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Properties

Label 19.9.d
Level $19$
Weight $9$
Character orbit 19.d
Rep. character $\chi_{19}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $26$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 19.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(19, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 0
Eisenstein series 4 4 0

Trace form

\( 26 q - 3 q^{2} - 171 q^{3} + 2029 q^{4} + 278 q^{5} - 275 q^{6} - 7504 q^{7} + 25574 q^{9} + O(q^{10}) \) \( 26 q - 3 q^{2} - 171 q^{3} + 2029 q^{4} + 278 q^{5} - 275 q^{6} - 7504 q^{7} + 25574 q^{9} + 2784 q^{10} - 26530 q^{11} - 88254 q^{13} + 122358 q^{14} + 246474 q^{15} - 375891 q^{16} + 14378 q^{17} + 481391 q^{19} - 627532 q^{20} + 43494 q^{21} + 680829 q^{22} - 60892 q^{23} + 162409 q^{24} - 1007371 q^{25} + 507252 q^{26} - 3333872 q^{28} - 109884 q^{29} + 6068704 q^{30} - 4485465 q^{32} - 1807311 q^{33} + 3137142 q^{34} + 542014 q^{35} - 10525926 q^{36} + 10867338 q^{38} + 3117892 q^{39} + 9687504 q^{40} + 16439685 q^{41} - 2916908 q^{42} - 7298466 q^{43} - 16490521 q^{44} - 32357068 q^{45} - 2654026 q^{47} + 71125161 q^{48} + 7642254 q^{49} - 68110752 q^{51} - 53430522 q^{52} + 9445632 q^{53} + 34820561 q^{54} - 21205876 q^{55} + 22269764 q^{57} - 5883596 q^{58} + 21006195 q^{59} + 209639046 q^{60} - 4744062 q^{61} - 58089324 q^{62} - 66326902 q^{63} - 101431266 q^{64} - 119841553 q^{66} + 102477003 q^{67} + 70594196 q^{68} - 122733774 q^{70} + 7935738 q^{71} + 46393554 q^{72} + 26449961 q^{73} - 104007498 q^{74} + 99727859 q^{76} - 38226872 q^{77} + 128944746 q^{78} + 148452324 q^{79} - 128268802 q^{80} + 87756319 q^{81} + 38787119 q^{82} - 143066578 q^{83} - 13463814 q^{85} + 259064682 q^{86} - 275422336 q^{87} + 62156112 q^{89} - 289880070 q^{90} + 299224752 q^{91} - 267189628 q^{92} + 264058076 q^{93} + 91155758 q^{95} - 508960698 q^{96} - 123441153 q^{97} - 579159765 q^{98} + 35656504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
19.9.d.a 19.d 19.d $26$ $7.740$ None \(-3\) \(-171\) \(278\) \(-7504\) $\mathrm{SU}(2)[C_{6}]$