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Properties

Label 1521.4.x
Level $1521$
Weight $4$
Character orbit 1521.x
Rep. character $\chi_{1521}(587,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1808$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 2240 1888 352
Cusp forms 2128 1808 320
Eisenstein series 112 80 32

Trace form

\( 1808 q + 6 q^{2} + 2 q^{3} + 6 q^{5} - 88 q^{6} - 10 q^{7} - 66 q^{8} + 2 q^{9} + O(q^{10}) \) \( 1808 q + 6 q^{2} + 2 q^{3} + 6 q^{5} - 88 q^{6} - 10 q^{7} - 66 q^{8} + 2 q^{9} + 12 q^{10} + 6 q^{11} - 162 q^{12} - 60 q^{14} + 50 q^{15} - 27004 q^{16} + 302 q^{18} - 112 q^{19} + 54 q^{20} + 416 q^{21} + 4 q^{22} + 6 q^{23} - 342 q^{24} - 904 q^{27} + 104 q^{28} + 246 q^{30} - 238 q^{31} - 522 q^{32} + 716 q^{33} - 30 q^{34} - 852 q^{35} + 3072 q^{36} - 160 q^{37} + 72 q^{38} + 108 q^{40} + 774 q^{41} + 174 q^{42} + 510 q^{43} - 336 q^{44} - 484 q^{45} + 24 q^{46} - 1134 q^{47} - 2414 q^{48} + 6 q^{49} - 5448 q^{50} - 1882 q^{54} + 4 q^{55} + 6 q^{56} - 3934 q^{57} + 1126 q^{58} + 6 q^{59} - 1604 q^{60} - 2 q^{61} - 2934 q^{62} - 2614 q^{63} - 4560 q^{66} + 1178 q^{67} + 3846 q^{68} + 186 q^{69} - 152 q^{70} + 3504 q^{71} + 3198 q^{72} - 328 q^{73} + 1818 q^{74} + 168 q^{75} + 802 q^{76} + 2952 q^{77} + 916 q^{79} + 7326 q^{80} + 5378 q^{81} + 12 q^{82} + 2826 q^{83} + 3338 q^{84} - 684 q^{85} - 2394 q^{86} - 1954 q^{87} + 6480 q^{89} - 4674 q^{90} - 19764 q^{92} + 4826 q^{93} + 3310 q^{94} + 12 q^{95} + 8870 q^{96} - 1318 q^{97} - 2160 q^{98} - 2410 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)