Properties

Label 99.6.p
Level $99$
Weight $6$
Character orbit 99.p
Rep. character $\chi_{99}(2,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $464$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(99, [\chi])\).

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 15 q^{2} - 27 q^{3} + 893 q^{4} - 96 q^{5} - 30 q^{6} - 5 q^{7} + 689 q^{9} + O(q^{10}) \) \( 464 q - 15 q^{2} - 27 q^{3} + 893 q^{4} - 96 q^{5} - 30 q^{6} - 5 q^{7} + 689 q^{9} + 105 q^{11} + 1290 q^{12} - 5 q^{13} - 9 q^{14} + 2016 q^{15} + 13373 q^{16} + 9630 q^{18} - 4490 q^{19} + 5847 q^{20} + 880 q^{22} + 174 q^{23} + 790 q^{24} - 29600 q^{25} - 5901 q^{27} - 20 q^{28} + 6240 q^{29} + 19100 q^{30} + 2214 q^{31} + 27634 q^{33} + 7712 q^{34} + 26734 q^{36} - 10026 q^{37} - 54243 q^{38} - 34775 q^{39} + 5115 q^{40} - 15 q^{41} + 451 q^{42} - 59352 q^{45} - 340 q^{46} - 31701 q^{47} - 31700 q^{48} - 110449 q^{49} + 46860 q^{50} + 178935 q^{51} - 5 q^{52} - 22338 q^{55} + 243846 q^{56} + 100500 q^{57} - 15179 q^{58} - 84267 q^{59} - 214115 q^{60} - 5 q^{61} + 120315 q^{63} - 364364 q^{64} + 322065 q^{66} + 10018 q^{67} + 559440 q^{68} - 146666 q^{69} + 116310 q^{70} - 343975 q^{72} - 20 q^{73} - 15 q^{74} - 201666 q^{75} - 647373 q^{77} + 106232 q^{78} - 5 q^{79} + 85649 q^{81} + 166972 q^{82} - 67020 q^{83} + 691065 q^{84} - 5 q^{85} + 553947 q^{86} - 282836 q^{88} + 1354880 q^{90} - 29804 q^{91} - 762477 q^{92} - 810490 q^{93} - 5 q^{94} - 784935 q^{95} - 201265 q^{96} - 235167 q^{97} - 1824397 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(99, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
99.6.p.a 99.p 99.p $464$ $15.878$ None \(-15\) \(-27\) \(-96\) \(-5\) $\mathrm{SU}(2)[C_{30}]$