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Properties

Label 1521.4.cg
Level $1521$
Weight $4$
Character orbit 1521.cg
Rep. character $\chi_{1521}(2,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $26112$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.cg (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 26304 26304 0
Cusp forms 26112 26112 0
Eisenstein series 192 192 0

Trace form

\( 26112 q - 72 q^{2} - 50 q^{3} - 26 q^{4} - 72 q^{5} - 140 q^{6} - 36 q^{7} - 66 q^{8} - 50 q^{9} + O(q^{10}) \) \( 26112 q - 72 q^{2} - 50 q^{3} - 26 q^{4} - 72 q^{5} - 140 q^{6} - 36 q^{7} - 66 q^{8} - 50 q^{9} - 92 q^{10} - 72 q^{11} - 214 q^{12} - 24 q^{13} - 66 q^{14} - 2 q^{15} + 34410 q^{16} + 250 q^{18} - 216 q^{19} - 24 q^{20} + 364 q^{21} - 48 q^{22} - 72 q^{23} - 3514 q^{24} - 26 q^{25} - 816 q^{26} - 356 q^{27} - 78 q^{29} - 3342 q^{30} - 264 q^{31} - 600 q^{32} + 664 q^{33} - 56 q^{34} - 780 q^{35} + 3020 q^{36} - 264 q^{37} - 6 q^{38} + 11546 q^{39} + 106 q^{40} + 696 q^{41} - 254 q^{42} + 484 q^{43} - 960 q^{44} - 6256 q^{45} - 288 q^{46} + 13608 q^{47} - 1210 q^{48} - 20 q^{49} - 5526 q^{50} - 52 q^{51} - 2 q^{52} - 1934 q^{54} - 100 q^{55} - 72 q^{56} - 3986 q^{57} + 1100 q^{58} - 72 q^{59} - 1656 q^{60} - 28 q^{61} - 2934 q^{62} + 12414 q^{63} - 104 q^{64} - 564 q^{65} - 1784 q^{66} + 1152 q^{67} - 840 q^{68} + 836 q^{69} - 178 q^{70} + 3504 q^{71} + 3146 q^{72} - 432 q^{73} + 5388 q^{74} - 12104 q^{75} + 776 q^{76} + 2874 q^{77} + 4480 q^{78} + 914 q^{79} + 7326 q^{80} + 1198 q^{81} - 92 q^{82} + 2748 q^{83} + 3286 q^{84} - 710 q^{85} - 2472 q^{86} - 2086 q^{87} - 6682 q^{88} - 24720 q^{89} - 4726 q^{90} + 1224 q^{91} - 3810 q^{92} - 4066 q^{93} - 28 q^{94} - 66 q^{95} + 368 q^{96} - 1344 q^{97} - 2160 q^{98} - 2462 q^{99} + O(q^{100}) \)

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.