Properties

Label 28.3.h
Level 28
Weight 3
Character orbit h
Rep. character \(\chi_{28}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
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 22 2 20
Cusp forms 10 2 8
Eisenstein series 12 0 12

Trace form

\( 2q + 3q^{3} + 3q^{5} - 14q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + 3q^{5} - 14q^{7} - 6q^{9} - 15q^{11} + 6q^{15} + 51q^{17} + 27q^{19} - 21q^{21} + 9q^{23} - 22q^{25} - 12q^{29} - 21q^{31} - 45q^{33} - 21q^{35} - 31q^{37} + 24q^{39} + 20q^{43} - 18q^{45} + 75q^{47} + 98q^{49} + 51q^{51} + 57q^{53} + 54q^{57} - 141q^{59} - 141q^{61} + 42q^{63} - 24q^{65} + 49q^{67} - 252q^{71} - 45q^{73} - 66q^{75} + 105q^{77} + 73q^{79} - 9q^{81} + 102q^{85} - 18q^{87} + 99q^{89} - 21q^{93} + 27q^{95} + 180q^{99} + O(q^{100}) \)

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.h.a \(2\) \(0.763\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(3\) \(-14\) \(q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-7q^{7}-6\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

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