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Properties

Label 206.2.a
Level $206$
Weight $2$
Character orbit 206.a
Rep. character $\chi_{206}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $52$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 206 = 2 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 206.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(52\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(206))\).

Total New Old
Modular forms 28 9 19
Cusp forms 25 9 16
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.

\(2\)\(103\)FrickeDim
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(4\)
Plus space\(+\)\(0\)
Minus space\(-\)\(9\)

Trace form

\( 9 q - q^{2} + 2 q^{3} + 9 q^{4} + 2 q^{6} + 4 q^{7} - q^{8} + 17 q^{9} + O(q^{10}) \) \( 9 q - q^{2} + 2 q^{3} + 9 q^{4} + 2 q^{6} + 4 q^{7} - q^{8} + 17 q^{9} + 6 q^{11} + 2 q^{12} + 6 q^{13} + 4 q^{15} + 9 q^{16} - 10 q^{17} - 13 q^{18} + 12 q^{19} + 2 q^{22} - 8 q^{23} + 2 q^{24} + 19 q^{25} - 6 q^{26} - 16 q^{27} + 4 q^{28} - 6 q^{29} - 12 q^{30} + 24 q^{31} - q^{32} - 24 q^{33} - 18 q^{34} - 32 q^{35} + 17 q^{36} + 12 q^{37} - 12 q^{38} - 20 q^{39} - 18 q^{41} - 24 q^{42} - 2 q^{43} + 6 q^{44} - 48 q^{45} + 12 q^{46} - 24 q^{47} + 2 q^{48} + 13 q^{49} - 31 q^{50} - 36 q^{51} + 6 q^{52} - 16 q^{53} - 4 q^{54} - 12 q^{55} - 24 q^{57} + 6 q^{58} + 4 q^{59} + 4 q^{60} - 6 q^{61} - 8 q^{62} + 4 q^{63} + 9 q^{64} - 8 q^{65} - 8 q^{66} + 18 q^{67} - 10 q^{68} + 28 q^{69} + 12 q^{70} + 24 q^{71} - 13 q^{72} + 34 q^{73} + 8 q^{74} - 18 q^{75} + 12 q^{76} - 12 q^{77} + 36 q^{78} + 32 q^{79} + 17 q^{81} - 18 q^{82} + 20 q^{83} + 12 q^{85} + 10 q^{86} - 36 q^{87} + 2 q^{88} + 18 q^{89} + 28 q^{90} + 16 q^{91} - 8 q^{92} + 40 q^{93} + 24 q^{94} + 8 q^{95} + 2 q^{96} - 10 q^{97} + 7 q^{98} + 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(206))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 103
206.2.a.a 206.a 1.a $1$ $1.645$ \(\Q\) None \(-1\) \(2\) \(4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+4q^{5}-2q^{6}-q^{8}+\cdots\)
206.2.a.b 206.a 1.a $2$ $1.645$ \(\Q(\sqrt{13}) \) None \(-2\) \(-3\) \(-5\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots\)
206.2.a.c 206.a 1.a $2$ $1.645$ \(\Q(\sqrt{29}) \) None \(-2\) \(1\) \(1\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
206.2.a.d 206.a 1.a $4$ $1.645$ 4.4.5744.1 None \(4\) \(2\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(206))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(206)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(103))\)\(^{\oplus 2}\)