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Properties

Label 143.4.a
Level $143$
Weight $4$
Character orbit 143.a
Rep. character $\chi_{143}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $4$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(143))\).

Total New Old
Modular forms 44 30 14
Cusp forms 40 30 10
Eisenstein series 4 0 4

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
\(+\)\(+\)$+$\(9\)
\(+\)\(-\)$-$\(4\)
\(-\)\(+\)$-$\(6\)
\(-\)\(-\)$+$\(11\)
Plus space\(+\)\(20\)
Minus space\(-\)\(10\)

Trace form

\( 30 q + 4 q^{3} + 144 q^{4} + 12 q^{5} - 8 q^{6} + 84 q^{8} + 182 q^{9} + O(q^{10}) \) \( 30 q + 4 q^{3} + 144 q^{4} + 12 q^{5} - 8 q^{6} + 84 q^{8} + 182 q^{9} - 108 q^{10} + 44 q^{11} + 284 q^{12} - 208 q^{14} + 212 q^{15} + 408 q^{16} + 160 q^{17} + 336 q^{18} + 88 q^{19} + 72 q^{20} + 16 q^{21} - 36 q^{23} - 984 q^{24} + 958 q^{25} + 156 q^{26} - 176 q^{27} + 228 q^{28} - 8 q^{29} + 908 q^{30} + 56 q^{31} + 612 q^{32} - 44 q^{33} + 1160 q^{34} + 412 q^{35} + 1550 q^{36} + 68 q^{37} - 1286 q^{38} - 672 q^{40} - 528 q^{41} - 1906 q^{42} + 96 q^{43} + 440 q^{44} - 1336 q^{45} + 8 q^{46} - 268 q^{47} - 710 q^{48} + 2046 q^{49} - 2892 q^{50} + 124 q^{51} + 812 q^{53} - 3868 q^{54} - 396 q^{55} - 1078 q^{56} - 832 q^{57} - 748 q^{58} - 28 q^{59} - 4332 q^{60} + 1672 q^{61} + 848 q^{62} + 2440 q^{63} - 1752 q^{64} - 416 q^{65} - 550 q^{66} - 1204 q^{67} + 468 q^{68} - 3548 q^{69} - 372 q^{70} + 1568 q^{71} + 2588 q^{72} + 360 q^{73} - 2920 q^{74} + 2060 q^{75} - 736 q^{76} - 176 q^{77} - 598 q^{78} - 1024 q^{79} - 288 q^{80} + 5326 q^{81} + 3068 q^{82} - 2256 q^{83} - 9700 q^{84} - 112 q^{85} - 6032 q^{86} + 3632 q^{87} + 4832 q^{89} - 4256 q^{90} + 728 q^{91} - 1394 q^{92} + 1524 q^{93} + 1160 q^{94} - 1768 q^{95} + 3020 q^{96} + 2860 q^{98} + 968 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(143))\) 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
143.4.a.a 143.a 1.a $4$ $8.437$ 4.4.297133.1 None \(0\) \(-4\) \(-6\) \(-17\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
143.4.a.b 143.a 1.a $6$ $8.437$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(-6\) \(-8\) \(-53\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4+\cdots)q^{4}+\cdots\)
143.4.a.c 143.a 1.a $9$ $8.437$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(8\) \(30\) \(25\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
143.4.a.d 143.a 1.a $11$ $8.437$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(6\) \(6\) \(-4\) \(45\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(143))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(143)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)