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Properties

Label 1521.4.bk
Level $1521$
Weight $4$
Character orbit 1521.bk
Rep. character $\chi_{1521}(61,\cdot)$
Character field $\Q(\zeta_{39})$
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.bk (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1521 \)
Character field: \(\Q(\zeta_{39})\)
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

\( 13056 q - 14 q^{2} - 25 q^{3} + 2154 q^{4} - 11 q^{5} - 11 q^{6} - 35 q^{7} - 22 q^{8} - 41 q^{9} + O(q^{10}) \) \( 13056 q - 14 q^{2} - 25 q^{3} + 2154 q^{4} - 11 q^{5} - 11 q^{6} - 35 q^{7} - 22 q^{8} - 41 q^{9} - 58 q^{10} - 22 q^{11} - 65 q^{12} + 132 q^{13} + 117 q^{14} - 522 q^{15} + 8586 q^{16} + 86 q^{17} + 945 q^{18} + 6 q^{19} - 299 q^{20} - 19 q^{21} - 20 q^{22} + 6704 q^{23} - 2006 q^{24} + 13389 q^{25} - 466 q^{26} + 68 q^{27} + 262 q^{28} + 602 q^{29} - 5501 q^{30} - 71 q^{31} + 490 q^{32} - 1093 q^{33} - 19 q^{34} + 515 q^{35} - 375 q^{36} + 34 q^{37} + 345 q^{38} + 2882 q^{39} + 191 q^{40} - 267 q^{41} + 1394 q^{42} - 179 q^{43} - 932 q^{44} - 3883 q^{45} - 138 q^{46} - 2451 q^{47} + 3687 q^{48} - 51667 q^{49} + 3091 q^{50} + 2822 q^{51} - 231 q^{52} - 1148 q^{53} - 698 q^{54} - 175 q^{55} - 2301 q^{56} - 4589 q^{57} - 640 q^{58} + 1182 q^{59} + 1057 q^{60} + 829 q^{61} + 601 q^{62} + 5135 q^{63} - 68010 q^{64} - 152 q^{65} - 18633 q^{66} + 577 q^{67} - 5773 q^{68} - 2039 q^{69} - 875 q^{70} - 354 q^{71} - 166 q^{72} + 292 q^{73} - 3983 q^{74} + 9286 q^{75} + 405 q^{76} + 2399 q^{77} - 577 q^{78} + 667 q^{79} + 4664 q^{80} - 2005 q^{81} - 1321 q^{82} + 4705 q^{83} - 11781 q^{84} - 607 q^{85} + 2051 q^{86} + 1421 q^{87} + 874 q^{88} + 8566 q^{89} - 5205 q^{90} - 827 q^{91} - 1943 q^{92} - 1740 q^{93} - 2743 q^{94} + 7463 q^{95} + 4470 q^{96} - 2123 q^{97} + 1521 q^{98} + 5555 q^{99} + O(q^{100}) \)

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.