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Properties

Label 1521.4.ba
Level $1521$
Weight $4$
Character orbit 1521.ba
Rep. character $\chi_{1521}(80,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $616$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.ba (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
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 2296 616 1680
Cusp forms 2072 616 1456
Eisenstein series 224 0 224

Trace form

\( 616 q + 8 q^{7} + O(q^{10}) \) \( 616 q + 8 q^{7} - 72 q^{10} + 5216 q^{16} + 56 q^{19} + 864 q^{22} - 344 q^{28} + 136 q^{31} - 48 q^{34} + 2020 q^{37} + 6672 q^{40} + 840 q^{43} - 336 q^{46} - 5976 q^{49} - 2784 q^{55} + 2616 q^{58} + 84 q^{61} - 1600 q^{67} + 4440 q^{70} + 4196 q^{73} + 9776 q^{76} + 3744 q^{79} + 5112 q^{82} + 6600 q^{85} - 16848 q^{88} - 7176 q^{94} - 452 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1521, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)