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Properties

Label 128.4.g
Level $128$
Weight $4$
Character orbit 128.g
Rep. character $\chi_{128}(17,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $44$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(128, [\chi])\).

Total New Old
Modular forms 208 52 156
Cusp forms 176 44 132
Eisenstein series 32 8 24

Trace form

\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.4.g.a 128.g 32.g $44$ $7.552$ None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{4}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)