↑

Properties

Label 28.3.g
Level $28$
Weight $3$
Character orbit 28.g
Rep. character $\chi_{28}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 28.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
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 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\( 12 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{8} + 4 q^{9} + O(q^{10}) \) \( 12 q - 2 q^{2} - 4 q^{4} - 2 q^{5} - 12 q^{6} - 8 q^{8} + 4 q^{9} - 2 q^{10} - 24 q^{12} - 24 q^{13} + 2 q^{14} + 16 q^{16} - 2 q^{17} + 56 q^{18} + 152 q^{20} - 78 q^{21} + 44 q^{22} - 44 q^{24} + 56 q^{26} + 8 q^{28} + 72 q^{29} - 74 q^{30} - 112 q^{32} - 14 q^{33} - 316 q^{34} - 160 q^{36} + 86 q^{37} - 2 q^{38} - 148 q^{40} + 8 q^{41} + 68 q^{42} + 64 q^{44} + 156 q^{45} + 162 q^{46} + 512 q^{48} + 108 q^{49} + 208 q^{50} - 64 q^{52} - 74 q^{53} + 182 q^{54} + 16 q^{56} - 220 q^{57} - 176 q^{58} - 232 q^{60} + 86 q^{61} - 532 q^{62} - 160 q^{64} - 140 q^{65} + 102 q^{66} - 68 q^{68} - 300 q^{69} + 90 q^{70} + 152 q^{72} - 234 q^{73} + 290 q^{74} + 576 q^{76} - 262 q^{77} + 64 q^{78} + 146 q^{81} + 272 q^{82} - 28 q^{84} + 268 q^{85} - 16 q^{86} - 188 q^{88} + 6 q^{89} - 640 q^{90} - 448 q^{92} + 162 q^{93} + 102 q^{94} - 320 q^{96} + 744 q^{97} - 190 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.3.g.a 28.g 28.g $12$ $0.763$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots\)