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Properties

Label 1521.4.be
Level $1521$
Weight $4$
Character orbit 1521.be
Rep. character $\chi_{1521}(118,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $2724$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.be (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 6600 2748 3852
Cusp forms 6504 2724 3780
Eisenstein series 96 24 72

Trace form

\( 2724 q + 13 q^{2} - 919 q^{4} + 19 q^{5} - 55 q^{7} + 13 q^{8} + O(q^{10}) \) \( 2724 q + 13 q^{2} - 919 q^{4} + 19 q^{5} - 55 q^{7} + 13 q^{8} + 5 q^{10} - 29 q^{11} - 268 q^{13} - 45 q^{14} - 3683 q^{16} + 51 q^{17} + 24 q^{19} - 179 q^{20} + 642 q^{22} - 1760 q^{23} - 5616 q^{25} - 65 q^{26} - 581 q^{28} + 245 q^{29} - 1303 q^{31} + 600 q^{32} + 1796 q^{34} + 357 q^{35} - 311 q^{37} - 280 q^{38} + 13 q^{40} + 415 q^{41} - 71 q^{43} - 483 q^{44} + 1879 q^{46} - 849 q^{47} - 9694 q^{49} - 131 q^{50} - 1834 q^{52} - 1287 q^{53} - 1605 q^{55} + 113 q^{56} + 1471 q^{58} + 2751 q^{59} - 1897 q^{61} - 3280 q^{62} - 15437 q^{64} - 455 q^{65} - 5267 q^{67} - 3636 q^{68} - 7870 q^{70} + 1645 q^{71} - 523 q^{73} - 2417 q^{74} + 1091 q^{76} + 785 q^{77} - 1109 q^{79} - 1366 q^{80} - 6685 q^{82} - 7519 q^{83} - 4917 q^{85} + 3925 q^{86} + 7595 q^{88} - 10908 q^{89} + 4923 q^{91} + 2501 q^{92} + 18455 q^{94} - 3302 q^{95} - 2777 q^{97} - 5411 q^{98} + O(q^{100}) \)

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

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