Properties

Label 160.6.x
Level $160$
Weight $6$
Character orbit 160.x
Rep. character $\chi_{160}(21,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $320$
Sturm bound $144$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(160, [\chi])\).

Total New Old
Modular forms 488 320 168
Cusp forms 472 320 152
Eisenstein series 16 0 16

Trace form

\( 320 q + O(q^{10}) \) \( 320 q + 200 q^{10} - 2480 q^{14} - 8360 q^{16} + 3240 q^{18} + 7600 q^{20} + 13592 q^{22} - 3344 q^{23} - 32480 q^{24} + 14928 q^{27} + 4360 q^{28} + 37160 q^{32} + 12760 q^{34} - 68856 q^{36} - 69640 q^{38} + 89808 q^{39} + 107240 q^{42} - 64144 q^{43} - 7440 q^{44} - 126656 q^{46} + 20880 q^{51} - 36944 q^{52} + 98912 q^{53} + 114008 q^{54} + 291320 q^{56} - 25992 q^{58} + 28960 q^{59} - 96160 q^{61} - 127224 q^{62} + 317520 q^{63} + 187440 q^{64} + 144880 q^{66} + 122320 q^{67} + 7152 q^{68} + 44640 q^{69} - 143840 q^{71} - 414072 q^{72} - 53960 q^{74} - 256000 q^{76} + 29792 q^{77} + 722328 q^{78} + 96800 q^{80} + 658480 q^{83} - 492520 q^{84} - 630824 q^{86} - 223280 q^{88} + 142200 q^{90} - 400224 q^{91} - 313192 q^{92} - 452792 q^{94} - 577600 q^{95} + 910184 q^{96} + 1602480 q^{98} - 339520 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)