Properties

Label 103.2.a
Level $103$
Weight $2$
Character orbit 103.a
Rep. character $\chi_{103}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(103))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 103
103.2.a.a 103.a 1.a $2$ $0.822$ \(\Q(\sqrt{5}) \) None 103.2.a.a \(-3\) \(-2\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
103.2.a.b 103.a 1.a $6$ $0.822$ 6.6.6999257.1 None 103.2.a.b \(4\) \(0\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots\)