Properties

Label 28.4.f
Level $28$
Weight $4$
Character orbit 28.f
Rep. character $\chi_{28}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 28.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(28, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20q + 4q^{4} - 6q^{5} + 72q^{8} - 56q^{9} + O(q^{10}) \) \( 20q + 4q^{4} - 6q^{5} + 72q^{8} - 56q^{9} - 12q^{10} - 168q^{12} - 56q^{14} - 104q^{16} - 6q^{17} + 68q^{18} + 238q^{21} - 184q^{22} + 348q^{24} - 36q^{25} + 396q^{26} + 448q^{28} - 352q^{29} + 644q^{30} - 40q^{32} + 30q^{33} + 208q^{36} + 258q^{37} - 1620q^{38} - 1548q^{40} - 980q^{42} - 1248q^{44} - 504q^{45} + 232q^{46} - 644q^{49} - 864q^{50} + 2592q^{52} + 570q^{53} + 4572q^{54} + 1904q^{56} + 1452q^{57} + 2244q^{58} - 736q^{60} + 294q^{61} + 2560q^{64} - 124q^{65} - 4272q^{66} - 6084q^{68} - 4144q^{70} - 4672q^{72} + 966q^{73} + 832q^{74} - 378q^{77} - 4056q^{78} + 7032q^{80} - 1262q^{81} + 7692q^{82} + 6188q^{84} - 2980q^{85} + 5696q^{86} - 1396q^{88} - 3186q^{89} + 3312q^{92} - 306q^{93} - 6780q^{94} - 11784q^{96} - 4900q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
28.4.f.a \(20\) \(1.652\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{10}q^{3}-\beta _{14}q^{4}+\cdots\)