↑

Properties

Label 1521.4.r
Level $1521$
Weight $4$
Character orbit 1521.r
Rep. character $\chi_{1521}(868,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $904$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1120 944 176
Cusp forms 1064 904 160
Eisenstein series 56 40 16

Trace form

\( 904 q + 3 q^{2} + q^{3} + 1767 q^{4} + 3 q^{6} + 17 q^{9} + O(q^{10}) \) \( 904 q + 3 q^{2} + q^{3} + 1767 q^{4} + 3 q^{6} + 17 q^{9} + 10 q^{10} + 3 q^{11} + 101 q^{12} - 138 q^{14} + 84 q^{15} - 6745 q^{16} + 138 q^{17} - 168 q^{18} + 96 q^{19} - 249 q^{21} + 31 q^{22} - 654 q^{23} + 834 q^{24} + 10302 q^{25} + 478 q^{27} - 18 q^{28} - 201 q^{29} - 267 q^{30} + 180 q^{31} - 117 q^{32} - 231 q^{33} + 24 q^{34} - 291 q^{35} - 601 q^{36} - 246 q^{37} + 1058 q^{38} - 340 q^{40} - 1684 q^{42} - 166 q^{43} + 603 q^{45} + 6 q^{46} + 372 q^{47} + 1632 q^{48} - 37934 q^{49} + 108 q^{51} + 2520 q^{53} - 480 q^{54} + 127 q^{55} - 5788 q^{56} + 1332 q^{57} + 3 q^{58} + 531 q^{59} + 711 q^{60} - 838 q^{61} - 627 q^{62} - 2895 q^{63} - 49046 q^{64} - 6306 q^{66} + 5436 q^{68} - 1015 q^{69} - 1005 q^{70} + 2598 q^{71} - 1821 q^{72} + 1550 q^{74} + 2404 q^{75} + 2128 q^{77} + 248 q^{79} + 1332 q^{80} + 2941 q^{81} + 1369 q^{82} + 1194 q^{83} - 8196 q^{84} - 3936 q^{85} - 2910 q^{86} + 991 q^{87} - 1825 q^{88} + 1056 q^{89} - 3223 q^{90} + 262 q^{92} - 1830 q^{93} - 578 q^{94} + 5068 q^{95} + 6777 q^{96} + 6339 q^{98} - 2331 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)