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Properties

Label 99.3.n
Level $99$
Weight $3$
Character orbit 99.n
Rep. character $\chi_{99}(5,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $176$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.n (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(99, [\chi])\).

Total New Old
Modular forms 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176 q - 9 q^{2} - 3 q^{3} - 43 q^{4} - 18 q^{5} + 14 q^{6} - 3 q^{7} - q^{9} - 16 q^{10} - 12 q^{11} - 10 q^{12} - 3 q^{13} - 9 q^{14} - 20 q^{15} + 53 q^{16} + 66 q^{18} + 24 q^{19} - 117 q^{20} - 4 q^{21}+ \cdots - 1145 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(99, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
99.3.n.a 99.n 99.n $176$ $2.698$ None 99.3.n.a \(-9\) \(-3\) \(-18\) \(-3\) $\mathrm{SU}(2)[C_{30}]$