↑

Properties

Label 361.4.k
Level $361$
Weight $4$
Character orbit 361.k
Rep. character $\chi_{361}(4,\cdot)$
Character field $\Q(\zeta_{171})$
Dimension $10152$
Sturm bound $126$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 361.k (of order \(171\) and degree \(108\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 361 \)
Character field: \(\Q(\zeta_{171})\)
Sturm bound: \(126\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(361, [\chi])\).

Total New Old
Modular forms 10368 10368 0
Cusp forms 10152 10152 0
Eisenstein series 216 216 0

Trace form

\( 10152 q - 108 q^{2} - 111 q^{3} - 90 q^{4} - 108 q^{5} - 156 q^{6} - 111 q^{7} - 39 q^{8} - 63 q^{9} + O(q^{10}) \) \( 10152 q - 108 q^{2} - 111 q^{3} - 90 q^{4} - 108 q^{5} - 156 q^{6} - 111 q^{7} - 39 q^{8} - 63 q^{9} - 189 q^{10} - 111 q^{11} + 105 q^{12} + 42 q^{13} - 207 q^{14} + 78 q^{15} - 618 q^{16} - 240 q^{17} - 378 q^{18} - 660 q^{19} + 468 q^{20} - 567 q^{21} + 1488 q^{22} - 120 q^{23} - 306 q^{24} + 384 q^{25} + 117 q^{26} + 4917 q^{27} + 1254 q^{28} + 516 q^{29} + 288 q^{30} + 477 q^{31} - 261 q^{32} + 3852 q^{33} + 294 q^{34} - 2115 q^{35} - 1173 q^{36} - 42 q^{37} + 2994 q^{38} + 810 q^{39} - 3000 q^{40} + 363 q^{41} - 351 q^{42} + 8190 q^{43} + 3309 q^{44} + 915 q^{45} + 1614 q^{46} + 1128 q^{47} - 9936 q^{48} + 13395 q^{49} + 1674 q^{50} - 123 q^{51} - 2847 q^{52} + 186 q^{53} - 7026 q^{54} - 429 q^{55} - 4752 q^{56} - 3456 q^{57} + 4002 q^{58} - 2211 q^{59} - 1230 q^{60} + 2202 q^{61} + 1206 q^{62} + 2865 q^{63} + 17961 q^{64} + 2319 q^{65} + 1476 q^{66} - 171 q^{67} + 1143 q^{68} - 29754 q^{69} - 29997 q^{70} + 678 q^{71} + 1572 q^{72} - 4182 q^{73} + 16347 q^{74} - 1446 q^{75} - 5652 q^{76} - 792 q^{77} - 2235 q^{78} - 1938 q^{79} + 2625 q^{80} - 1650 q^{81} - 2319 q^{82} + 3 q^{83} + 1323 q^{84} + 2280 q^{85} - 73860 q^{86} + 345 q^{87} - 1215 q^{88} + 2892 q^{89} - 62982 q^{90} + 29733 q^{91} + 1338 q^{92} + 21 q^{93} + 972 q^{94} + 8892 q^{95} + 1044 q^{96} + 2421 q^{97} + 2289 q^{98} - 606 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(361, [\chi])\) into newform subspaces

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