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Properties

Label 1521.4.cb
Level $1521$
Weight $4$
Character orbit 1521.cb
Rep. character $\chi_{1521}(20,\cdot)$
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.cb (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

\( 26112 q - 72 q^{2} - 50 q^{3} - 20 q^{4} - 72 q^{5} - 2 q^{6} + 66 q^{8} - 50 q^{9} + O(q^{10}) \) \( 26112 q - 72 q^{2} - 50 q^{3} - 20 q^{4} - 72 q^{5} - 2 q^{6} + 66 q^{8} - 50 q^{9} - 92 q^{10} - 48 q^{11} + 110 q^{12} - 24 q^{13} - 66 q^{14} - 284 q^{15} - 17244 q^{16} - 86 q^{18} - 216 q^{19} - 72 q^{20} - 134 q^{21} + 24 q^{22} - 144 q^{23} - 3130 q^{24} - 26 q^{25} + 816 q^{26} - 356 q^{27} - 72 q^{29} + 6450 q^{30} + 96 q^{31} - 216 q^{32} - 746 q^{33} - 8 q^{34} + 780 q^{35} - 46 q^{36} - 264 q^{37} - 150 q^{38} - 5860 q^{39} + 106 q^{40} + 696 q^{41} + 520 q^{42} - 26 q^{43} + 960 q^{44} - 5026 q^{45} - 288 q^{46} + 324 q^{47} + 722 q^{48} - 26 q^{49} - 1578 q^{50} - 52 q^{51} + 1918 q^{52} + 820 q^{54} - 100 q^{55} - 66 q^{56} + 982 q^{57} - 586 q^{58} - 3132 q^{59} + 858 q^{60} - 22 q^{61} + 2934 q^{62} - 3576 q^{63} - 104 q^{64} - 2916 q^{65} + 322 q^{66} - 612 q^{67} - 78 q^{68} - 3298 q^{69} + 1832 q^{70} - 3504 q^{71} + 3050 q^{72} - 432 q^{73} - 78 q^{74} - 6626 q^{75} + 1160 q^{76} - 3030 q^{77} + 3610 q^{78} + 914 q^{79} - 7326 q^{80} - 1922 q^{81} - 92 q^{82} + 192 q^{83} - 3806 q^{84} + 3508 q^{85} + 8244 q^{86} - 2386 q^{87} + 3308 q^{88} + 24720 q^{89} + 4622 q^{90} + 1224 q^{91} - 3810 q^{92} - 12880 q^{93} - 22 q^{94} - 72 q^{95} + 2750 q^{96} + 1032 q^{97} + 2160 q^{98} - 800 q^{99} + O(q^{100}) \)

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.