Properties

Label 114.3.g
Level $114$
Weight $3$
Character orbit 114.g
Rep. character $\chi_{114}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 114.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 88 24 64
Cusp forms 72 24 48
Eisenstein series 16 0 16

Trace form

\( 24 q - 2 q^{3} + 24 q^{4} + 4 q^{6} + 8 q^{7} - 2 q^{9} + O(q^{10}) \) \( 24 q - 2 q^{3} + 24 q^{4} + 4 q^{6} + 8 q^{7} - 2 q^{9} - 8 q^{12} + 28 q^{13} - 2 q^{15} - 48 q^{16} + 80 q^{18} - 96 q^{19} + 60 q^{21} - 16 q^{22} - 8 q^{24} - 24 q^{25} - 56 q^{27} + 8 q^{28} + 88 q^{30} + 88 q^{31} + 8 q^{33} - 88 q^{34} + 4 q^{36} - 208 q^{37} - 156 q^{39} + 8 q^{42} + 232 q^{43} - 460 q^{45} - 160 q^{46} - 8 q^{48} + 168 q^{49} - 38 q^{51} - 56 q^{52} + 40 q^{54} + 192 q^{55} - 150 q^{57} + 96 q^{58} + 4 q^{60} - 12 q^{61} + 232 q^{63} - 192 q^{64} - 24 q^{66} + 352 q^{67} + 380 q^{69} + 72 q^{70} + 80 q^{72} - 244 q^{73} + 144 q^{75} + 292 q^{78} + 8 q^{79} - 230 q^{81} - 184 q^{82} + 240 q^{84} + 564 q^{85} + 404 q^{87} - 64 q^{88} + 56 q^{90} - 388 q^{91} - 104 q^{93} - 160 q^{94} - 32 q^{96} - 156 q^{97} + 208 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
114.3.g.a $24$ $3.106$ None \(0\) \(-2\) \(0\) \(8\)

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

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