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Properties

Label 19.8.c
Level $19$
Weight $8$
Character orbit 19.c
Rep. character $\chi_{19}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $1$
Sturm bound $13$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 19.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(19, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

Trace form

\( 20 q - 9 q^{2} - 68 q^{3} - 475 q^{4} + 545 q^{6} - 1456 q^{7} + 2322 q^{8} - 6052 q^{9} + O(q^{10}) \) \( 20 q - 9 q^{2} - 68 q^{3} - 475 q^{4} + 545 q^{6} - 1456 q^{7} + 2322 q^{8} - 6052 q^{9} - 1732 q^{10} + 7248 q^{11} + 30354 q^{12} - 12888 q^{13} - 7578 q^{14} - 13244 q^{15} - 1027 q^{16} - 63024 q^{17} - 93132 q^{18} + 72752 q^{19} + 156588 q^{20} - 18148 q^{21} + 23317 q^{22} + 56532 q^{23} - 45783 q^{24} - 86450 q^{25} + 198888 q^{26} - 58424 q^{27} + 287154 q^{28} - 178704 q^{29} - 384728 q^{30} + 292880 q^{31} - 640377 q^{32} - 408506 q^{33} + 262520 q^{34} + 621336 q^{35} + 486770 q^{36} - 1408096 q^{37} + 205086 q^{38} + 815736 q^{39} + 925470 q^{40} - 926994 q^{41} - 936278 q^{42} - 1837988 q^{43} - 511371 q^{44} + 1933888 q^{45} + 5286604 q^{46} + 1416996 q^{47} + 144447 q^{48} + 681652 q^{49} - 4138710 q^{50} - 2505268 q^{51} - 3586666 q^{52} - 356328 q^{53} + 228251 q^{54} + 865080 q^{55} - 3446916 q^{56} + 1706388 q^{57} + 11381072 q^{58} - 2297052 q^{59} - 2670886 q^{60} - 1496632 q^{61} + 1024512 q^{62} - 88344 q^{63} + 1773542 q^{64} + 585816 q^{65} - 2197457 q^{66} - 6475124 q^{67} + 4032876 q^{68} + 6329016 q^{69} - 12864588 q^{70} - 8042868 q^{71} + 9440430 q^{72} - 485798 q^{73} + 6232812 q^{74} + 20769104 q^{75} - 6953413 q^{76} + 8525208 q^{77} - 7305352 q^{78} - 5604964 q^{79} - 448650 q^{80} + 7714382 q^{81} + 2321819 q^{82} - 14535552 q^{83} - 42654252 q^{84} - 12944460 q^{85} + 2747550 q^{86} + 6535176 q^{87} + 18704514 q^{88} + 5024424 q^{89} - 15096092 q^{90} + 28222480 q^{91} - 30094896 q^{92} + 26255544 q^{93} + 51863760 q^{94} - 43373748 q^{95} + 116808910 q^{96} - 12341194 q^{97} + 1851183 q^{98} - 26743912 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
19.8.c.a 19.c 19.c $20$ $5.935$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-9\) \(-68\) \(0\) \(-1456\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(7\beta _{2}+\beta _{7})q^{3}+(-48+\cdots)q^{4}+\cdots\)