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 $2$

Related objects

Downloads

Learn more

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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
114.2.e.a \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(4\) \(-6\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
114.2.e.b \(2\) \(0.910\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(2\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)

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

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