↑

Properties

Label 28.3.h
Level $28$
Weight $3$
Character orbit 28.h
Rep. character $\chi_{28}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 22 2 20
Cusp forms 10 2 8
Eisenstein series 12 0 12

Trace form

\( 2 q + 3 q^{3} + 3 q^{5} - 14 q^{7} - 6 q^{9} + O(q^{10}) \) \( 2 q + 3 q^{3} + 3 q^{5} - 14 q^{7} - 6 q^{9} - 15 q^{11} + 6 q^{15} + 51 q^{17} + 27 q^{19} - 21 q^{21} + 9 q^{23} - 22 q^{25} - 12 q^{29} - 21 q^{31} - 45 q^{33} - 21 q^{35} - 31 q^{37} + 24 q^{39} + 20 q^{43} - 18 q^{45} + 75 q^{47} + 98 q^{49} + 51 q^{51} + 57 q^{53} + 54 q^{57} - 141 q^{59} - 141 q^{61} + 42 q^{63} - 24 q^{65} + 49 q^{67} - 252 q^{71} - 45 q^{73} - 66 q^{75} + 105 q^{77} + 73 q^{79} - 9 q^{81} + 102 q^{85} - 18 q^{87} + 99 q^{89} - 21 q^{93} + 27 q^{95} + 180 q^{99} + O(q^{100}) \)

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.h.a 28.h 7.d $2$ $0.763$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(3\) \(-14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-7q^{7}-6\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)