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Properties

Label 1521.4.bj
Level $1521$
Weight $4$
Character orbit 1521.bj
Rep. character $\chi_{1521}(55,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $5448$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.bj (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
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 13200 5496 7704
Cusp forms 13008 5448 7560
Eisenstein series 192 48 144

Trace form

\( 5448 q + 23 q^{2} + 883 q^{4} + 14 q^{5} - 35 q^{7} + 92 q^{8} + O(q^{10}) \) \( 5448 q + 23 q^{2} + 883 q^{4} + 14 q^{5} - 35 q^{7} + 92 q^{8} + 13 q^{10} - 7 q^{11} + 16 q^{13} + 246 q^{14} + 3587 q^{16} - 57 q^{17} + 228 q^{19} + 239 q^{20} - 495 q^{22} + 1604 q^{23} - 11292 q^{25} - 61 q^{26} - 310 q^{28} - 119 q^{29} + 1078 q^{31} - 1038 q^{32} - 269 q^{34} - 222 q^{35} + 707 q^{37} + 997 q^{38} - 16 q^{40} + 653 q^{41} + 329 q^{43} + 1050 q^{44} - 616 q^{46} + 3504 q^{47} + 9910 q^{49} - 2020 q^{50} + 1513 q^{52} + 2970 q^{53} + 2160 q^{55} - 2264 q^{56} + 1187 q^{58} + 9159 q^{59} + 337 q^{61} + 1783 q^{62} - 31960 q^{64} - 952 q^{65} + 2993 q^{67} + 5502 q^{68} + 8836 q^{70} + 5657 q^{71} + 2938 q^{73} + 4529 q^{74} + 20542 q^{76} + 2752 q^{77} - 2554 q^{79} + 4162 q^{80} + 10831 q^{82} - 8570 q^{83} + 3138 q^{85} - 310 q^{86} + 17710 q^{88} + 7446 q^{89} - 435 q^{91} + 5002 q^{92} - 27140 q^{94} - 9043 q^{95} + 1415 q^{97} + 1193 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)