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Properties

Label 1521.4.z
Level $1521$
Weight $4$
Character orbit 1521.z
Rep. character $\chi_{1521}(239,\cdot)$
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.z (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

\( 1808 q + 6 q^{2} + 8 q^{3} + 6 q^{5} + 50 q^{6} - 10 q^{7} + 8 q^{9} + O(q^{10}) \) \( 1808 q + 6 q^{2} + 8 q^{3} + 6 q^{5} + 50 q^{6} - 10 q^{7} + 8 q^{9} - 18 q^{11} - 60 q^{14} + 194 q^{15} + 13508 q^{16} + 302 q^{18} - 112 q^{19} - 42 q^{20} - 82 q^{21} + 4 q^{22} - 840 q^{24} + 32 q^{27} - 88 q^{28} + 12 q^{29} + 122 q^{31} + 246 q^{32} + 878 q^{33} + 18 q^{34} + 344 q^{37} - 276 q^{40} + 774 q^{41} - 468 q^{42} - 370 q^{45} - 24 q^{46} + 750 q^{47} - 404 q^{48} + 198 q^{50} - 2242 q^{54} + 16 q^{55} + 2672 q^{57} - 560 q^{58} + 3066 q^{59} - 3212 q^{60} + 4 q^{61} + 626 q^{63} - 3552 q^{66} - 586 q^{67} - 3828 q^{68} - 200 q^{70} - 1470 q^{72} + 680 q^{73} + 14580 q^{74} + 802 q^{76} - 1892 q^{79} - 4120 q^{81} + 5382 q^{83} + 6722 q^{84} - 684 q^{85} - 5910 q^{86} - 6628 q^{87} - 8532 q^{92} - 6190 q^{93} + 3316 q^{94} - 8584 q^{96} - 1318 q^{97} + 2042 q^{99} + O(q^{100}) \)

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

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