Properties

Label 128.8.g
Level $128$
Weight $8$
Character orbit 128.g
Rep. character $\chi_{128}(17,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $108$
Sturm bound $128$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(128, [\chi])\).

Total New Old
Modular forms 464 116 348
Cusp forms 432 108 324
Eisenstein series 32 8 24

Trace form

\( 108 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 108 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} + 143420 q^{23} - 4 q^{25} - 476084 q^{27} - 4 q^{29} + 714992 q^{31} - 8 q^{33} - 816500 q^{35} - 4 q^{37} + 283948 q^{39} - 4 q^{41} - 366180 q^{43} + 8744 q^{45} - 3002072 q^{51} - 1815636 q^{53} + 4191012 q^{55} - 4 q^{57} + 1835940 q^{59} - 4559780 q^{61} - 10001872 q^{63} - 8 q^{65} + 1940684 q^{67} + 9580892 q^{69} + 12348708 q^{71} - 4 q^{73} - 11573008 q^{75} - 11914452 q^{77} + 9565884 q^{83} + 312496 q^{85} - 40789108 q^{87} - 4 q^{89} + 3406996 q^{91} - 8752 q^{93} + 54872008 q^{95} - 8 q^{97} + 9738480 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)