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

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

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 \(4\) \(0\) \(3\) \(-2\) \(-\) \(q+(1-\beta _{1})q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots\)