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Properties

Label 1063.2.a
Level $1063$
Weight $2$
Character orbit 1063.a
Rep. character $\chi_{1063}(1,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $4$
Sturm bound $177$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1063 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1063.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(177\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1063))\).

Total New Old
Modular forms 89 89 0
Cusp forms 88 88 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.

\(1063\)Dim
\(+\)\(35\)
\(-\)\(53\)

Trace form

\( 88 q + q^{2} + 89 q^{4} + 2 q^{5} - 4 q^{7} + 3 q^{8} + 86 q^{9} + O(q^{10}) \) \( 88 q + q^{2} + 89 q^{4} + 2 q^{5} - 4 q^{7} + 3 q^{8} + 86 q^{9} - 8 q^{10} + 2 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} + 87 q^{16} + 8 q^{17} + 27 q^{18} - 2 q^{20} - 18 q^{21} + 20 q^{23} + 6 q^{24} + 84 q^{25} - 12 q^{26} + 12 q^{27} - 22 q^{28} - 4 q^{29} - 14 q^{30} - 2 q^{31} + 7 q^{32} - 8 q^{33} + 6 q^{34} - 8 q^{35} + 99 q^{36} + 6 q^{37} + 16 q^{38} - 8 q^{39} - 14 q^{40} + 8 q^{41} + 18 q^{42} - 8 q^{43} - 22 q^{44} - 12 q^{45} + 24 q^{46} + 8 q^{47} - 2 q^{48} + 62 q^{49} + 19 q^{50} + 10 q^{51} + 14 q^{52} + 24 q^{53} - 16 q^{54} - 12 q^{55} + 8 q^{56} - 36 q^{57} - 12 q^{58} - 4 q^{59} + 8 q^{60} - 2 q^{62} - 24 q^{63} + 117 q^{64} + 10 q^{65} + 6 q^{66} - 20 q^{67} - 18 q^{68} + 4 q^{69} - 74 q^{70} - 16 q^{71} + 41 q^{72} - 6 q^{73} + 16 q^{74} + 8 q^{76} + 36 q^{77} - 66 q^{78} - 26 q^{79} - 18 q^{80} + 104 q^{81} - 16 q^{82} + 28 q^{83} - 114 q^{84} + 2 q^{85} - 28 q^{86} + 18 q^{87} - 34 q^{88} - 96 q^{90} - 54 q^{91} + 32 q^{92} + 24 q^{93} - 4 q^{94} - 28 q^{95} + 14 q^{96} - 8 q^{97} - 3 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1063))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 1063
1063.2.a.a 1063.a 1.a $2$ $8.488$ \(\Q(\sqrt{5}) \) None 1063.2.a.a \(1\) \(-2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
1063.2.a.b 1063.a 1.a $2$ $8.488$ \(\Q(\sqrt{5}) \) None 1063.2.a.b \(1\) \(0\) \(2\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
1063.2.a.c 1063.a 1.a $33$ $8.488$ None 1063.2.a.c \(-14\) \(-9\) \(-12\) \(-10\) $+$ $\mathrm{SU}(2)$
1063.2.a.d 1063.a 1.a $51$ $8.488$ None 1063.2.a.d \(13\) \(11\) \(14\) \(10\) $-$ $\mathrm{SU}(2)$