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Properties

Label 228.3.s
Level $228$
Weight $3$
Character orbit 228.s
Rep. character $\chi_{228}(5,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $78$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 228.s (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 516 78 438
Cusp forms 444 78 366
Eisenstein series 72 0 72

Trace form

\( 78 q + 6 q^{3} + 6 q^{9} + O(q^{10}) \) \( 78 q + 6 q^{3} + 6 q^{9} - 81 q^{13} + 33 q^{15} - 51 q^{19} + 132 q^{25} + 30 q^{27} + 69 q^{33} + 96 q^{37} - 48 q^{39} + 15 q^{43} - 45 q^{45} - 111 q^{49} + 192 q^{51} + 72 q^{55} + 168 q^{57} - 180 q^{61} - 240 q^{63} - 57 q^{67} - 117 q^{69} - 117 q^{73} - 108 q^{79} - 330 q^{81} + 18 q^{85} + 24 q^{87} - 438 q^{91} - 480 q^{93} - 360 q^{97} - 129 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.s.a 228.s 57.l $6$ $6.213$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q-3\zeta_{18}^{4}q^{3}+(-5\zeta_{18}-3\zeta_{18}^{2}+8\zeta_{18}^{4}+\cdots)q^{7}+\cdots\)
228.3.s.b 228.s 57.l $72$ $6.213$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

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