Properties

Label 99.8.j
Level $99$
Weight $8$
Character orbit 99.j
Rep. character $\chi_{99}(8,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $112$
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.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
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 352 112 240
Cusp forms 320 112 208
Eisenstein series 32 0 32

Trace form

\( 112 q - 1792 q^{4} + O(q^{10}) \) \( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97} + O(q^{100}) \)

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.j.a 99.j 33.f $112$ $30.926$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

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