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Properties

Label 128.5.h
Level $128$
Weight $5$
Character orbit 128.h
Rep. character $\chi_{128}(15,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $60$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
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: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(128, [\chi])\).

Total New Old
Modular forms 272 68 204
Cusp forms 240 60 180
Eisenstein series 32 8 24

Trace form

\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 1156 q^{23} - 4 q^{25} - 3644 q^{27} - 4 q^{29} - 8 q^{33} + 5188 q^{35} - 4 q^{37} + 2692 q^{39} - 4 q^{41} - 5564 q^{43} - 328 q^{45} + 8 q^{47} - 8384 q^{51} + 956 q^{53} + 11780 q^{55} - 4 q^{57} + 13060 q^{59} + 7548 q^{61} - 8 q^{65} - 18876 q^{67} - 19588 q^{69} - 19964 q^{71} - 4 q^{73} + 200 q^{75} + 9404 q^{77} + 50184 q^{79} - 10556 q^{83} + 2496 q^{85} - 49276 q^{87} - 4 q^{89} - 31868 q^{91} + 320 q^{93} - 8 q^{97} + 46920 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
128.5.h.a 128.h 32.h $60$ $13.231$ None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{5}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)