Properties

Label 286.2.a
Level $286$
Weight $2$
Character orbit 286.a
Rep. character $\chi_{286}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $7$
Sturm bound $84$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 286 = 2 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 286.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(84\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(286))\).

Total New Old
Modular forms 46 9 37
Cusp forms 39 9 30
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(7\)

Trace form

\( 9q - q^{2} + 9q^{4} + 2q^{5} + 4q^{6} - 8q^{7} - q^{8} + 9q^{9} + O(q^{10}) \) \( 9q - q^{2} + 9q^{4} + 2q^{5} + 4q^{6} - 8q^{7} - q^{8} + 9q^{9} - 6q^{10} + q^{11} - q^{13} + 8q^{15} + 9q^{16} + 14q^{17} - 13q^{18} - 12q^{19} + 2q^{20} + 8q^{21} - q^{22} - 4q^{23} + 4q^{24} - q^{25} + 5q^{26} + 12q^{27} - 8q^{28} + 10q^{29} - 4q^{30} - 4q^{31} - q^{32} + 4q^{33} - 2q^{34} + 28q^{35} + 9q^{36} - 6q^{37} + 4q^{38} - 4q^{39} - 6q^{40} - 2q^{41} - 12q^{42} - 12q^{43} + q^{44} - 14q^{45} + 8q^{46} - 20q^{47} + 9q^{49} - 15q^{50} - 28q^{51} - q^{52} + 14q^{53} - 8q^{54} + 6q^{55} - 24q^{57} - 18q^{58} + 12q^{59} + 8q^{60} - 30q^{61} - 4q^{62} - 48q^{63} + 9q^{64} + 2q^{65} - 4q^{66} - 20q^{67} + 14q^{68} - 32q^{69} + 52q^{71} - 13q^{72} - 10q^{73} - 14q^{74} - 28q^{75} - 12q^{76} + 2q^{80} + 17q^{81} - 26q^{82} + 12q^{83} + 8q^{84} - 36q^{85} + 8q^{86} - q^{88} + 2q^{89} + 22q^{90} - 4q^{91} - 4q^{92} + 32q^{93} + 8q^{94} + 24q^{95} + 4q^{96} - 6q^{97} + 23q^{98} + 13q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(286))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11 13
286.2.a.a \(1\) \(2.284\) \(\Q\) None \(-1\) \(-2\) \(3\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}-q^{7}+\cdots\)
286.2.a.b \(1\) \(2.284\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
286.2.a.c \(1\) \(2.284\) \(\Q\) None \(1\) \(-1\) \(-3\) \(-5\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-5q^{7}+\cdots\)
286.2.a.d \(1\) \(2.284\) \(\Q\) None \(1\) \(-1\) \(1\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
286.2.a.e \(1\) \(2.284\) \(\Q\) None \(1\) \(2\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
286.2.a.f \(1\) \(2.284\) \(\Q\) None \(1\) \(2\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
286.2.a.g \(3\) \(2.284\) 3.3.961.1 None \(-3\) \(1\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(286))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(286)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 2}\)