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

Related objects

Downloads

Learn more about

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

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

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 \(2\) \(0.224\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)