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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 103
206.2.a.a \(1\) \(1.645\) \(\Q\) None \(-1\) \(2\) \(4\) \(0\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+4q^{5}-2q^{6}-q^{8}+\cdots\)
206.2.a.b \(2\) \(1.645\) \(\Q(\sqrt{13}) \) None \(-2\) \(-3\) \(-5\) \(5\) \(+\) \(-\) \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots\)
206.2.a.c \(2\) \(1.645\) \(\Q(\sqrt{29}) \) None \(-2\) \(1\) \(1\) \(-3\) \(+\) \(-\) \(q-q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
206.2.a.d \(4\) \(1.645\) 4.4.5744.1 None \(4\) \(2\) \(0\) \(2\) \(-\) \(+\) \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{6}+\cdots\)

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

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