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

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

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