Properties

Label 222.2.n
Level $222$
Weight $2$
Character orbit 222.n
Rep. character $\chi_{222}(25,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $48$
Newform subspaces $2$
Sturm bound $76$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 222 = 2 \cdot 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 222.n (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(76\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(222, [\chi])\).

Total New Old
Modular forms 252 48 204
Cusp forms 204 48 156
Eisenstein series 48 0 48

Trace form

\( 48 q + O(q^{10}) \) \( 48 q - 12 q^{10} + 36 q^{14} + 36 q^{19} - 12 q^{21} + 24 q^{25} + 12 q^{26} - 36 q^{29} - 24 q^{30} - 24 q^{33} - 72 q^{35} - 48 q^{36} - 36 q^{37} - 24 q^{38} + 12 q^{39} - 60 q^{41} - 24 q^{42} - 12 q^{44} - 36 q^{46} - 12 q^{47} - 12 q^{49} + 72 q^{50} + 36 q^{53} + 72 q^{55} + 60 q^{57} - 24 q^{58} - 24 q^{59} + 12 q^{61} + 24 q^{64} - 72 q^{65} + 24 q^{67} + 12 q^{69} + 12 q^{70} - 12 q^{71} - 24 q^{73} + 36 q^{76} - 120 q^{77} - 24 q^{79} + 60 q^{83} - 12 q^{84} - 48 q^{85} + 72 q^{86} + 12 q^{87} + 36 q^{88} - 24 q^{89} + 24 q^{91} - 12 q^{92} + 48 q^{93} - 12 q^{94} + 60 q^{95} - 36 q^{97} + 24 q^{98} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(222, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
222.2.n.a 222.n 37.h $24$ $1.773$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$
222.2.n.b 222.n 37.h $24$ $1.773$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(222, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(222, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)