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 $1$

Related objects

Downloads

Learn more

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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 859
859.2.a.a 859.a 1.a $29$ $6.859$ None \(-10\) \(-5\) \(-21\) \(-4\) $+$ $\mathrm{SU}(2)$
859.2.a.b 859.a 1.a $42$ $6.859$ None \(10\) \(1\) \(21\) \(2\) $-$ $\mathrm{SU}(2)$