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

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

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 \(-2\) \(0\) \(-2\) \(0\) \(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots\)