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Properties

Label 863.2.a
Level $863$
Weight $2$
Character orbit 863.a
Rep. character $\chi_{863}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $3$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 863 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 863.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(863))\).

Total New Old
Modular forms 73 73 0
Cusp forms 72 72 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.

\(863\)Dim
\(+\)\(26\)
\(-\)\(46\)

Trace form

\( 72 q - q^{2} + 69 q^{4} - 8 q^{6} + 4 q^{7} - 3 q^{8} + 74 q^{9} + O(q^{10}) \) \( 72 q - q^{2} + 69 q^{4} - 8 q^{6} + 4 q^{7} - 3 q^{8} + 74 q^{9} - 2 q^{10} - 2 q^{11} - 16 q^{12} + 10 q^{13} - 10 q^{14} - 6 q^{15} + 59 q^{16} + 10 q^{17} - 7 q^{18} + 4 q^{19} + 4 q^{20} - 2 q^{21} - 14 q^{22} - 10 q^{23} - 22 q^{24} + 82 q^{25} - 10 q^{26} - 12 q^{27} + 28 q^{28} + 2 q^{29} - 30 q^{30} + 4 q^{31} - 17 q^{32} + 18 q^{33} + 12 q^{34} + 4 q^{35} + 49 q^{36} - 2 q^{37} + 46 q^{38} - 6 q^{39} + 2 q^{40} + 4 q^{41} - 4 q^{42} + 14 q^{43} - 14 q^{44} - 14 q^{45} - 22 q^{46} - 6 q^{47} - 4 q^{48} + 80 q^{49} + 17 q^{50} - 16 q^{51} + 52 q^{52} - 16 q^{53} - 30 q^{54} + 2 q^{55} - 22 q^{56} + 4 q^{57} + 34 q^{58} + 10 q^{59} + 14 q^{60} + 12 q^{61} + 16 q^{62} - 4 q^{63} + 25 q^{64} - 8 q^{65} + 2 q^{66} - 12 q^{67} + 22 q^{68} - 26 q^{69} + 16 q^{70} + 20 q^{71} - 53 q^{72} + 32 q^{73} - 26 q^{74} - 8 q^{75} + 14 q^{77} + 28 q^{78} + 12 q^{79} + 18 q^{80} + 80 q^{81} - 6 q^{82} + 2 q^{83} - 10 q^{84} + 4 q^{85} - 2 q^{86} + 34 q^{87} - 52 q^{88} - 36 q^{89} + 88 q^{90} + 34 q^{91} - 48 q^{92} - 36 q^{93} - 82 q^{94} - 12 q^{95} - 44 q^{96} + 48 q^{97} - 11 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(863))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 863
863.2.a.a 863.a 1.a $4$ $6.891$ 4.4.1957.1 None \(1\) \(-4\) \(-9\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
863.2.a.b 863.a 1.a $22$ $6.891$ None \(-6\) \(-2\) \(-2\) \(-20\) $+$ $\mathrm{SU}(2)$
863.2.a.c 863.a 1.a $46$ $6.891$ None \(4\) \(6\) \(11\) \(28\) $-$ $\mathrm{SU}(2)$