Properties

Label 28.3.b
Level $28$
Weight $3$
Character orbit 28.b
Rep. character $\chi_{28}(13,\cdot)$
Character field $\Q$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
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 11 2 9
Cusp forms 5 2 3
Eisenstein series 6 0 6

Trace form

\( 2 q + 10 q^{7} - 30 q^{9} + O(q^{10}) \) \( 2 q + 10 q^{7} - 30 q^{9} - 12 q^{11} + 48 q^{15} + 48 q^{21} - 60 q^{23} + 2 q^{25} - 12 q^{29} - 48 q^{35} + 20 q^{37} - 48 q^{39} + 20 q^{43} + 2 q^{49} + 192 q^{51} + 180 q^{53} - 240 q^{57} - 150 q^{63} + 48 q^{65} - 140 q^{67} + 84 q^{71} - 60 q^{77} + 148 q^{79} + 18 q^{81} - 192 q^{85} + 48 q^{91} + 240 q^{95} + 180 q^{99} + O(q^{100}) \)

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.b.a 28.b 7.b $2$ $0.763$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)