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Properties

Label 114.2.i
Level $114$
Weight $2$
Character orbit 114.i
Rep. character $\chi_{114}(25,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $24$
Newform subspaces $4$
Sturm bound $40$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(114, [\chi])\).

Total New Old
Modular forms 144 24 120
Cusp forms 96 24 72
Eisenstein series 48 0 48

Trace form

\( 24 q + 12 q^{7} + O(q^{10}) \) \( 24 q + 12 q^{7} + 12 q^{11} - 24 q^{14} - 24 q^{15} - 12 q^{17} - 24 q^{19} - 24 q^{20} - 24 q^{21} + 24 q^{22} + 12 q^{25} - 12 q^{26} - 12 q^{31} + 12 q^{33} + 12 q^{34} - 12 q^{35} + 12 q^{38} - 12 q^{41} + 12 q^{42} - 24 q^{43} + 12 q^{44} + 12 q^{45} + 12 q^{46} + 12 q^{47} - 24 q^{49} + 48 q^{53} + 24 q^{56} + 12 q^{57} - 24 q^{58} + 36 q^{59} + 12 q^{60} - 24 q^{61} + 36 q^{62} - 12 q^{64} - 12 q^{65} + 12 q^{68} + 24 q^{69} + 24 q^{70} + 60 q^{71} + 48 q^{73} + 36 q^{74} + 12 q^{76} + 24 q^{77} + 24 q^{78} - 24 q^{79} - 36 q^{82} - 36 q^{83} + 12 q^{84} - 24 q^{85} - 24 q^{86} - 12 q^{87} + 12 q^{88} - 36 q^{89} - 36 q^{91} - 36 q^{92} + 36 q^{93} - 72 q^{94} + 12 q^{95} - 24 q^{97} - 72 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(114, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.2.i.a 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-9\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
114.2.i.b 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
114.2.i.c 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
114.2.i.d 114.i 19.e $6$ $0.910$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(9\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+\zeta_{18}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

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