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Properties

Label 1521.4.bc
Level $1521$
Weight $4$
Character orbit 1521.bc
Rep. character $\chi_{1521}(488,\cdot)$
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.bc (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

\( 1808 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 6 q^{5} + 50 q^{6} + 26 q^{7} + 66 q^{8} + 2 q^{9} + O(q^{10}) \) \( 1808 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 6 q^{5} + 50 q^{6} + 26 q^{7} + 66 q^{8} + 2 q^{9} + 12 q^{10} + 30 q^{11} + 162 q^{12} - 60 q^{14} - 232 q^{15} + 13502 q^{16} - 34 q^{18} - 112 q^{19} + 6 q^{20} - 82 q^{21} - 2 q^{22} + 12 q^{23} + 42 q^{24} - 904 q^{27} + 104 q^{28} + 6 q^{29} - 570 q^{30} + 122 q^{31} - 138 q^{32} - 694 q^{33} + 18 q^{34} + 852 q^{35} + 6 q^{36} - 160 q^{37} - 72 q^{38} + 108 q^{40} + 774 q^{41} + 1404 q^{42} + 336 q^{44} + 746 q^{45} + 24 q^{46} + 402 q^{47} + 1342 q^{48} - 1500 q^{50} + 872 q^{54} + 4 q^{55} + 12 q^{56} + 1034 q^{57} - 560 q^{58} - 3054 q^{59} + 910 q^{60} + 4 q^{61} + 2934 q^{62} + 4016 q^{63} - 4560 q^{66} - 586 q^{67} - 1842 q^{69} + 1858 q^{70} - 3504 q^{71} + 3102 q^{72} - 328 q^{73} + 5646 q^{75} + 1186 q^{76} - 2952 q^{77} + 916 q^{79} - 7326 q^{80} - 3118 q^{81} + 12 q^{82} + 270 q^{83} - 3754 q^{84} + 3534 q^{85} + 8322 q^{86} - 4198 q^{87} + 6 q^{88} - 6480 q^{89} + 4674 q^{90} - 19764 q^{92} - 3988 q^{93} - 6620 q^{94} + 6 q^{95} + 11252 q^{96} + 1058 q^{97} + 2160 q^{98} - 748 q^{99} + O(q^{100}) \)

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

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