Properties

Label 55.2.a
Level 55
Weight 2
Character orbit a
Rep. character \(\chi_{55}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 55.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(55))\).

Total New Old
Modular forms 8 3 5
Cusp forms 5 3 2
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.

\(5\)\(11\)FrickeDim.
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3q + 3q^{2} + q^{4} - q^{5} - 8q^{6} - 4q^{7} + 3q^{8} + 7q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + q^{4} - q^{5} - 8q^{6} - 4q^{7} + 3q^{8} + 7q^{9} - q^{10} + q^{11} - 16q^{12} - 6q^{13} - 4q^{14} + 5q^{16} + 14q^{17} + 7q^{18} - 4q^{19} - 3q^{20} + q^{22} + 4q^{23} - 8q^{24} + 3q^{25} + 2q^{26} - 4q^{28} + 10q^{29} + 8q^{30} - 8q^{31} - q^{32} + 22q^{34} + 4q^{35} + 13q^{36} - 6q^{37} - 4q^{38} - 16q^{39} - 9q^{40} + 14q^{41} + 16q^{42} - 8q^{43} + 3q^{44} - 13q^{45} - 4q^{46} - 12q^{47} - 13q^{49} + 3q^{50} - 16q^{51} + 6q^{52} + 10q^{53} - 16q^{54} - 3q^{55} - 12q^{56} - 6q^{58} - 4q^{59} + 16q^{60} - 6q^{61} - 8q^{62} - 20q^{63} - 7q^{64} + 10q^{65} - 8q^{66} - 8q^{67} + 18q^{68} + 16q^{69} + 4q^{70} + 8q^{71} + 39q^{72} + 6q^{73} - 22q^{74} + 4q^{76} - 4q^{77} + 16q^{78} + 16q^{79} - 7q^{80} + 11q^{81} + 14q^{82} - 16q^{83} + 32q^{84} - 2q^{85} - 8q^{86} + 32q^{87} + 9q^{88} + 6q^{89} - 13q^{90} + 16q^{91} - 20q^{92} - 4q^{94} - 4q^{95} - 8q^{96} + 6q^{97} - 13q^{98} + 13q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(55))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 11
55.2.a.a \(1\) \(0.439\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
55.2.a.b \(2\) \(0.439\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-4\) \(+\) \(-\) \(q+(1+\beta )q^{2}-2\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(55))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(55)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)