Properties

Label 114.2.a
Level 114
Weight 2
Character orbit a
Rep. character \(\chi_{114}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(114))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19
114.2.a.a \(1\) \(0.910\) \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
114.2.a.b \(1\) \(0.910\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
114.2.a.c \(1\) \(0.910\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)

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

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