Properties

Label 96.8.n
Level $96$
Weight $8$
Character orbit 96.n
Rep. character $\chi_{96}(13,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $224$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 96.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(96, [\chi])\).

Total New Old
Modular forms 456 224 232
Cusp forms 440 224 216
Eisenstein series 16 0 16

Trace form

\( 224 q + O(q^{10}) \) \( 224 q + 13000 q^{10} - 30672 q^{12} + 52384 q^{14} + 21112 q^{16} - 40824 q^{18} - 164000 q^{20} + 511464 q^{22} + 286832 q^{23} - 81864 q^{24} + 727960 q^{26} + 390920 q^{28} + 1429968 q^{31} - 1071320 q^{32} + 403160 q^{34} - 1633008 q^{35} + 1244920 q^{38} - 4089528 q^{40} - 732368 q^{43} + 3370472 q^{44} + 2715808 q^{46} + 2317416 q^{50} - 2993328 q^{51} - 8882216 q^{52} + 3631264 q^{53} + 157464 q^{54} + 4191008 q^{55} + 10737272 q^{56} + 7269664 q^{58} + 3671872 q^{59} - 2168208 q^{60} + 4559776 q^{61} - 10347504 q^{62} - 4000752 q^{63} - 22412520 q^{64} - 3757104 q^{66} + 776272 q^{67} + 17922136 q^{68} - 9580896 q^{69} - 1696200 q^{70} + 24697408 q^{71} - 21862880 q^{74} - 11260512 q^{75} + 5188008 q^{76} + 23828896 q^{77} - 14742648 q^{78} + 69474376 q^{80} - 6997080 q^{82} - 39909568 q^{86} - 37691824 q^{88} + 3406992 q^{91} - 684560 q^{92} + 50770592 q^{94} + 54100440 q^{96} - 52426160 q^{98} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.8.n.a 96.n 32.g $224$ $29.989$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{8}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)