↑

Properties

Label 176.6.w
Level $176$
Weight $6$
Character orbit 176.w
Rep. character $\chi_{176}(5,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $944$
Sturm bound $144$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 176.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(176, [\chi])\).

Total New Old
Modular forms 976 976 0
Cusp forms 944 944 0
Eisenstein series 32 32 0

Trace form

\( 944 q - 6 q^{2} - 6 q^{3} + 38 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{8} + O(q^{10}) \) \( 944 q - 6 q^{2} - 6 q^{3} + 38 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{8} - 16 q^{10} + 596 q^{11} - 1600 q^{12} - 6 q^{13} + 4340 q^{14} - 12 q^{15} + 4174 q^{16} - 12 q^{17} + 2296 q^{18} - 6 q^{19} - 3806 q^{20} - 988 q^{21} + 20710 q^{22} - 16166 q^{24} + 17704 q^{26} - 978 q^{27} + 12482 q^{28} - 8150 q^{29} + 4226 q^{30} - 12 q^{31} + 44144 q^{32} - 16 q^{33} + 6492 q^{34} - 12506 q^{35} - 4102 q^{36} - 31950 q^{37} - 37274 q^{38} - 31186 q^{40} - 46330 q^{42} + 30744 q^{43} + 44954 q^{44} - 11544 q^{45} + 63514 q^{46} - 12 q^{47} + 47014 q^{48} + 509000 q^{49} + 37546 q^{50} + 966 q^{51} + 62602 q^{52} + 74178 q^{53} - 300724 q^{54} + 170176 q^{56} - 50386 q^{58} + 14474 q^{59} + 30454 q^{60} - 6 q^{61} + 205206 q^{62} + 24292 q^{63} - 144106 q^{64} - 32 q^{65} + 54126 q^{66} + 61144 q^{67} + 76140 q^{68} + 1452 q^{69} - 37100 q^{70} + 355102 q^{72} - 269052 q^{74} + 301394 q^{75} - 917904 q^{76} - 41070 q^{77} - 353380 q^{78} - 249652 q^{79} + 171460 q^{80} + 1338432 q^{81} + 163626 q^{82} + 189654 q^{83} + 265608 q^{84} + 12494 q^{85} - 149106 q^{86} + 606622 q^{88} + 341748 q^{90} - 202682 q^{91} + 728442 q^{92} + 966 q^{93} + 242444 q^{94} + 577588 q^{95} - 148906 q^{96} - 12 q^{97} - 2061020 q^{98} - 926340 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(176, [\chi])\) into newform subspaces

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