Properties

Label 115.2.a
Level 115
Weight 2
Character orbit a
Rep. character \(\chi_{115}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 3
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 115 = 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 115.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(115))\).

Total New Old
Modular forms 14 7 7
Cusp forms 11 7 4
Eisenstein series 3 0 3

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

\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(4\)
Plus space\(+\)\(2\)
Minus space\(-\)\(5\)

Trace form

\( 7q + q^{2} - 4q^{3} + 9q^{4} + q^{5} + 2q^{6} - 4q^{7} + 3q^{8} - q^{9} + O(q^{10}) \) \( 7q + q^{2} - 4q^{3} + 9q^{4} + q^{5} + 2q^{6} - 4q^{7} + 3q^{8} - q^{9} + 3q^{10} + 4q^{11} - 22q^{12} - 10q^{13} - 12q^{14} + 17q^{16} - 2q^{17} + 3q^{18} - 4q^{19} - q^{20} + 12q^{21} - 8q^{22} - 5q^{23} - 24q^{24} + 7q^{25} + 12q^{26} - 4q^{27} - 8q^{28} + 16q^{29} - 4q^{30} - 2q^{31} - 3q^{32} - 10q^{34} - 2q^{35} + 11q^{36} + 2q^{37} + 28q^{38} + 8q^{39} + 15q^{40} + 8q^{41} + 8q^{42} - 12q^{43} - 32q^{44} + 13q^{45} + 3q^{46} + 16q^{47} - 34q^{48} + q^{49} + q^{50} - 4q^{51} - 32q^{52} + 18q^{53} - 22q^{54} + 4q^{55} - 24q^{56} + 40q^{58} + 10q^{59} - 16q^{60} - 6q^{61} - 34q^{62} - 12q^{63} + 23q^{64} + 10q^{65} + 36q^{66} + 8q^{67} + 26q^{68} + 4q^{69} - 12q^{70} - 6q^{71} + 51q^{72} - 26q^{73} + 34q^{74} - 4q^{75} - 28q^{76} + 12q^{77} + 26q^{78} + 12q^{79} - q^{80} - 17q^{81} + 16q^{82} - 16q^{83} + 16q^{84} - 8q^{86} - 8q^{87} + 12q^{88} + 14q^{89} + 3q^{90} - 44q^{91} - 5q^{92} - 12q^{93} + 22q^{94} - 4q^{95} - 46q^{96} - 22q^{97} + 17q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(115))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 23
115.2.a.a \(1\) \(0.918\) \(\Q\) None \(2\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots\)
115.2.a.b \(2\) \(0.918\) \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots\)
115.2.a.c \(4\) \(0.918\) 4.4.15317.1 None \(2\) \(-2\) \(4\) \(-3\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(115))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(115)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)