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Properties

Label 1521.4.bt
Level $1521$
Weight $4$
Character orbit 1521.bt
Rep. character $\chi_{1521}(10,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $5424$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.bt (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
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 13200 5472 7728
Cusp forms 13008 5424 7584
Eisenstein series 192 48 144

Trace form

\( 5424 q + 23 q^{2} - 921 q^{4} + 26 q^{5} - 5 q^{7} + 26 q^{8} + O(q^{10}) \) \( 5424 q + 23 q^{2} - 921 q^{4} + 26 q^{5} - 5 q^{7} + 26 q^{8} - 29 q^{10} + 35 q^{11} + 37 q^{13} + 6 q^{14} + 3515 q^{16} + 34 q^{17} + 515 q^{20} + 341 q^{22} + 1656 q^{23} + 11036 q^{25} - 367 q^{26} - 266 q^{28} - 104 q^{29} - 1430 q^{31} + 720 q^{32} + 1599 q^{34} + 792 q^{35} + 370 q^{37} + 1121 q^{38} + 1588 q^{40} + 998 q^{41} + 329 q^{43} - 78 q^{44} - 390 q^{46} - 156 q^{47} - 9515 q^{49} - 2302 q^{50} + 465 q^{52} + 3873 q^{53} + 6682 q^{55} - 1428 q^{56} - 2567 q^{58} - 7871 q^{59} - 478 q^{61} + 1721 q^{62} + 26136 q^{64} - 733 q^{65} + 6787 q^{67} - 6314 q^{68} - 3097 q^{71} - 26 q^{73} + 1345 q^{74} - 14232 q^{76} + 444 q^{77} + 5214 q^{79} + 9978 q^{80} + 9745 q^{82} + 12246 q^{83} + 4006 q^{85} + 1118 q^{86} - 10110 q^{88} + 3294 q^{89} + 1067 q^{91} - 2258 q^{92} - 6190 q^{94} + 2153 q^{95} + 5557 q^{97} - 7963 q^{98} + O(q^{100}) \)

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

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