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Properties

Label 114.3.f
Level $114$
Weight $3$
Character orbit 114.f
Rep. character $\chi_{114}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 114.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(114, [\chi])\).

Total New Old
Modular forms 88 16 72
Cusp forms 72 16 56
Eisenstein series 16 0 16

Trace form

\( 16 q + 16 q^{4} - 4 q^{5} - 24 q^{7} + 24 q^{9} + O(q^{10}) \) \( 16 q + 16 q^{4} - 4 q^{5} - 24 q^{7} + 24 q^{9} + 56 q^{11} + 48 q^{14} + 36 q^{15} - 32 q^{16} - 40 q^{17} + 24 q^{19} - 16 q^{20} - 36 q^{21} + 48 q^{22} - 28 q^{23} - 104 q^{25} - 96 q^{26} - 24 q^{28} - 24 q^{29} + 48 q^{30} - 108 q^{33} - 24 q^{34} + 100 q^{35} - 48 q^{36} + 48 q^{38} + 96 q^{39} - 72 q^{41} + 24 q^{42} - 172 q^{43} + 56 q^{44} - 24 q^{45} - 16 q^{47} + 144 q^{49} - 60 q^{53} + 56 q^{55} + 108 q^{57} - 192 q^{58} - 84 q^{59} + 72 q^{60} - 24 q^{61} + 72 q^{62} - 36 q^{63} - 128 q^{64} - 24 q^{66} - 180 q^{67} - 160 q^{68} + 168 q^{70} + 360 q^{71} - 112 q^{73} - 96 q^{74} + 72 q^{76} + 184 q^{77} - 144 q^{78} + 276 q^{79} - 16 q^{80} - 72 q^{81} + 264 q^{82} + 656 q^{83} + 32 q^{85} + 552 q^{86} - 144 q^{87} - 420 q^{89} + 516 q^{91} + 56 q^{92} + 84 q^{93} - 676 q^{95} + 648 q^{97} - 240 q^{98} + 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(114, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.3.f.a 114.f 19.d $8$ $3.106$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-12\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{6}q^{2}+(-1-\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots\)
114.3.f.b 114.f 19.d $8$ $3.106$ 8.0.\(\cdots\).10 None \(0\) \(12\) \(4\) \(-24\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(2-\beta _{4})q^{3}+(2-2\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(114, [\chi])\) into lower level spaces

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