↑

Properties

Label 342.10.u
Level $342$
Weight $10$
Character orbit 342.u
Rep. character $\chi_{342}(55,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $450$
Sturm bound $600$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 342.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(342, [\chi])\).

Total New Old
Modular forms 3288 450 2838
Cusp forms 3192 450 2742
Eisenstein series 96 0 96

Trace form

\( 450 q - 11436 q^{7} + 12288 q^{8} + O(q^{10}) \) \( 450 q - 11436 q^{7} + 12288 q^{8} - 22596 q^{11} + 405450 q^{13} + 193728 q^{14} - 1027254 q^{17} - 1764702 q^{19} - 872448 q^{20} - 6018432 q^{22} + 3096012 q^{23} - 9879924 q^{25} - 1147296 q^{26} - 437760 q^{28} - 3513852 q^{29} + 2615190 q^{31} + 319680 q^{34} + 1805190 q^{35} - 24758556 q^{37} + 7363536 q^{38} - 40057839 q^{41} - 266472264 q^{43} + 60527616 q^{44} - 84226944 q^{46} - 179184516 q^{47} - 1326760491 q^{49} + 246449616 q^{50} + 41518080 q^{52} - 18247230 q^{53} - 406313784 q^{55} - 142884864 q^{56} - 103047552 q^{58} + 122879253 q^{59} + 324542838 q^{61} + 693800352 q^{62} - 3774873600 q^{64} + 186804270 q^{65} + 352035885 q^{67} + 185345280 q^{68} + 943073088 q^{70} + 2370357858 q^{71} - 381573618 q^{73} + 309873888 q^{74} - 235451904 q^{76} + 426872076 q^{77} - 239800776 q^{79} + 1998537648 q^{82} + 1455690732 q^{83} - 207123180 q^{85} - 365688384 q^{86} - 359817216 q^{88} + 1702042344 q^{89} - 1060402260 q^{91} + 1988014080 q^{92} + 4029810240 q^{94} + 6454978638 q^{95} + 6894317217 q^{97} - 5092520832 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)