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Properties

Label 47.4.a
Level $47$
Weight $4$
Character orbit 47.a
Rep. character $\chi_{47}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 47 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 47.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(47))\).

Total New Old
Modular forms 13 11 2
Cusp forms 11 11 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(47\)Dim
\(+\)\(8\)
\(-\)\(3\)

Trace form

\( 11 q - 2 q^{2} + 2 q^{3} + 50 q^{4} + 8 q^{5} + 8 q^{6} - 6 q^{7} + 18 q^{8} + 51 q^{9} + O(q^{10}) \) \( 11 q - 2 q^{2} + 2 q^{3} + 50 q^{4} + 8 q^{5} + 8 q^{6} - 6 q^{7} + 18 q^{8} + 51 q^{9} + 20 q^{10} + 70 q^{11} - 7 q^{12} + 32 q^{13} - 115 q^{14} - 112 q^{15} + 2 q^{16} - 46 q^{17} - 293 q^{18} + 50 q^{19} - 200 q^{20} - 136 q^{21} + 6 q^{22} + 184 q^{23} - 133 q^{24} + 269 q^{25} - 304 q^{26} + 320 q^{27} - 492 q^{28} - 164 q^{29} - 410 q^{30} + 172 q^{31} + 207 q^{32} + 248 q^{33} + 616 q^{34} - 272 q^{35} - 398 q^{36} + 222 q^{37} + 32 q^{38} + 380 q^{39} + 14 q^{40} + 374 q^{41} + 239 q^{42} + 914 q^{43} + 1616 q^{44} + 696 q^{45} - 406 q^{46} - 235 q^{47} - 204 q^{48} + 695 q^{49} + 410 q^{50} - 1178 q^{51} - 68 q^{52} + 1206 q^{53} - 1615 q^{54} - 1100 q^{55} - 504 q^{56} + 956 q^{57} + 2176 q^{58} - 1082 q^{59} - 1646 q^{60} + 1318 q^{61} - 2108 q^{62} + 60 q^{63} - 1174 q^{64} - 2996 q^{65} - 8 q^{66} - 366 q^{67} - 2127 q^{68} - 2188 q^{69} + 4342 q^{70} + 118 q^{71} - 786 q^{72} + 58 q^{73} + 1516 q^{74} - 4122 q^{75} + 1150 q^{76} - 1380 q^{77} + 1780 q^{78} - 1582 q^{79} - 1352 q^{80} + 2435 q^{81} + 518 q^{82} - 2352 q^{83} - 1071 q^{84} + 1764 q^{85} + 1504 q^{86} - 768 q^{87} + 1108 q^{88} + 2002 q^{89} + 2122 q^{90} + 4092 q^{91} + 4800 q^{92} - 2300 q^{93} - 376 q^{94} - 1052 q^{95} + 2204 q^{96} - 342 q^{97} - 1218 q^{98} - 3262 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(47))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 47
47.4.a.a 47.a 1.a $3$ $2.773$ 3.3.1101.1 None \(-5\) \(-5\) \(-6\) \(-45\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
47.4.a.b 47.a 1.a $8$ $2.773$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(7\) \(14\) \(39\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(5+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)