Properties

Label 228.3.o
Level $228$
Weight $3$
Character orbit 228.o
Rep. character $\chi_{228}(125,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $3$
Sturm bound $120$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 228.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
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 28 144
Cusp forms 148 28 120
Eisenstein series 24 0 24

Trace form

\( 28 q - 2 q^{3} + 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 28 q - 2 q^{3} + 4 q^{7} - 2 q^{9} - 12 q^{13} - 11 q^{15} + 46 q^{19} - 30 q^{21} + 88 q^{25} + 88 q^{27} + 12 q^{31} + 53 q^{33} - 68 q^{37} - 78 q^{39} + 120 q^{43} - 154 q^{45} + 96 q^{49} - 23 q^{51} - 120 q^{55} - 135 q^{57} + 44 q^{61} - 2 q^{63} - 18 q^{67} - 142 q^{69} + 178 q^{73} - 138 q^{75} - 20 q^{79} - 122 q^{81} + 18 q^{85} - 394 q^{87} + 18 q^{91} + 268 q^{93} - 136 q^{97} - 197 q^{99} + O(q^{100}) \)

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.o.a 228.o 57.h $2$ $6.213$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-26\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{3}-13q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\)
228.3.o.b 228.o 57.h $2$ $6.213$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(22\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{3}+11q^{7}+(-9+9\zeta_{6})q^{9}+\cdots\)
228.3.o.c 228.o 57.h $24$ $6.213$ None \(0\) \(-8\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$

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

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