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Properties

Label 1521.4.q
Level $1521$
Weight $4$
Character orbit 1521.q
Rep. character $\chi_{1521}(316,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1148 396 752
Cusp forms 1036 376 660
Eisenstein series 112 20 92

Trace form

\( 376 q - 3 q^{2} + 737 q^{4} + 21 q^{7} + O(q^{10}) \) \( 376 q - 3 q^{2} + 737 q^{4} + 21 q^{7} + 69 q^{10} + 9 q^{11} - 76 q^{14} - 2723 q^{16} + 4 q^{17} + 39 q^{19} + 489 q^{20} - 58 q^{22} - 239 q^{23} - 8310 q^{25} - 240 q^{28} - 254 q^{29} + 837 q^{32} + 722 q^{35} + 396 q^{37} - 1380 q^{38} - 1050 q^{40} + 972 q^{41} + 939 q^{43} - 468 q^{46} + 8783 q^{49} - 2328 q^{50} - 1714 q^{53} - 408 q^{55} - 2338 q^{56} - 2853 q^{58} + 1047 q^{59} - 248 q^{61} - 3320 q^{62} - 18982 q^{64} - 1455 q^{67} + 21 q^{68} + 2337 q^{71} + 3455 q^{74} + 1290 q^{76} - 3742 q^{77} + 6912 q^{79} + 9939 q^{80} + 1125 q^{82} + 2745 q^{85} + 156 q^{88} + 3255 q^{89} - 8868 q^{92} + 566 q^{94} - 2466 q^{95} + 1917 q^{97} - 7989 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)