Properties

Label 55.2.a
Level $55$
Weight $2$
Character orbit 55.a
Rep. character $\chi_{55}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(55))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11
55.2.a.a 55.a 1.a $1$ $0.439$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
55.2.a.b 55.a 1.a $2$ $0.439$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-2\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)

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

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