Properties

Label 96.9.m
Level $96$
Weight $9$
Character orbit 96.m
Rep. character $\chi_{96}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $256$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 96.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(96, [\chi])\).

Total New Old
Modular forms 520 256 264
Cusp forms 504 256 248
Eisenstein series 16 0 16

Trace form

\( 256 q + O(q^{10}) \) \( 256 q - 35000 q^{10} + 45360 q^{12} - 291168 q^{14} + 111352 q^{16} + 52488 q^{18} - 1380000 q^{20} - 540184 q^{22} - 1691136 q^{23} + 149688 q^{24} - 3364200 q^{26} + 3615240 q^{28} - 4840920 q^{32} - 8276520 q^{34} + 4831488 q^{35} + 16322040 q^{38} + 14395976 q^{40} + 3719424 q^{43} + 22652136 q^{44} - 11790688 q^{46} + 5145192 q^{50} + 27724032 q^{51} + 33503192 q^{52} + 10717440 q^{53} - 9920232 q^{54} - 46326784 q^{55} - 56874888 q^{56} + 11797280 q^{58} + 89877504 q^{59} + 81854064 q^{60} - 48952064 q^{61} + 43931664 q^{62} - 5886312 q^{64} - 113657904 q^{66} - 37352192 q^{67} + 1507800 q^{68} + 17273088 q^{69} + 288032952 q^{70} + 159664128 q^{71} - 56030304 q^{74} + 25837056 q^{75} - 264189016 q^{76} + 189928704 q^{77} - 183989880 q^{78} - 144406528 q^{79} + 360917832 q^{80} + 428364200 q^{82} + 18570048 q^{86} - 463482160 q^{88} - 350400768 q^{91} + 152934384 q^{92} + 354090144 q^{94} - 343391400 q^{96} - 239975856 q^{98} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.9.m.a 96.m 32.h $256$ $39.108$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{9}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)