Properties

Label 114.2.e
Level $114$
Weight $2$
Character orbit 114.e
Rep. character $\chi_{114}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $2$
Sturm bound $40$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 48 4 44
Cusp forms 32 4 28
Eisenstein series 16 0 16

Trace form

\( 4 q + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{7} - 2 q^{9} + 4 q^{10} - 4 q^{12} + 10 q^{13} + 4 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 8 q^{20} - 2 q^{21} - 4 q^{22} - 6 q^{25} - 8 q^{26} - 4 q^{27} + 2 q^{28} - 4 q^{29} + 8 q^{30} - 4 q^{31} + 4 q^{34} - 12 q^{35} - 2 q^{36} + 4 q^{37} + 8 q^{38} + 20 q^{39} + 4 q^{40} - 8 q^{41} - 4 q^{42} + 2 q^{43} - 8 q^{45} - 16 q^{46} - 12 q^{47} + 2 q^{48} - 8 q^{49} + 32 q^{50} + 4 q^{51} + 10 q^{52} + 8 q^{53} + 8 q^{55} - 8 q^{56} + 6 q^{57} + 8 q^{58} + 20 q^{59} - 4 q^{60} - 10 q^{61} - 4 q^{62} + 2 q^{63} + 4 q^{64} + 56 q^{65} + 4 q^{66} - 6 q^{67} + 8 q^{68} - 12 q^{70} - 16 q^{71} + 14 q^{73} - 12 q^{74} - 12 q^{75} + 6 q^{76} - 16 q^{77} - 4 q^{78} - 6 q^{79} + 4 q^{80} - 2 q^{81} - 8 q^{83} + 4 q^{84} - 16 q^{86} - 8 q^{87} + 8 q^{88} - 4 q^{89} + 4 q^{90} - 18 q^{91} - 2 q^{93} - 16 q^{94} - 4 q^{95} - 12 q^{97} - 8 q^{98} + O(q^{100}) \)

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.e.a 114.e 19.c $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.e.b 114.e 19.c $2$ $0.910$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)

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

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