrut 188q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 640q^{90} \) \(\mathstrut -\mathstrut 448q^{92} \) \(\mathstrut +\mathstrut 162q^{93} \) \(\mathstrut +\mathstrut 102q^{94} \) \(\mathstrut -\mathstrut 320q^{96} \) \(\mathstrut +\mathstrut 744q^{97} \) \(\mathstrut -\mathstrut 190q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(28, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
28.3.g.a \(12\) \(0.763\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(-2\) \(0\) \(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots\)