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Properties

Label 143.2.a
Level $143$
Weight $2$
Character orbit 143.a
Rep. character $\chi_{143}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $3$
Sturm bound $28$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(143))\).

Total New Old
Modular forms 16 11 5
Cusp forms 13 11 2
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.

\(11\)\(13\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(6\)
\(-\)\(+\)$-$\(4\)
Plus space\(+\)\(1\)
Minus space\(-\)\(10\)

Trace form

\( 11 q + 3 q^{2} + 2 q^{3} + 9 q^{4} - 4 q^{6} + 8 q^{7} + 3 q^{8} + 13 q^{9} + O(q^{10}) \) \( 11 q + 3 q^{2} + 2 q^{3} + 9 q^{4} - 4 q^{6} + 8 q^{7} + 3 q^{8} + 13 q^{9} - 2 q^{10} - 3 q^{11} + q^{13} - 16 q^{14} - 6 q^{15} + 17 q^{16} + 2 q^{17} - 9 q^{18} - 18 q^{20} - 12 q^{21} + 3 q^{22} + 14 q^{23} - 36 q^{24} + 31 q^{25} - 3 q^{26} + 2 q^{27} + 12 q^{28} - 10 q^{29} - 48 q^{30} - 10 q^{31} - 21 q^{32} - 2 q^{33} - 34 q^{34} - 28 q^{35} - 13 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} - 14 q^{40} + 14 q^{41} + 6 q^{42} + 20 q^{43} - 3 q^{44} + 2 q^{45} - 16 q^{47} - 6 q^{48} + 23 q^{49} + 25 q^{50} - 12 q^{51} + 7 q^{52} - 2 q^{53} + 36 q^{54} - 6 q^{56} + 52 q^{57} + 18 q^{58} - 6 q^{59} + 2 q^{61} + 28 q^{62} + 33 q^{64} + 2 q^{65} + 2 q^{66} + 10 q^{67} + 2 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} - q^{72} + 38 q^{73} + 50 q^{74} - 28 q^{75} - 36 q^{76} + 4 q^{77} - 2 q^{78} + 12 q^{79} + 26 q^{80} + 3 q^{81} + 18 q^{82} - 28 q^{83} + 44 q^{84} + 40 q^{85} - 8 q^{86} - 20 q^{87} + 15 q^{88} - 20 q^{89} + 14 q^{90} + 86 q^{92} + 2 q^{93} + 32 q^{94} - 52 q^{95} - 64 q^{96} + 36 q^{97} - 17 q^{98} - 9 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(143))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 13
143.2.a.a 143.a 1.a $1$ $1.142$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\)
143.2.a.b 143.a 1.a $4$ $1.142$ 4.4.1957.1 None \(3\) \(0\) \(0\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
143.2.a.c 143.a 1.a $6$ $1.142$ 6.6.194616205.1 None \(0\) \(3\) \(1\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(143))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(143)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)