Properties

Label 103.2.a
Level 103
Weight 2
Character orbit a
Rep. character \(\chi_{103}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 2
Sturm bound 17
Trace bound 1

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Defining parameters

Level: \( N \) = \( 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 103.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(17\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(103))\).

Total New Old
Modular forms 9 9 0
Cusp forms 8 8 0
Eisenstein series 1 1 0

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

\(103\)Dim.
\(+\)\(2\)
\(-\)\(6\)

Trace form

\( 8q + q^{2} - 2q^{3} + 9q^{4} - 4q^{7} + 3q^{8} + 4q^{9} + O(q^{10}) \) \( 8q + q^{2} - 2q^{3} + 9q^{4} - 4q^{7} + 3q^{8} + 4q^{9} - 8q^{10} - 4q^{11} - 16q^{12} - 4q^{13} - 6q^{14} - 6q^{15} + 15q^{16} + 12q^{17} + 3q^{18} - 2q^{19} - 6q^{20} - 12q^{21} - 4q^{22} + 12q^{23} - 30q^{24} - 2q^{25} + 7q^{26} + 10q^{27} - 13q^{28} + 6q^{29} - 16q^{31} + 12q^{32} + 18q^{33} + 26q^{34} + 8q^{35} - 9q^{36} - 23q^{38} + 8q^{39} - 2q^{40} + 14q^{41} + 22q^{42} - 10q^{43} - 16q^{44} + 14q^{45} + 9q^{46} - 2q^{47} - 54q^{48} - 14q^{49} + 13q^{50} + 4q^{51} - 32q^{52} + 10q^{53} + 8q^{54} - 8q^{55} - 7q^{56} + 18q^{57} + 18q^{58} + 18q^{59} + 14q^{60} + 16q^{61} + 38q^{62} - 16q^{63} + 65q^{64} + 20q^{65} - 6q^{66} - 10q^{67} - 7q^{68} - 22q^{69} - 16q^{70} - 24q^{71} + 43q^{72} - 22q^{73} - 14q^{75} - 8q^{76} + 30q^{77} - 32q^{78} - 14q^{79} - 40q^{80} + 33q^{82} - 6q^{83} + 64q^{84} + 2q^{85} + 10q^{86} - 6q^{87} - 12q^{88} - 32q^{89} - 26q^{90} - 30q^{91} + 60q^{92} - 32q^{93} - 8q^{94} - 6q^{95} - 18q^{96} + 2q^{97} + 20q^{98} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(103))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 103
103.2.a.a \(2\) \(0.822\) \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(-3\) \(-2\) \(+\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
103.2.a.b \(6\) \(0.822\) 6.6.6999257.1 None \(4\) \(0\) \(3\) \(-2\) \(-\) \(q+(1-\beta _{1})q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots\)