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Properties

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

\( 13056 q - 13 q^{2} - 25 q^{3} + 4325 q^{4} - 13 q^{5} - 68 q^{6} - 10 q^{7} - 52 q^{8} - 9 q^{9} + O(q^{10}) \) \( 13056 q - 13 q^{2} - 25 q^{3} + 4325 q^{4} - 13 q^{5} - 68 q^{6} - 10 q^{7} - 52 q^{8} - 9 q^{9} - 42 q^{10} - 13 q^{11} + 75 q^{12} - 156 q^{13} - 139 q^{14} + 609 q^{15} - 17243 q^{16} + 86 q^{17} - 1067 q^{18} + 18 q^{19} + 374 q^{20} + 223 q^{21} - 88 q^{22} - 3248 q^{23} - 1328 q^{24} - 13411 q^{25} - 562 q^{26} + 200 q^{27} - 70 q^{28} + 389 q^{29} + 3404 q^{30} - 193 q^{31} + 299 q^{32} - 395 q^{33} - 37 q^{34} - 355 q^{35} + 118 q^{36} - 298 q^{37} + 257 q^{38} - 5387 q^{39} - 341 q^{40} - 394 q^{41} + 653 q^{42} + 70 q^{43} - 156 q^{44} - 1848 q^{45} - 150 q^{46} - 567 q^{47} - 5940 q^{48} - 26322 q^{49} + 695 q^{50} + 1184 q^{51} - 415 q^{52} + 2516 q^{53} + 2161 q^{54} + 75 q^{55} + 1785 q^{56} - 4205 q^{57} - 13 q^{58} - 13 q^{59} - 737 q^{60} + 406 q^{61} + 305 q^{62} - 9411 q^{63} + 67638 q^{64} - 376 q^{65} + 14522 q^{66} - 892 q^{67} - 1963 q^{68} + 2630 q^{69} + 1005 q^{70} + 2546 q^{71} - 17724 q^{72} - 52 q^{73} - 180 q^{74} + 8384 q^{75} - 666 q^{76} + 1027 q^{77} + 34 q^{78} + 247 q^{79} + 1254 q^{80} - 905 q^{81} + 1221 q^{82} - 7317 q^{83} + 12876 q^{84} - 13 q^{85} + 2897 q^{86} + 1299 q^{87} - 3867 q^{88} + 978 q^{89} - 3421 q^{90} - 589 q^{91} - 735 q^{92} - 4371 q^{93} - 1380 q^{94} - 9420 q^{95} - 2578 q^{96} - 802 q^{97} + 6287 q^{98} + 2331 q^{99} + O(q^{100}) \)

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.