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Properties

Label 1521.4.bs
Level $1521$
Weight $4$
Character orbit 1521.bs
Rep. character $\chi_{1521}(43,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $13056$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.bs (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{78})\)
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

\( 13056 q - 10 q^{2} - 25 q^{3} - 2182 q^{4} - 13 q^{5} - 23 q^{6} - 13 q^{7} - 52 q^{8} - 9 q^{9} + O(q^{10}) \) \( 13056 q - 10 q^{2} - 25 q^{3} - 2182 q^{4} - 13 q^{5} - 23 q^{6} - 13 q^{7} - 52 q^{8} - 9 q^{9} - 42 q^{10} - 10 q^{11} + 75 q^{12} - 156 q^{13} - 139 q^{14} + 630 q^{15} + 8602 q^{16} + 86 q^{17} - 1403 q^{18} + 18 q^{19} - 13 q^{20} - 275 q^{21} + 44 q^{22} + 6496 q^{23} - 752 q^{24} - 13411 q^{25} - 562 q^{26} + 200 q^{27} - 70 q^{28} - 214 q^{29} - 1537 q^{30} + 167 q^{31} - 754 q^{32} - 257 q^{33} + 11 q^{34} - 355 q^{35} + 73 q^{36} - 298 q^{37} + 569 q^{38} + 3706 q^{39} - 341 q^{40} - 13 q^{41} - 766 q^{42} - 179 q^{43} - 156 q^{44} - 2283 q^{45} - 150 q^{46} - 7233 q^{47} - 3477 q^{48} + 52605 q^{49} - 13 q^{50} - 3886 q^{51} - 199 q^{52} + 2516 q^{53} + 1054 q^{54} + 75 q^{55} - 3609 q^{56} + 5947 q^{57} - 10 q^{58} + 518 q^{59} + 685 q^{60} - 851 q^{61} + 305 q^{62} + 849 q^{63} + 67638 q^{64} + 2324 q^{65} + 15575 q^{66} - 13 q^{67} + 3887 q^{68} - 895 q^{69} - 1005 q^{70} + 2546 q^{71} + 6096 q^{72} - 52 q^{73} + 321 q^{74} - 64 q^{75} - 1677 q^{76} + 1027 q^{77} - 2657 q^{78} + 247 q^{79} + 1254 q^{80} + 1747 q^{81} + 1221 q^{82} - 4929 q^{83} + 6351 q^{84} - 3949 q^{85} - 2923 q^{86} + 33 q^{87} + 1914 q^{88} + 978 q^{89} - 3421 q^{90} - 589 q^{91} - 5727 q^{92} - 6276 q^{93} + 2721 q^{94} + 2253 q^{95} + 10976 q^{96} - 13 q^{97} + 6287 q^{98} - 2331 q^{99} + O(q^{100}) \)

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.