Properties

Label 28.2.d
Level 28
Weight 2
Character orbit d
Rep. character \(\chi_{28}(27,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 28.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(28, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 10q^{25} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut -\mathstrut 11q^{32} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut +\mathstrut 14q^{46} \) \(\mathstrut -\mathstrut 14q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 15q^{72} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 18q^{81} \) \(\mathstrut -\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 14q^{92} \) \(\mathstrut +\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(28, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
28.2.d.a \(2\) \(0.224\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)