Properties

Label 99.8.d
Level $99$
Weight $8$
Character orbit 99.d
Rep. character $\chi_{99}(98,\cdot)$
Character field $\Q$
Dimension $28$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
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 88 28 60
Cusp forms 80 28 52
Eisenstein series 8 0 8

Trace form

\( 28 q + 1792 q^{4} + O(q^{10}) \) \( 28 q + 1792 q^{4} + 136936 q^{16} + 69696 q^{22} - 877308 q^{25} - 21616 q^{31} + 161304 q^{34} + 408464 q^{37} - 5023892 q^{49} + 439472 q^{55} + 2851344 q^{58} - 15376208 q^{64} - 17729872 q^{67} + 3438408 q^{70} + 54779784 q^{82} + 26540976 q^{88} - 19094256 q^{91} + 10561400 q^{97} + O(q^{100}) \)

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.d.a 99.d 33.d $28$ $30.926$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{8}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)