Properties

Label 128.3.h
Level $128$
Weight $3$
Character orbit 128.h
Rep. character $\chi_{128}(15,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $28$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(128, [\chi])\).

Total New Old
Modular forms 144 36 108
Cusp forms 112 28 84
Eisenstein series 32 8 24

Trace form

\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.3.h.a 128.h 32.h $28$ $3.488$ None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)