Properties

Label 28.4.e
Level $28$
Weight $4$
Character orbit 28.e
Rep. character $\chi_{28}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
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 30 4 26
Cusp forms 18 4 14
Eisenstein series 12 0 12

Trace form

\( 4q + 14q^{5} + 24q^{7} - 20q^{9} + O(q^{10}) \) \( 4q + 14q^{5} + 24q^{7} - 20q^{9} - 32q^{11} - 56q^{13} - 296q^{15} + 154q^{17} + 224q^{19} + 370q^{21} - 68q^{23} - 144q^{25} - 472q^{29} + 196q^{31} + 518q^{33} + 400q^{35} - 346q^{37} - 296q^{39} - 840q^{41} - 688q^{43} + 140q^{45} - 84q^{47} + 100q^{49} + 296q^{51} + 438q^{53} + 1624q^{55} + 444q^{57} + 56q^{59} - 98q^{61} - 360q^{63} + 396q^{65} - 336q^{67} - 1036q^{69} + 1792q^{71} - 966q^{73} - 2072q^{75} - 2398q^{77} + 52q^{79} + 1798q^{81} + 784q^{83} + 3340q^{85} - 2072q^{87} - 294q^{89} - 1520q^{91} - 518q^{93} - 1124q^{95} - 840q^{97} + 640q^{99} + O(q^{100}) \)

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.e.a \(4\) \(1.652\) \(\Q(\sqrt{-3}, \sqrt{37})\) None \(0\) \(0\) \(14\) \(24\) \(q-\beta _{2}q^{3}+(7-7\beta _{1}-2\beta _{2}-2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)