Properties

Label 5.6.a
Level $5$
Weight $6$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(5))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 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.

\(5\)Dim.
\(-\)\(1\)

Trace form

\( q + 2 q^{2} - 4 q^{3} - 28 q^{4} + 25 q^{5} - 8 q^{6} + 192 q^{7} - 120 q^{8} - 227 q^{9} + O(q^{10}) \) \( q + 2 q^{2} - 4 q^{3} - 28 q^{4} + 25 q^{5} - 8 q^{6} + 192 q^{7} - 120 q^{8} - 227 q^{9} + 50 q^{10} - 148 q^{11} + 112 q^{12} + 286 q^{13} + 384 q^{14} - 100 q^{15} + 656 q^{16} - 1678 q^{17} - 454 q^{18} + 1060 q^{19} - 700 q^{20} - 768 q^{21} - 296 q^{22} + 2976 q^{23} + 480 q^{24} + 625 q^{25} + 572 q^{26} + 1880 q^{27} - 5376 q^{28} - 3410 q^{29} - 200 q^{30} - 2448 q^{31} + 5152 q^{32} + 592 q^{33} - 3356 q^{34} + 4800 q^{35} + 6356 q^{36} + 182 q^{37} + 2120 q^{38} - 1144 q^{39} - 3000 q^{40} - 9398 q^{41} - 1536 q^{42} - 1244 q^{43} + 4144 q^{44} - 5675 q^{45} + 5952 q^{46} - 12088 q^{47} - 2624 q^{48} + 20057 q^{49} + 1250 q^{50} + 6712 q^{51} - 8008 q^{52} + 23846 q^{53} + 3760 q^{54} - 3700 q^{55} - 23040 q^{56} - 4240 q^{57} - 6820 q^{58} - 20020 q^{59} + 2800 q^{60} + 32302 q^{61} - 4896 q^{62} - 43584 q^{63} - 10688 q^{64} + 7150 q^{65} + 1184 q^{66} + 60972 q^{67} + 46984 q^{68} - 11904 q^{69} + 9600 q^{70} - 32648 q^{71} + 27240 q^{72} - 38774 q^{73} + 364 q^{74} - 2500 q^{75} - 29680 q^{76} - 28416 q^{77} - 2288 q^{78} - 33360 q^{79} + 16400 q^{80} + 47641 q^{81} - 18796 q^{82} + 16716 q^{83} + 21504 q^{84} - 41950 q^{85} - 2488 q^{86} + 13640 q^{87} + 17760 q^{88} + 101370 q^{89} - 11350 q^{90} + 54912 q^{91} - 83328 q^{92} + 9792 q^{93} - 24176 q^{94} + 26500 q^{95} - 20608 q^{96} - 119038 q^{97} + 40114 q^{98} + 33596 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.6.a.a 5.a 1.a $1$ $0.802$ \(\Q\) None \(2\) \(-4\) \(25\) \(192\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)