Properties

Label 28.4.d
Level $28$
Weight $4$
Character orbit 28.d
Rep. character $\chi_{28}(27,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 28.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(28, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10q - 3q^{2} - 7q^{4} - 27q^{8} + 50q^{9} + O(q^{10}) \) \( 10q - 3q^{2} - 7q^{4} - 27q^{8} + 50q^{9} - 103q^{14} + 17q^{16} - 47q^{18} - 64q^{21} + 310q^{22} - 222q^{25} + 197q^{28} - 260q^{29} + 256q^{30} + 877q^{32} - 1219q^{36} + 492q^{37} - 1024q^{42} - 834q^{44} - 1390q^{46} + 794q^{49} + 2313q^{50} + 12q^{53} + 1633q^{56} - 192q^{57} + 270q^{58} + 2944q^{60} - 4327q^{64} + 448q^{65} - 3200q^{70} - 1319q^{72} - 2746q^{74} - 612q^{77} + 7680q^{78} - 3526q^{81} + 4480q^{84} + 1024q^{85} + 1654q^{86} + 4966q^{88} - 6678q^{92} - 2304q^{93} - 4859q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
28.4.d.a \(2\) \(1.652\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(5\) \(0\) \(0\) \(0\) \(q+(3-\beta )q^{2}+(7-5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots\)
28.4.d.b \(8\) \(1.652\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)