Properties

Label 28.3.c
Level 28
Weight 3
Character orbit c
Rep. character \(\chi_{28}(15,\cdot)\)
Character field \(\Q\)
Dimension 6
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
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 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6q - q^{2} + q^{4} - 4q^{5} + 6q^{6} - 13q^{8} - 10q^{9} + O(q^{10}) \) \( 6q - q^{2} + q^{4} - 4q^{5} + 6q^{6} - 13q^{8} - 10q^{9} - 28q^{10} + 6q^{12} + 12q^{13} + 7q^{14} + 17q^{16} - 4q^{17} + 43q^{18} - 32q^{20} + 52q^{22} + 122q^{24} - 30q^{25} - 56q^{26} - 35q^{28} - 36q^{29} - 64q^{30} - 101q^{32} + 80q^{33} + 58q^{34} - 131q^{36} + 28q^{37} - 190q^{38} + 40q^{40} - 20q^{41} + 70q^{42} + 164q^{44} + 12q^{45} + 120q^{46} - 98q^{48} - 42q^{49} + 161q^{50} + 292q^{52} + 92q^{53} - 44q^{54} - 49q^{56} + 160q^{57} - 166q^{58} - 176q^{60} - 164q^{61} + 148q^{62} - 215q^{64} - 136q^{65} - 408q^{66} + 62q^{68} - 48q^{69} + 84q^{70} + 151q^{72} - 132q^{73} + 250q^{74} - 78q^{76} + 112q^{77} + 248q^{78} + 312q^{80} - 218q^{81} - 86q^{82} - 98q^{84} - 232q^{85} - 164q^{86} - 100q^{88} + 348q^{89} + 52q^{90} - 104q^{92} + 288q^{93} - 276q^{94} + 170q^{96} + 252q^{97} + 7q^{98} + O(q^{100}) \)

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.c.a \(6\) \(0.763\) 6.0.1539727.2 None \(-1\) \(0\) \(-4\) \(0\) \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(-\beta _{1}-\beta _{4})q^{4}+\cdots\)