↑

Properties

Label 1521.4.bl
Level $1521$
Weight $4$
Character orbit 1521.bl
Rep. character $\chi_{1521}(40,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $13056$
Sturm bound $728$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.bl (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1521, [\chi])\).

Total New Old
Modular forms 13152 13152 0
Cusp forms 13056 13056 0
Eisenstein series 96 96 0

Trace form

\( 13056 q - 11 q^{2} - 22 q^{3} + 2157 q^{4} - 11 q^{5} - 8 q^{6} + q^{7} - 88 q^{8} - 86 q^{9} + O(q^{10}) \) \( 13056 q - 11 q^{2} - 22 q^{3} + 2157 q^{4} - 11 q^{5} - 8 q^{6} + q^{7} - 88 q^{8} - 86 q^{9} - 76 q^{10} - 19 q^{11} + 64 q^{12} + 132 q^{13} + 69 q^{14} + 852 q^{15} + 8613 q^{16} - 316 q^{17} + 1113 q^{18} + 24 q^{19} - 251 q^{20} - 268 q^{21} - 56 q^{22} - 3232 q^{23} + 2950 q^{24} + 13389 q^{25} + 788 q^{26} - 202 q^{27} - 716 q^{28} - 199 q^{29} - 560 q^{30} + 109 q^{31} - 179 q^{32} + 248 q^{33} + 5 q^{34} - 1144 q^{35} - 372 q^{36} + 292 q^{37} + 333 q^{38} + 2387 q^{39} + 335 q^{40} - 267 q^{41} - 676 q^{42} - 179 q^{43} + 2500 q^{44} + 5144 q^{45} + 132 q^{46} + 4191 q^{47} - 6744 q^{48} + 25817 q^{49} - 107 q^{50} - 2056 q^{51} - 783 q^{52} - 1652 q^{53} + 28 q^{54} - 544 q^{55} + 1779 q^{56} + 1864 q^{57} - 637 q^{58} + 657 q^{59} + 238 q^{60} + 829 q^{61} - 3392 q^{62} + 1514 q^{63} - 67632 q^{64} - 368 q^{65} - 16131 q^{66} + 577 q^{67} - 493 q^{68} - 1937 q^{69} + 178 q^{70} - 1260 q^{71} - 9343 q^{72} - 716 q^{73} + 505 q^{74} - 11708 q^{75} - 1707 q^{76} - 1135 q^{77} + 1874 q^{78} - 1367 q^{79} + 3968 q^{80} + 1490 q^{81} - 5224 q^{82} + 6067 q^{83} + 31518 q^{84} + 1175 q^{85} - 3355 q^{86} + 2504 q^{87} + 2437 q^{88} - 23336 q^{89} + 3432 q^{90} + 1510 q^{91} + 5485 q^{92} + 7488 q^{93} + 1307 q^{94} - 970 q^{95} - 17784 q^{96} + 253 q^{97} + 1728 q^{98} + 3554 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

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