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Properties

Label 5.10.a
Level $5$
Weight $10$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $5$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(5))\).

Total New Old
Modular forms 5 3 2
Cusp forms 3 3 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
\(+\)\(1\)
\(-\)\(2\)

Trace form

\( 3 q - 18 q^{2} + 146 q^{3} + 596 q^{4} + 625 q^{5} - 4424 q^{6} + 5942 q^{7} - 12600 q^{8} - 4181 q^{9} + O(q^{10}) \) \( 3 q - 18 q^{2} + 146 q^{3} + 596 q^{4} + 625 q^{5} - 4424 q^{6} + 5942 q^{7} - 12600 q^{8} - 4181 q^{9} - 1250 q^{10} - 22224 q^{11} + 227152 q^{12} - 914 q^{13} - 474288 q^{14} + 233750 q^{15} - 144112 q^{16} + 907662 q^{17} - 1008394 q^{18} - 1305260 q^{19} + 932500 q^{20} + 601116 q^{21} + 4083944 q^{22} - 1581774 q^{23} - 3754080 q^{24} + 1171875 q^{25} - 2375964 q^{26} + 313100 q^{27} + 3305504 q^{28} + 529410 q^{29} - 3905000 q^{30} - 1751884 q^{31} - 4067808 q^{32} + 717232 q^{33} + 19920572 q^{34} - 1588750 q^{35} + 14797508 q^{36} - 36053298 q^{37} + 3821400 q^{38} + 33625748 q^{39} - 17475000 q^{40} - 15901014 q^{41} - 61126176 q^{42} + 46492906 q^{43} - 5121168 q^{44} + 5745625 q^{45} + 48651696 q^{46} + 22853022 q^{47} - 38239424 q^{48} - 9204929 q^{49} - 7031250 q^{50} - 54632204 q^{51} + 139262232 q^{52} + 703446 q^{53} - 72617360 q^{54} + 43870000 q^{55} - 10570560 q^{56} + 87911000 q^{57} - 231081500 q^{58} - 140181180 q^{59} + 78130000 q^{60} - 228831074 q^{61} + 331039104 q^{62} + 198326886 q^{63} - 213219264 q^{64} + 144346250 q^{65} + 430656992 q^{66} - 45604738 q^{67} - 265631256 q^{68} - 153977772 q^{69} - 254010000 q^{70} - 197098404 q^{71} - 139728600 q^{72} + 533029126 q^{73} + 639347892 q^{74} + 57031250 q^{75} + 354443280 q^{76} - 996146736 q^{77} - 794572208 q^{78} + 101918360 q^{79} - 299990000 q^{80} - 486443657 q^{81} - 268068116 q^{82} + 1664055066 q^{83} + 1378576512 q^{84} - 51263750 q^{85} - 161213784 q^{86} - 523405300 q^{87} - 368023200 q^{88} + 810150030 q^{89} - 697116250 q^{90} + 189838876 q^{91} - 700560288 q^{92} - 31047288 q^{93} - 1063675648 q^{94} + 445137500 q^{95} + 1404784256 q^{96} + 618891222 q^{97} - 621046626 q^{98} - 1654739152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.10.a.a 5.a 1.a $1$ $2.575$ \(\Q\) None 5.10.a.a \(-8\) \(-114\) \(-625\) \(4242\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
5.10.a.b 5.a 1.a $2$ $2.575$ \(\Q(\sqrt{1009}) \) None 5.10.a.b \(-10\) \(260\) \(1250\) \(1700\) $-$ $\mathrm{SU}(2)$ \(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)