Properties

Label 99.8.p
Level $99$
Weight $8$
Character orbit 99.p
Rep. character $\chi_{99}(2,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $656$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.p (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 656 q - 15 q^{2} + 33 q^{3} + 5117 q^{4} - 222 q^{5} + 1710 q^{6} - 5 q^{7} - 5725 q^{9} + O(q^{10}) \) \( 656 q - 15 q^{2} + 33 q^{3} + 5117 q^{4} - 222 q^{5} + 1710 q^{6} - 5 q^{7} - 5725 q^{9} + 9393 q^{11} - 27942 q^{12} - 5 q^{13} - 9 q^{14} + 22800 q^{15} + 311549 q^{16} + 120870 q^{18} - 10490 q^{19} + 55671 q^{20} - 35516 q^{22} - 140658 q^{23} - 330890 q^{24} - 1192250 q^{25} - 23433 q^{27} - 20 q^{28} + 450390 q^{29} - 210220 q^{30} - 99330 q^{31} - 343484 q^{33} + 177704 q^{34} + 177022 q^{36} + 151770 q^{37} + 4281453 q^{38} + 3829465 q^{39} + 81915 q^{40} - 15 q^{41} - 591509 q^{42} + 4078212 q^{45} - 1300 q^{46} + 986667 q^{47} + 6404620 q^{48} - 8235433 q^{49} + 1171860 q^{50} - 53985 q^{51} - 5 q^{52} + 1333566 q^{55} + 2569734 q^{56} + 12786480 q^{57} - 1038899 q^{58} + 9215937 q^{59} + 14658901 q^{60} - 5 q^{61} - 459885 q^{63} - 35716364 q^{64} - 6836247 q^{66} - 8049662 q^{67} - 17851680 q^{68} + 23301904 q^{69} - 1622346 q^{70} + 28129145 q^{72} - 20 q^{73} - 15 q^{74} + 37489194 q^{75} - 46153767 q^{77} - 37220872 q^{78} - 5 q^{79} - 31488949 q^{81} - 5685788 q^{82} + 40067400 q^{83} + 36520905 q^{84} - 5 q^{85} + 21934239 q^{86} + 25796812 q^{88} + 6237200 q^{90} + 28718692 q^{91} - 50648541 q^{92} + 32879354 q^{93} - 5 q^{94} + 48932505 q^{95} + 157922135 q^{96} + 20930877 q^{97} + 165749363 q^{99} + O(q^{100}) \)

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.p.a 99.p 99.p $656$ $30.926$ None \(-15\) \(33\) \(-222\) \(-5\) $\mathrm{SU}(2)[C_{30}]$