Properties

Label 114.2.a
Level $114$
Weight $2$
Character orbit 114.a
Rep. character $\chi_{114}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(114))\).

Total New Old
Modular forms 24 3 21
Cusp forms 17 3 14
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q + q^{2} - q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + q^{8} + 3 q^{9} + O(q^{10}) \) \( 3 q + q^{2} - q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + q^{8} + 3 q^{9} + 2 q^{10} - q^{12} - 2 q^{13} - 8 q^{14} - 2 q^{15} + 3 q^{16} - 2 q^{17} + q^{18} + q^{19} + 2 q^{20} - 8 q^{21} - 8 q^{22} - 12 q^{23} + q^{24} - 11 q^{25} - 2 q^{26} - q^{27} - 2 q^{29} - 2 q^{30} + 12 q^{31} + q^{32} + 2 q^{34} + 3 q^{36} - 2 q^{37} - q^{38} - 6 q^{39} + 2 q^{40} + 26 q^{41} - 12 q^{43} + 2 q^{45} - 8 q^{46} + 12 q^{47} - q^{48} + 11 q^{49} - q^{50} + 14 q^{51} - 2 q^{52} - 2 q^{53} + q^{54} - 8 q^{55} - 8 q^{56} + q^{57} + 10 q^{58} + 4 q^{59} - 2 q^{60} + 18 q^{61} + 3 q^{64} + 4 q^{65} + 8 q^{66} - 4 q^{67} - 2 q^{68} - 8 q^{71} + q^{72} + 6 q^{73} + 14 q^{74} + q^{75} + q^{76} + 16 q^{77} - 6 q^{78} - 4 q^{79} + 2 q^{80} + 3 q^{81} + 6 q^{82} - 16 q^{83} - 8 q^{84} - 12 q^{85} + 12 q^{86} + 14 q^{87} - 8 q^{88} - 14 q^{89} + 2 q^{90} + 16 q^{91} - 12 q^{92} - 8 q^{93} - 8 q^{94} - 2 q^{95} + q^{96} - 10 q^{97} - 7 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(114))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 19
114.2.a.a 114.a 1.a $1$ $0.910$ \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
114.2.a.b 114.a 1.a $1$ $0.910$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
114.2.a.c 114.a 1.a $1$ $0.910$ \(\Q\) None \(1\) \(1\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(114))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(114)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)