Properties

Label 262.2.a
Level 262
Weight 2
Character orbit a
Rep. character \(\chi_{262}(1,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 6
Sturm bound 66
Trace bound 3

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Defining parameters

Level: \( N \) = \( 262 = 2 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 262.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(66\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(262))\).

Total New Old
Modular forms 35 10 25
Cusp forms 32 10 22
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.

\(2\)\(131\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(4\)
Minus space\(-\)\(6\)

Trace form

\( 10q - 2q^{3} + 10q^{4} - 2q^{5} + O(q^{10}) \) \( 10q - 2q^{3} + 10q^{4} - 2q^{5} - 2q^{11} - 2q^{12} - 6q^{13} - 4q^{15} + 10q^{16} - 4q^{17} + 8q^{18} + 4q^{19} - 2q^{20} - 12q^{21} + 8q^{23} - 4q^{25} + 8q^{26} - 8q^{27} - 12q^{29} + 12q^{30} - 8q^{31} + 10q^{33} - 4q^{34} + 6q^{35} - 20q^{37} + 2q^{38} - 14q^{39} + 20q^{41} - 4q^{42} + 2q^{43} - 2q^{44} - 20q^{45} - 12q^{47} - 2q^{48} - 2q^{49} - 16q^{50} + 12q^{51} - 6q^{52} - 4q^{53} + 24q^{55} - 12q^{57} + 6q^{58} + 22q^{59} - 4q^{60} - 22q^{61} - 16q^{62} + 26q^{63} + 10q^{64} + 4q^{65} + 12q^{67} - 4q^{68} - 8q^{69} + 8q^{70} - 4q^{71} + 8q^{72} + 8q^{73} - 18q^{74} + 20q^{75} + 4q^{76} + 28q^{77} - 8q^{78} - 16q^{79} - 2q^{80} - 22q^{81} + 8q^{82} - 16q^{83} - 12q^{84} + 12q^{85} + 12q^{86} + 4q^{87} + 14q^{89} - 20q^{90} - 28q^{91} + 8q^{92} - 4q^{93} + 20q^{94} + 12q^{95} - 52q^{97} - 16q^{98} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(262))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 131
262.2.a.a \(1\) \(2.092\) \(\Q\) None \(-1\) \(0\) \(0\) \(-5\) \(+\) \(+\) \(q-q^{2}+q^{4}-5q^{7}-q^{8}-3q^{9}+2q^{11}+\cdots\)
262.2.a.b \(1\) \(2.092\) \(\Q\) None \(1\) \(-2\) \(-2\) \(-3\) \(-\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}-3q^{7}+\cdots\)
262.2.a.c \(2\) \(2.092\) \(\Q(\sqrt{13}) \) None \(-2\) \(-1\) \(-5\) \(3\) \(+\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\beta q^{6}+\cdots\)
262.2.a.d \(2\) \(2.092\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(2\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+(2-\beta )q^{5}-\beta q^{6}+\cdots\)
262.2.a.e \(2\) \(2.092\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(4\) \(-\) \(+\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)
262.2.a.f \(2\) \(2.092\) \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(-1\) \(-1\) \(-\) \(+\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(262))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(262)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 2}\)