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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.4.d.a 28.d 28.d $2$ $1.652$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(5\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(3-\beta )q^{2}+(7-5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots\)
28.4.d.b 28.d 28.d $8$ $1.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)