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

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

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.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

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