↑

Properties

Label 228.2.q
Level $228$
Weight $2$
Character orbit 228.q
Rep. character $\chi_{228}(25,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $18$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 228.q (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(228, [\chi])\).

Total New Old
Modular forms 276 18 258
Cusp forms 204 18 186
Eisenstein series 72 0 72

Trace form

\( 18 q - 6 q^{7} + O(q^{10}) \) \( 18 q - 6 q^{7} - 6 q^{11} + 3 q^{13} + 12 q^{15} + 24 q^{17} + 15 q^{19} + 15 q^{21} + 12 q^{25} + 3 q^{27} - 36 q^{29} - 12 q^{31} - 6 q^{33} - 48 q^{35} - 12 q^{41} - 57 q^{43} - 6 q^{45} - 6 q^{47} - 21 q^{49} - 6 q^{53} + 18 q^{55} + 12 q^{57} + 18 q^{59} + 24 q^{61} - 6 q^{63} - 12 q^{65} - 33 q^{67} + 24 q^{69} - 12 q^{71} - 3 q^{73} - 42 q^{75} - 48 q^{77} + 24 q^{79} + 18 q^{83} + 66 q^{85} - 12 q^{87} + 48 q^{91} - 24 q^{93} - 6 q^{95} - 6 q^{97} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.2.q.a 228.q 19.e $6$ $1.821$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}^{4}q^{3}+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+\cdots\)
228.2.q.b 228.q 19.e $12$ $1.821$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{5}+\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)