Properties

Label 206.2.a
Level 206
Weight 2
Character orbit a
Rep. character \(\chi_{206}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(206))\) into irreducible Hecke orbits

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

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