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Properties

Label 5.8.a
Level $5$
Weight $8$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $4$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 5.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(5))\).

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
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3 q + 6 q^{2} - 28 q^{3} + 164 q^{4} - 125 q^{5} - 344 q^{6} - 1744 q^{7} + 2280 q^{8} + 5671 q^{9} + O(q^{10}) \) \( 3 q + 6 q^{2} - 28 q^{3} + 164 q^{4} - 125 q^{5} - 344 q^{6} - 1744 q^{7} + 2280 q^{8} + 5671 q^{9} - 4250 q^{10} + 4716 q^{11} - 26624 q^{12} + 7402 q^{13} + 30528 q^{14} - 8500 q^{15} - 112 q^{16} - 39594 q^{17} + 29582 q^{18} + 12820 q^{19} - 3500 q^{20} + 9816 q^{21} + 103832 q^{22} - 111168 q^{23} - 171840 q^{24} + 46875 q^{25} - 111084 q^{26} + 305720 q^{27} + 53648 q^{28} - 153870 q^{29} + 211000 q^{30} + 149936 q^{31} + 100896 q^{32} - 449216 q^{33} - 281812 q^{34} - 193000 q^{35} - 211852 q^{36} - 12894 q^{37} + 702120 q^{38} + 589352 q^{39} - 75000 q^{40} + 732246 q^{41} - 1649808 q^{42} - 75908 q^{43} + 1445808 q^{44} - 679625 q^{45} - 1485024 q^{46} - 502344 q^{47} + 1964032 q^{48} + 713779 q^{49} + 93750 q^{50} + 1754536 q^{51} - 1415784 q^{52} - 3672078 q^{53} - 288080 q^{54} - 546500 q^{55} - 431520 q^{56} + 2021840 q^{57} + 3386980 q^{58} - 2457540 q^{59} + 2512000 q^{60} + 1333066 q^{61} + 4839072 q^{62} - 1831968 q^{63} - 5032896 q^{64} + 40250 q^{65} - 6448768 q^{66} + 3719156 q^{67} - 5744952 q^{68} - 1367928 q^{69} + 1938000 q^{70} + 5725176 q^{71} + 1178760 q^{72} + 301582 q^{73} + 1109508 q^{74} - 437500 q^{75} - 876240 q^{76} + 2894832 q^{77} + 7266064 q^{78} + 4332080 q^{79} - 5102000 q^{80} - 7423037 q^{81} - 12540308 q^{82} - 3652188 q^{83} + 4967808 q^{84} + 1885750 q^{85} + 17787096 q^{86} - 20541640 q^{87} + 10712160 q^{88} + 8036190 q^{89} - 4107250 q^{90} - 11701424 q^{91} - 6316944 q^{92} + 14003664 q^{93} + 11417168 q^{94} - 8087500 q^{95} + 4714496 q^{96} - 272394 q^{97} - 38814042 q^{98} + 2910812 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\) 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
5.8.a.a 5.a 1.a $1$ $1.562$ \(\Q\) None \(-14\) \(-48\) \(125\) \(-1644\) $-$ $\mathrm{SU}(2)$ \(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
5.8.a.b 5.a 1.a $2$ $1.562$ \(\Q(\sqrt{19}) \) None \(20\) \(20\) \(-250\) \(-100\) $+$ $\mathrm{SU}(2)$ \(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)