Properties

Label 228.3.l
Level $228$
Weight $3$
Character orbit 228.l
Rep. character $\chi_{228}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $4$
Sturm bound $120$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 228.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(228, [\chi])\).

Total New Old
Modular forms 172 12 160
Cusp forms 148 12 136
Eisenstein series 24 0 24

Trace form

\( 12 q + 2 q^{5} + 20 q^{7} + 18 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{5} + 20 q^{7} + 18 q^{9} - 4 q^{11} + 6 q^{13} - 18 q^{15} - 4 q^{17} + 40 q^{19} + 14 q^{23} + 26 q^{25} + 156 q^{29} + 54 q^{33} + 82 q^{35} - 72 q^{39} - 72 q^{41} + 6 q^{43} + 12 q^{45} - 28 q^{47} - 240 q^{49} - 6 q^{53} - 124 q^{55} + 96 q^{57} - 318 q^{59} + 38 q^{61} + 30 q^{63} + 282 q^{67} - 54 q^{73} - 428 q^{77} - 42 q^{79} - 54 q^{81} + 8 q^{83} - 136 q^{85} - 144 q^{87} - 6 q^{89} - 18 q^{91} - 60 q^{93} + 50 q^{95} - 144 q^{97} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(228, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
228.3.l.a 228.l 19.d $2$ $6.213$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-6\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-6+6\zeta_{6})q^{5}-5q^{7}+\cdots\)
228.3.l.b 228.l 19.d $2$ $6.213$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots\)
228.3.l.c 228.l 19.d $2$ $6.213$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(2\) \(22\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+11q^{7}+\cdots\)
228.3.l.d 228.l 19.d $6$ $6.213$ 6.0.954288.1 None \(0\) \(-9\) \(4\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2})q^{3}+(2-2\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

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