↑

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 $1$

Related objects

Downloads

Learn more about

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

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

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 13
143.2.a.a \(1\) \(1.142\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(q-q^{3}-2q^{4}-q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\)
143.2.a.b \(4\) \(1.142\) 4.4.1957.1 None \(3\) \(0\) \(0\) \(6\) \(-\) \(+\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
143.2.a.c \(6\) \(1.142\) 6.6.194616205.1 None \(0\) \(3\) \(1\) \(4\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

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

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