Properties

Label 859.2.a
Level $859$
Weight $2$
Character orbit 859.a
Rep. character $\chi_{859}(1,\cdot)$
Character field $\Q$
Dimension $71$
Newform subspaces $2$
Sturm bound $143$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 859 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 859.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(143\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(859))\).

Total New Old
Modular forms 72 72 0
Cusp forms 71 71 0
Eisenstein series 1 1 0

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

\(859\)Dim.
\(+\)\(29\)
\(-\)\(42\)

Trace form

\( 71q - 4q^{3} + 68q^{4} - 6q^{6} - 2q^{7} + 69q^{9} + O(q^{10}) \) \( 71q - 4q^{3} + 68q^{4} - 6q^{6} - 2q^{7} + 69q^{9} - 2q^{10} - 2q^{11} - 18q^{12} - 2q^{13} + 2q^{14} - 10q^{15} + 58q^{16} + 6q^{17} + 8q^{18} - 20q^{19} + 4q^{20} + 2q^{21} + 8q^{22} - 10q^{23} - 6q^{24} + 71q^{25} - 4q^{26} - 34q^{27} + 14q^{28} + 10q^{29} - 14q^{30} - 8q^{31} + 30q^{32} - 14q^{33} + 10q^{34} - 8q^{35} + 46q^{36} - 6q^{37} + 8q^{38} + 2q^{39} - 8q^{40} - 6q^{41} - 2q^{42} - 22q^{43} - 12q^{44} + 10q^{45} - 6q^{46} + 18q^{47} - 48q^{48} + 55q^{49} + 36q^{50} - 6q^{51} - 40q^{52} + 16q^{53} - 8q^{54} - 22q^{55} + 6q^{56} - 14q^{57} + 50q^{58} - 8q^{59} - 4q^{60} + 10q^{61} - 22q^{62} - 2q^{63} + 36q^{64} - 4q^{65} - 60q^{66} - 10q^{67} + 44q^{68} + 10q^{69} + 8q^{70} - 14q^{71} + 76q^{74} - 16q^{75} - 50q^{76} - 4q^{77} + 2q^{78} + 28q^{79} - 12q^{80} + 47q^{81} + 28q^{82} - 4q^{83} - 14q^{84} - 4q^{85} - 4q^{86} - 4q^{87} + 44q^{88} + 28q^{89} - 74q^{90} - 40q^{91} - 30q^{92} - 62q^{93} + 2q^{95} - 90q^{96} + 28q^{97} - 68q^{98} - 22q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(859))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 859
859.2.a.a \(29\) \(6.859\) None \(-10\) \(-5\) \(-21\) \(-4\) \(+\)
859.2.a.b \(42\) \(6.859\) None \(10\) \(1\) \(21\) \(2\) \(-\)