Properties

Label 862.2.a
Level 862
Weight 2
Character orbit a
Rep. character \(\chi_{862}(1,\cdot)\)
Character field \(\Q\)
Dimension 35
Newforms 11
Sturm bound 216
Trace bound 5

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Defining parameters

Level: \( N \) = \( 862 = 2 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 862.a (trivial)
Character field: \(\Q\)
Newforms: \( 11 \)
Sturm bound: \(216\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(862))\).

Total New Old
Modular forms 110 35 75
Cusp forms 107 35 72
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.

\(2\)\(431\)FrickeDim.
\(+\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(16\)
Minus space\(-\)\(19\)

Trace form

\( 35q - q^{2} - 4q^{3} + 35q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} + 31q^{9} + O(q^{10}) \) \( 35q - q^{2} - 4q^{3} + 35q^{4} - 6q^{5} - 4q^{6} - 8q^{7} - q^{8} + 31q^{9} - 6q^{10} - 4q^{12} + 35q^{16} - 2q^{17} + 3q^{18} - 8q^{19} - 6q^{20} + 4q^{23} - 4q^{24} + 21q^{25} - 4q^{27} - 8q^{28} - 2q^{29} + 4q^{30} - 28q^{31} - q^{32} + 12q^{33} - 14q^{34} - 4q^{35} + 31q^{36} - 24q^{37} - 4q^{38} + 16q^{39} - 6q^{40} - 6q^{41} - 8q^{42} - 18q^{43} - 42q^{45} - 4q^{46} - 20q^{47} - 4q^{48} + 7q^{49} - 15q^{50} + 28q^{51} + 22q^{53} - 40q^{54} - 12q^{55} - 20q^{57} - 22q^{58} - 18q^{61} - 4q^{62} - 4q^{63} + 35q^{64} - 12q^{65} - 8q^{66} - 14q^{67} - 2q^{68} + 16q^{69} - 28q^{70} - 12q^{71} + 3q^{72} - 42q^{73} + 4q^{74} + 4q^{75} - 8q^{76} - 12q^{77} + 16q^{78} - 4q^{79} - 6q^{80} + 75q^{81} - 26q^{82} + 38q^{83} - 4q^{85} + 2q^{86} + 24q^{87} + 6q^{89} + 14q^{90} - 24q^{91} + 4q^{92} + 36q^{93} - 12q^{94} + 52q^{95} - 4q^{96} - 22q^{97} + 23q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(862))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 431
862.2.a.a \(1\) \(6.883\) \(\Q\) None \(-1\) \(-3\) \(-1\) \(-2\) \(+\) \(+\) \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-2q^{7}+\cdots\)
862.2.a.b \(1\) \(6.883\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
862.2.a.c \(1\) \(6.883\) \(\Q\) None \(1\) \(-1\) \(-3\) \(2\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+2q^{7}+\cdots\)
862.2.a.d \(1\) \(6.883\) \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
862.2.a.e \(1\) \(6.883\) \(\Q\) None \(1\) \(0\) \(2\) \(4\) \(-\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots\)
862.2.a.f \(1\) \(6.883\) \(\Q\) None \(1\) \(1\) \(-3\) \(2\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+2q^{7}+\cdots\)
862.2.a.g \(2\) \(6.883\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(+\) \(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
862.2.a.h \(5\) \(6.883\) 5.5.181057.1 None \(5\) \(5\) \(3\) \(-3\) \(-\) \(+\) \(q+q^{2}+(1-\beta _{2})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
862.2.a.i \(6\) \(6.883\) 6.6.11017801.1 None \(-6\) \(-2\) \(-2\) \(3\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{2}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
862.2.a.j \(6\) \(6.883\) 6.6.9783113.1 None \(6\) \(-8\) \(-8\) \(-9\) \(-\) \(-\) \(q+q^{2}+(-1+\beta _{2}+\beta _{4})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
862.2.a.k \(10\) \(6.883\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(4\) \(-3\) \(+\) \(-\) \(q-q^{2}+\beta _{5}q^{3}+q^{4}+(-\beta _{7}-\beta _{9})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(862))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(862)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(431))\)\(^{\oplus 2}\)