Properties

Label 99.8.m
Level $99$
Weight $8$
Character orbit 99.m
Rep. character $\chi_{99}(4,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $656$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.m (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(99, [\chi])\).

Total New Old
Modular forms 688 688 0
Cusp forms 656 656 0
Eisenstein series 32 32 0

Trace form

\( 656 q + 13 q^{2} - 45 q^{3} + 5117 q^{4} - 74 q^{5} - 1294 q^{6} - 3 q^{7} - 6668 q^{8} + 1163 q^{9} + O(q^{10}) \) \( 656 q + 13 q^{2} - 45 q^{3} + 5117 q^{4} - 74 q^{5} - 1294 q^{6} - 3 q^{7} - 6668 q^{8} + 1163 q^{9} - 544 q^{10} + 3131 q^{11} + 18650 q^{12} - 3 q^{13} - 515 q^{14} - 21416 q^{15} + 311549 q^{16} - 6704 q^{17} - 77334 q^{18} + 6270 q^{19} - 84099 q^{20} + 256832 q^{21} + 34996 q^{22} + 221694 q^{23} - 53994 q^{24} + 1120250 q^{25} - 133804 q^{26} + 29295 q^{27} - 66060 q^{28} + 487120 q^{29} + 647118 q^{30} + 99324 q^{31} - 1802760 q^{32} - 1299668 q^{33} - 177208 q^{34} - 1389642 q^{35} + 154614 q^{36} - 151794 q^{37} - 471605 q^{38} - 224855 q^{39} + 106583 q^{40} + 975505 q^{41} - 5925059 q^{42} - 720650 q^{43} - 3117934 q^{44} - 1511840 q^{45} + 756 q^{46} + 158821 q^{47} - 6239960 q^{48} + 8235427 q^{49} + 3717606 q^{50} - 748887 q^{51} - 65283 q^{52} - 8401720 q^{53} - 29174618 q^{54} - 1333598 q^{55} + 4218834 q^{56} + 4108974 q^{57} + 1037869 q^{58} - 3883405 q^{59} + 9556791 q^{60} - 3 q^{61} - 1378934 q^{62} - 8591443 q^{63} - 35716364 q^{64} - 20951300 q^{65} - 23570487 q^{66} + 3711370 q^{67} + 5780506 q^{68} - 16405140 q^{69} - 7188604 q^{70} + 28467282 q^{71} + 20534207 q^{72} + 9608280 q^{73} + 43858953 q^{74} - 13191764 q^{75} + 434296 q^{76} + 6119027 q^{77} + 22508624 q^{78} - 9090579 q^{79} + 5818856 q^{80} + 16699595 q^{81} - 5685788 q^{82} + 49843106 q^{83} + 48240411 q^{84} + 2791747 q^{85} - 27455591 q^{86} - 121536 q^{87} - 21667796 q^{88} + 16511344 q^{89} - 141533716 q^{90} + 22130348 q^{91} - 55193155 q^{92} - 69307496 q^{93} - 5201099 q^{94} + 7179039 q^{95} + 28278755 q^{96} - 26736381 q^{97} + 197330000 q^{98} + 29658991 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(99, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
99.8.m.a 99.m 99.m $656$ $30.926$ None \(13\) \(-45\) \(-74\) \(-3\) $\mathrm{SU}(2)[C_{15}]$