Properties

Label 28.3.b
Level 28
Weight 3
Character orbit b
Rep. character \(\chi_{28}(13,\cdot)\)
Character field \(\Q\)
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
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 11 2 9
Cusp forms 5 2 3
Eisenstein series 6 0 6

Trace form

\(2q \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 30q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 30q^{9} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 48q^{15} \) \(\mathstrut +\mathstrut 48q^{21} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 48q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 192q^{51} \) \(\mathstrut +\mathstrut 180q^{53} \) \(\mathstrut -\mathstrut 240q^{57} \) \(\mathstrut -\mathstrut 150q^{63} \) \(\mathstrut +\mathstrut 48q^{65} \) \(\mathstrut -\mathstrut 140q^{67} \) \(\mathstrut +\mathstrut 84q^{71} \) \(\mathstrut -\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 148q^{79} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut -\mathstrut 192q^{85} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 240q^{95} \) \(\mathstrut +\mathstrut 180q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.b.a \(2\) \(0.763\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(10\) \(q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots\)

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

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