Properties

Label 99.8.g
Level $99$
Weight $8$
Character orbit 99.g
Rep. character $\chi_{99}(32,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $164$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 172 172 0
Cusp forms 164 164 0
Eisenstein series 8 8 0

Trace form

\( 164 q - 43 q^{3} - 5122 q^{4} + 207 q^{5} - 25 q^{9} + O(q^{10}) \) \( 164 q - 43 q^{3} - 5122 q^{4} + 207 q^{5} - 25 q^{9} - 9408 q^{11} + 11282 q^{12} - 6 q^{14} - 14060 q^{15} - 311554 q^{16} - 53766 q^{20} + 35511 q^{22} + 140628 q^{23} + 1192245 q^{25} + 337178 q^{27} + 99325 q^{31} + 92354 q^{33} - 177714 q^{34} + 281648 q^{36} - 151790 q^{37} + 888852 q^{38} + 1782594 q^{42} + 38863 q^{45} - 986682 q^{47} + 4746920 q^{48} + 8235428 q^{49} - 1333586 q^{55} - 2569764 q^{56} - 691746 q^{58} + 12923613 q^{59} - 1601426 q^{60} + 35717624 q^{64} - 11217708 q^{66} + 699007 q^{67} - 3513479 q^{69} + 5740056 q^{70} - 14839869 q^{75} + 6403392 q^{77} - 20423958 q^{78} - 4629541 q^{81} - 3789672 q^{82} - 3411414 q^{86} + 12330003 q^{88} + 13655508 q^{91} - 39357234 q^{92} + 316801 q^{93} + 18791833 q^{97} + 3239687 q^{99} + O(q^{100}) \)

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.g.a 99.g 99.g $4$ $30.926$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) \(0\) \(83\) \(-1521\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(48\beta _{2}+13\beta _{3})q^{3}+2^{7}\beta _{2}q^{4}+(-507+\cdots)q^{5}+\cdots\)
99.8.g.b 99.g 99.g $160$ $30.926$ None \(0\) \(-126\) \(1728\) \(0\) $\mathrm{SU}(2)[C_{6}]$