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Properties

Label 5.16.a
Level $5$
Weight $16$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $8$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(5))\).

Total New Old
Modular forms 9 5 4
Cusp forms 7 5 2
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
\(+\)\(3\)
\(-\)\(2\)

Trace form

\( 5 q - 306 q^{2} + 5258 q^{3} + 59940 q^{4} - 78125 q^{5} + 1919560 q^{6} - 4326106 q^{7} + 3018600 q^{8} + 20955685 q^{9} + O(q^{10}) \) \( 5 q - 306 q^{2} + 5258 q^{3} + 59940 q^{4} - 78125 q^{5} + 1919560 q^{6} - 4326106 q^{7} + 3018600 q^{8} + 20955685 q^{9} - 24531250 q^{10} + 121338960 q^{11} + 258612544 q^{12} - 248058342 q^{13} - 1073267520 q^{14} - 138906250 q^{15} + 1505992080 q^{16} - 4320523806 q^{17} + 5282035958 q^{18} - 775009500 q^{19} + 1497812500 q^{20} + 5804469060 q^{21} - 12567256712 q^{22} + 710131458 q^{23} - 221515200 q^{24} + 30517578125 q^{25} + 112557966660 q^{26} - 147114144100 q^{27} - 151565090608 q^{28} + 235886996550 q^{29} - 174280625000 q^{30} - 68488976140 q^{31} - 641389196256 q^{32} + 783433600816 q^{33} + 587053169980 q^{34} - 196538593750 q^{35} - 15749665420 q^{36} - 821087058806 q^{37} + 1685828089800 q^{38} + 2484580240820 q^{39} - 2369596875000 q^{40} - 1072810264890 q^{41} - 9276717500112 q^{42} + 2542794692658 q^{43} + 13640356674480 q^{44} - 5849013828125 q^{45} + 1555694787360 q^{46} - 13697280311106 q^{47} + 3181970775808 q^{48} + 16879264557065 q^{49} - 1867675781250 q^{50} + 11500945220260 q^{51} - 46582060820456 q^{52} + 15422281085058 q^{53} + 29202669382000 q^{54} - 9719683750000 q^{55} + 10606660024800 q^{56} - 43954185568600 q^{57} + 55409886578900 q^{58} + 20237006867700 q^{59} - 20352905000000 q^{60} - 795505275990 q^{61} - 62750540178912 q^{62} - 52433003461242 q^{63} - 29818237389760 q^{64} - 5174632656250 q^{65} + 75224119483520 q^{66} + 184267352518694 q^{67} - 114413077226808 q^{68} - 106467212395380 q^{69} + 102936686250000 q^{70} - 247301572468740 q^{71} + 453115808123400 q^{72} + 121189601096058 q^{73} - 66925257585420 q^{74} + 32092285156250 q^{75} - 224365667320400 q^{76} + 217227988844688 q^{77} - 536216138865584 q^{78} - 568365724733800 q^{79} + 323035011250000 q^{80} + 86479922549905 q^{81} + 823442138616188 q^{82} + 19801694051058 q^{83} - 1204388014907520 q^{84} + 266986175468750 q^{85} + 56619581135160 q^{86} + 1316818252719500 q^{87} - 593233866448800 q^{88} - 1060447537450350 q^{89} + 271194423593750 q^{90} + 1584879389290060 q^{91} - 594285852866256 q^{92} - 343159219528584 q^{93} + 1273046114801680 q^{94} - 634123276562500 q^{95} - 1485879758256640 q^{96} - 1472059883554406 q^{97} + 1919570413071342 q^{98} + 1183651192813520 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(5))\) 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
5.16.a.a 5.a 1.a $2$ $7.135$ \(\Q(\sqrt{3169}) \) None \(-310\) \(1740\) \(156250\) \(-3420900\) $-$ $\mathrm{SU}(2)$ \(q+(-155-\beta )q^{2}+(870-2\beta )q^{3}+(19778+\cdots)q^{4}+\cdots\)
5.16.a.b 5.a 1.a $3$ $7.135$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(4\) \(3518\) \(-234375\) \(-905206\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1170-2^{4}\beta _{1}+8\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)